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Vibration
Volume 7
Issue 2
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Vibration, Volume 7, Issue 2 (June 2024) – 17 articles

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22 pages, 5370 KiB  
Article
A Novel Semi-Active Control Approach for Flexible Structures: Vibration Control through Boundary Conditioning Using Magnetorheological Elastomers
by Jomar Morales and Ramin Sedaghati
Vibration 2024, 7(2), 605-626; https://doi.org/10.3390/vibration7020032 - 18 Jun 2024
Viewed by 449
Abstract
This research study explores an alternative method of vibration control of flexible beam type structures via boundary conditioning using magnetorheological elastomer at the support location. The Rayleigh–Ritz method has been used to formulate dynamic equations of motions of the beam with MRE support [...] Read more.
This research study explores an alternative method of vibration control of flexible beam type structures via boundary conditioning using magnetorheological elastomer at the support location. The Rayleigh–Ritz method has been used to formulate dynamic equations of motions of the beam with MRE support and to extract its natural frequencies and mode shapes. The MRE-based adaptive continuous beam is then converted into an equivalent single-degree-of-freedom system for the purpose of control implementation, assuming that the system’s response is dominated by its fundamental mode. Two different types of control strategies are formulated including proportional–integral–derivative control and on–off control. The performance of controllers is evaluated for three different loading conditions including shock, harmonic, and random vibration excitations. Full article
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<p>Comparison of Experimental Data and Curve Fitting Representation of Storage and Loss Moduli vs. Magnetic Flux Densities at 2 Hz and 15% Shear Strain [<a href="#B16-vibration-07-00032" class="html-bibr">16</a>].</p> Full article ">Figure 2
<p>Demagnetization Curve for N52 Permanent Magnet.</p> Full article ">Figure 3
<p>Electromagnet Layout with Parametric Dimensions.</p> Full article ">Figure 4
<p>(<b>a</b>) FEMM Results for Input Current of −3 A; (<b>b</b>) FEMM Results for Input Current of 3 A.</p> Full article ">Figure 5
<p>Comparison of the FEMM Results with the Curve Fitted 4th-Order Polynomial of the Magnetic Flux Density vs. Input Current Curve.</p> Full article ">Figure 6
<p>(<b>a</b>) Overhang Beam with Spring at Overhang Support; (<b>b</b>) Equivalent Beam Model with MRE in Direct shear.</p> Full article ">Figure 7
<p>Shear and Bending Moment Shown in Red of (<b>a</b>) Cantilever Beam and (<b>b</b>) Overhanging Beam.</p> Full article ">Figure 8
<p>Equivalent Single-Degree-of-Freedom System.</p> Full article ">Figure 9
<p>Curve Fit for Equivalent Stiffness Storage and Loss Components, Equivalent Mass, and Equivalent Damping.</p> Full article ">Figure 10
<p>Comparison of Transient Response and Input Current between Passive and Semi-active Systems due to different Control Strategies.</p> Full article ">Figure 11
<p>Steady-State Time Response and Control Current for Different Controllers under Harmonic Input at (<b>a</b>) 5.14 Hz and (<b>b</b>) at 7.06 Hz.</p> Full article ">Figure 12
<p>Time Response and Controller Input for Random Input over (<b>a</b>) 50 Seconds and (<b>b</b>) 5 Seconds.</p> Full article ">Figure A1
<p>Static and Dynamic Shear Strain Representations on Deflected MRE.</p> Full article ">Figure A2
<p>Free-Body Diagram of Proposed Beam Model under Static Loading.</p> Full article ">
10 pages, 738 KiB  
Article
Acute Whole-Body Vibration Does Not Alter Passive Muscle Stiffness in Physically Active Males
by Marco Spadafora, Federico Quinzi, Carmen Giulia Lia, Francesca Greco, Katia Folino, Loretta Francesca Cosco and Gian Pietro Emerenziani
Vibration 2024, 7(2), 595-604; https://doi.org/10.3390/vibration7020031 - 13 Jun 2024
Viewed by 522
Abstract
Whole-body vibration (WBV) is a widely used training method to increase muscle strength and power. However, its working mechanisms are still poorly understood, and studies investigating the effects of WBV on muscle stiffness are scant. Therefore, the aim of this study is to [...] Read more.
Whole-body vibration (WBV) is a widely used training method to increase muscle strength and power. However, its working mechanisms are still poorly understood, and studies investigating the effects of WBV on muscle stiffness are scant. Therefore, the aim of this study is to investigate the acute effects of WBV on stiffness and countermovement jump (CMJ). Twenty-four recreationally active males, on separate days and in random order, performed a static squat under two different conditions: with WBV (WBV) or without vibration (CC). Muscle stiffness was assessed through the Wartenberg pendulum test, and CMJ was recorded. RM-ANOVA was employed to test differences between conditions in the above-mentioned variables. In the CC condition, stiffness was significantly lower after the exposure to the static squat (p = 0.006), whereas no difference was observed after the exposure to WBV. WBV and CC did not affect CMJ. No significant correlation was observed between changes in CMJ and changes in stiffness. Our results show that WBV may mitigate the reduction in muscle stiffness observed after static squats. However, current results do not support the notion that WBV exposure may account for an increase in CMJ performance. Full article
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<p>Schematic representation of the experimental protocol adopted in the present study. WBV—whole-body vibration; CC—control condition; CMJ—countermovement jump.</p> Full article ">Figure 2
<p>(<b>a</b>) Participants’ positioning for the Wartenberg pendulum test. (<b>b</b>) Knee angular velocity and (<b>c</b>) knee flexion–extension angle from a representative participant. Positive values represent knee flexion. Acronyms: T—pendulum period; ω<sub>Peak</sub>—peak knee flexion angular velocity; θ<sub>1</sub>—knee flexion angle of the first cycle; θ<sub>2</sub>—knee flexion angle of the second cycle.</p> Full article ">
13 pages, 7741 KiB  
Article
Finite Element Analysis versus Empirical Modal Analysis of a Basketball Rim and Backboard
by Daniel Winarski, Kip P. Nygren and Tyson Winarski
Vibration 2024, 7(2), 582-594; https://doi.org/10.3390/vibration7020030 - 7 Jun 2024
Viewed by 642
Abstract
The first goal of this research was to document the process of using the MODAL analysis system of the ANSYS 2024R1 student edition to create a finite element model of the modes and frequencies of vibration of one basketball rim and backboard design. [...] Read more.
The first goal of this research was to document the process of using the MODAL analysis system of the ANSYS 2024R1 student edition to create a finite element model of the modes and frequencies of vibration of one basketball rim and backboard design. This finite element model included the use of steel for the rim and its mount, a tempered glass backboard, and an aluminum frame behind the backboard. After a mesh was created, fixed support boundary conditions were applied to the four corners of the aluminum frame, followed by the theoretical modal analysis. The second goal was to validate this model by comparing the finite element calculated mode shapes and frequencies to the empirical modal analysis previously measured at the United States Military Academy at West Point, New York. Five mode shapes and frequencies agreed rather well between the theoretical finite element analysis and previously published empirical modal analysis, specifically where the rim was vibrating in the vertical direction, which was the direction that the accelerometer was aligned for the empirical modal analysis. These five modes were addressed from a finite element model validation standpoint by a 99.5% confidence in a 98.09% cross-correlation with empirical modal analysis data, and from a verification standpoint by employing a refined-mesh. However, three theoretical mode shapes missed by the empirical modal analysis were found where the vibration of the rim was confined to the horizontal plane, which was orthogonal to the orientation of our accelerometer. Full article
(This article belongs to the Special Issue Vibrations in Sports)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>DesignModeler Geometry—Tree Outline 1-of-3.</p> Full article ">Figure 2
<p>DesignModeler Geometry—Tree Outline 2-of-3.</p> Full article ">Figure 3
<p>DesignModeler Geometry—Tree Outline 3-of-3.</p> Full article ">Figure 4
<p>Top and front views of rim and backboard: major dimensions.</p> Full article ">Figure 5
<p>Four parabolic elements.</p> Full article ">Figure 6
<p>Mesh and fixed supports at corner vertices of aluminum frame.</p> Full article ">Figure 7
<p>Mesh and fixed supports of 4618-element (<b>left</b>) and 8410-element (<b>right</b>) models.</p> Full article ">Figure 8
<p>Empirical modal 23.62 Hz (<b>top</b>) versus ANSYS FEM 21.328 Hz (<b>bottom</b>).</p> Full article ">Figure 9
<p>Empirical modal 33.08 Hz (<b>top</b>) versus ANSYS FEM 35.888 Hz (<b>bottom</b>).</p> Full article ">Figure 10
<p>Empirical modal 51.45 Hz (<b>top</b>) versus ANSYS FEM 47.177 Hz (<b>bottom</b>).</p> Full article ">Figure 11
<p>Empirical modal 78.14 Hz (<b>top</b>) versus ANSYS FEM 78.028 Hz (<b>bottom</b>).</p> Full article ">Figure 12
<p>Empirical modal 94.38 Hz (<b>top</b>) versus ANSYS FEM 114.81 Hz (<b>bottom</b>).</p> Full article ">Figure 13
<p>8410-element model: correlation of theoretical and empirical modal frequencies.</p> Full article ">Figure 14
<p>Missed modes predicted by ANSYS FEM at 11, 28, and 44 Hz.</p> Full article ">
22 pages, 10012 KiB  
Article
Remaining Useful Life Prediction Method Enhanced by Data Augmentation and Similarity Fusion
by Huaqing Wang, Ye Li, Ye Jin, Shengkai Zhao, Changkun Han and Liuyang Song
Vibration 2024, 7(2), 560-581; https://doi.org/10.3390/vibration7020029 - 5 Jun 2024
Viewed by 714
Abstract
Precise prediction of the remaining useful life (RUL) of rolling bearings is crucial for ensuring the smooth functioning of machinery and minimizing maintenance costs. The time-domain features can reflect the degenerative state of the bearings and reduce the impact of random noise present [...] Read more.
Precise prediction of the remaining useful life (RUL) of rolling bearings is crucial for ensuring the smooth functioning of machinery and minimizing maintenance costs. The time-domain features can reflect the degenerative state of the bearings and reduce the impact of random noise present in the original signal, which is often used for life prediction. However, obtaining ideal training data for RUL prediction is challenging. Thus, this paper presents a bearing RUL prediction method based on unsupervised learning sample augmentation, establishes a VAE-GAN model, and expands the time-domain features that are calculated based on the original vibration signals. By combining the advantages of VAE and GAN in data generation, the generated data can better represent the degradation state of the bearings. The original data and generated data are mixed to realize data augmentation. At the same time, the dynamic time warping (DTW) algorithm is introduced to measure the similarity of the dataset, establishing the mapping relationship between the training set and target sequence, thereby enhancing the prediction accuracy of supervised learning. Experiments employing the XJTU-SY rolling element bearing accelerated life test dataset, IMS dataset, and pantograph data indicate that the proposed method yields high accuracy in bearing RUL prediction. Full article
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<p>The framework of proposed method.</p> Full article ">Figure 2
<p>Structure of VAE.</p> Full article ">Figure 3
<p>Structure of GAN.</p> Full article ">Figure 4
<p>Test bed. (<b>a</b>) XJTU-SY bearing dataset; (<b>b</b>) IMS dataset; (<b>c</b>) Slide plates of pantograph.</p> Full article ">Figure 5
<p>Generated data by VAE-GAN with noise standard deviation of different value. (<b>a</b>) value = 0.001; (<b>b</b>) value = 0.01; (<b>c</b>) value = 0.1; (<b>d</b>) value = 1.</p> Full article ">Figure 6
<p>The correlation coefficients matrix heat map of feature parameter with different noise standard deviation. (<b>a</b>) value = 0.001; (<b>b</b>) value = 0.01.</p> Full article ">Figure 7
<p>The kernel density map of generated data with different noise standard deviation. (<b>a</b>) value = 0.001; (<b>b</b>) value = 0.01.</p> Full article ">Figure 8
<p><span class="html-italic">MCD</span> values at different standard deviations.</p> Full article ">Figure 9
<p>CI values of training set.</p> Full article ">Figure 10
<p>RUL prediction results of experiment 1. (<b>a</b>) Bearing A5; (<b>b</b>) Bearing B1; (<b>c</b>) Bearing C4.</p> Full article ">Figure 11
<p>Visualization of RUL prediction of experiment 1. (<b>a</b>) <span class="html-italic">RMSE</span>; (<b>b</b>) <span class="html-italic">R</span><sup>2</sup><span class="html-italic">-SCORE</span>.</p> Full article ">Figure 12
<p>RUL prediction results of experiment 2. (<b>a</b>) Bearing A5; (<b>b</b>) Bearing B1.</p> Full article ">Figure 13
<p>Visualization of RUL prediction of experiment 2. (<b>a</b>) <span class="html-italic">RMSE</span>; (<b>b</b>) <span class="html-italic">R</span><sup>2</sup><span class="html-italic">-SCORE</span>.</p> Full article ">Figure 14
<p>Visualization of RUL prediction under different training data. (<b>a</b>) <span class="html-italic">RMSE</span>; (<b>b</b>) <span class="html-italic">R</span><sup>2</sup><span class="html-italic">-SCORE</span>.</p> Full article ">Figure 15
<p>RUL prediction results on IMS dataset. (<b>a</b>)Bearing B2; (<b>b</b>)Bearing B4.</p> Full article ">Figure 16
<p>Visualization of RUL prediction results on IMS dataset. (<b>a</b>) <span class="html-italic">RMSE</span>; (<b>b</b>) <span class="html-italic">R</span><sup>2</sup><span class="html-italic">-SCORE</span>.</p> Full article ">Figure 17
<p>RUL prediction results on pantograph data. (<b>a</b>) 37B; (<b>b</b>) 39D.</p> Full article ">Figure 18
<p>Visualization of RUL prediction results on pantograph data. (<b>a</b>) <span class="html-italic">RMSE</span>; (<b>b</b>) <span class="html-italic">R</span><sup>2</sup><span class="html-italic">-SCORE</span>.</p> Full article ">
39 pages, 22218 KiB  
Article
A Deep Transfer Learning Model for the Fault Diagnosis of Double Roller Bearing Using Scattergram Filter Bank 1
by Mohsin Albdery and István Szabó
Vibration 2024, 7(2), 521-559; https://doi.org/10.3390/vibration7020028 - 5 Jun 2024
Viewed by 662
Abstract
In this study, a deep transfer learning model was developed using ResNet-101 architecture to diagnose double roller bearing defects. Vibration data were collected for three different load scenarios, including conditions without load, and for five different rotational speeds, ranging from 500 to 2500 [...] Read more.
In this study, a deep transfer learning model was developed using ResNet-101 architecture to diagnose double roller bearing defects. Vibration data were collected for three different load scenarios, including conditions without load, and for five different rotational speeds, ranging from 500 to 2500 RPM. Significantly, the speed condition of 2500 RPM has not previously been investigated, therefore offering a potential avenue for future investigations. This study offers a thorough examination of bearing conditions using multidirectional vibration data collected from accelerometers positioned in both vertical and horizontal orientations. In addition to transfer learning using ResNet-101, four additional models (VGG-16, VGG19, ResNet-18, and ResNet-50) were trained. Transfer learning using ResNet-101 consistently achieved the highest accuracy in all scenarios, with accuracy rates ranging from 90.78% to 99%. Scattergram Filter Bank 1 was used as the image input for training as a preprocessing method to enhance feature extraction. Research has effectively applied transfer learning to improve fault diagnosis accuracy, especially in limited data scenarios. This shows the capability of the method to differentiate between normal and faulty bearing conditions using signal-to-image transformation, emphasizing the potential of transfer learning to augment diagnostic performance in scenarios with limited training data. Full article
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<p>Schematic diagram of the experimental test rig.</p> Full article ">Figure 2
<p>(<b>a</b>) Spherical roller bearing 22209 EK, and (<b>b</b>) dimensions [<a href="#B43-vibration-07-00028" class="html-bibr">43</a>].</p> Full article ">Figure 3
<p>Common rolling element faults [<a href="#B44-vibration-07-00028" class="html-bibr">44</a>].</p> Full article ">Figure 4
<p>Creating defective components of experimental work using an EDM: (<b>a</b>) inner race, (<b>b</b>) outer race, and (<b>c</b>) roller.</p> Full article ">Figure 5
<p>Inner race defects: (<b>a</b>) inner race defect 0.5 mm, (<b>b</b>) inner race defect 1 mm, and (<b>c</b>) inner race defect 2 mm.</p> Full article ">Figure 6
<p>Outer race defects: (<b>a</b>) outer race defect 0.5 mm, (<b>b</b>) outer race defect 1 mm, and (<b>c</b>) outer race defect 2 mm.</p> Full article ">Figure 7
<p>Roller race defects: (<b>a</b>) roller defect 0.5 mm, (<b>b</b>) roller defect 1 mm, and (<b>c</b>) roller defect 2 mm.</p> Full article ">Figure 8
<p>The alignment procedure using the Fixturlaser XA system.</p> Full article ">Figure 9
<p>Hydraulic load system.</p> Full article ">Figure 10
<p>Data acquisition and power control.</p> Full article ">Figure 11
<p>SKF optical tachometer TMOT6.</p> Full article ">Figure 12
<p>The measurement of vibrations using the SKF Microlog loading case.</p> Full article ">Figure 13
<p>CMSS 2200 accelerometer sensor with magnetic base.</p> Full article ">Figure 14
<p>Schematic diagram of the experimental procedure.</p> Full article ">Figure 15
<p>The vibration measurements within the unloading case.</p> Full article ">Figure 16
<p>(<b>a</b>) Segmentation of the signal, and (<b>b</b>) Scalogram filter bank 1 for each bearing condition.</p> Full article ">Figure 16 Cont.
<p>(<b>a</b>) Segmentation of the signal, and (<b>b</b>) Scalogram filter bank 1 for each bearing condition.</p> Full article ">Figure 16 Cont.
<p>(<b>a</b>) Segmentation of the signal, and (<b>b</b>) Scalogram filter bank 1 for each bearing condition.</p> Full article ">Figure 17
<p>(<b>a</b>) IMS bearing test rig, (<b>b</b>) Rexnord ZA-2115 double row bearing, (<b>c</b>) inner race defect in bearing 3, test 1, (<b>d</b>) roller element defect in bearing 4, test 1, and (<b>e</b>) outer race defect in bearing 1, test 2 [<a href="#B35-vibration-07-00028" class="html-bibr">35</a>].</p> Full article ">Figure 18
<p>Raw vibration data for L0-RS1 in vertical and horizontal directions.</p> Full article ">Figure 18 Cont.
<p>Raw vibration data for L0-RS1 in vertical and horizontal directions.</p> Full article ">Figure 18 Cont.
<p>Raw vibration data for L0-RS1 in vertical and horizontal directions.</p> Full article ">Figure 19
<p>Confusion matrix chart of fault diagnosis results for TL_ ResNet-101 obtained for Case Study 1 (L0). (<b>a</b>) L0-RS1, (<b>b</b>) L0-RS2, (<b>c</b>) L0-RS3, (<b>d</b>) L0-RS4, and (<b>e</b>) L0-RS5.</p> Full article ">Figure 19 Cont.
<p>Confusion matrix chart of fault diagnosis results for TL_ ResNet-101 obtained for Case Study 1 (L0). (<b>a</b>) L0-RS1, (<b>b</b>) L0-RS2, (<b>c</b>) L0-RS3, (<b>d</b>) L0-RS4, and (<b>e</b>) L0-RS5.</p> Full article ">Figure 20
<p>Transfer learning model accuracy for Case Study 1.</p> Full article ">Figure 21
<p>Training accuracy for Case Study 2.</p> Full article ">Figure 22
<p>Training accuracy for Case Study 3.</p> Full article ">Figure 23
<p>Confusion matrix of ResNet-101: (<b>a</b>) L0-RS1, (<b>b</b>) L0-RS2, (<b>c</b>) L0-RS3, (<b>d</b>) L0-RS4, and (<b>e</b>) L0-RS5.</p> Full article ">Figure A1
Full article ">Figure A1 Cont.
Full article ">Figure A2
Full article ">Figure A3
Full article ">
18 pages, 8511 KiB  
Article
Simulation on Buffet Response and Mitigation of Variant-Tailed Aircraft in Maneuver State
by Dawei Liu, Peng Zhang, Binbin Lv, Hongtao Guo, Li Yu, Yanru Chen and Bo Lu
Vibration 2024, 7(2), 503-520; https://doi.org/10.3390/vibration7020027 - 27 May 2024
Viewed by 560
Abstract
This study proposes a computational fluid dynamics and computational structure dynamics (CFD/CSD) coupled method for calculating the buffet response of a variant tail wing. The large-scale separated flow in the buffet is simulated by the detached vortex approach, vibration deformation of the tail [...] Read more.
This study proposes a computational fluid dynamics and computational structure dynamics (CFD/CSD) coupled method for calculating the buffet response of a variant tail wing. The large-scale separated flow in the buffet is simulated by the detached vortex approach, vibration deformation of the tail wing is solved by the dynamic mesh generation technique, and structural modeling is based on the mode method. The aerodynamic elastic coupling is calculated through the cyclic iteration of aerodynamics and the structural solution in the time domain. We verify the correctness of the proposed method through a typical delta wing calculation case, further simulate the buffet response of a variant tail wing in maneuver state, and finally realize buffet mitigation using an active excitation method. Overall, this study can provide an important reference for the design of variant-tailed aircraft. Full article
(This article belongs to the Topic Advances on Structural Engineering, 2nd Volume)
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<p>Calculation process for buffet response of variant tail wing aircraft based on CFD/CSD coupling.</p> Full article ">Figure 2
<p>Schematic diagram of triangular wing geometric model.</p> Full article ">Figure 3
<p>Diagram of triangle wing calculation grid. (<b>a</b>) Flow field calculation grid; (<b>b</b>) Structural field calculation grid.</p> Full article ">Figure 4
<p>Modal vibration mode of delta wing structure.</p> Full article ">Figure 5
<p>Response time history of delta wing tip vibration.</p> Full article ">Figure 6
<p>FFT spectrum analysis of vibration response of delta wing tips.</p> Full article ">Figure 7
<p>Instantaneous vorticity cloud map at typical chord length positions of delta wings.</p> Full article ">Figure 8
<p>Flow field calculation grid.</p> Full article ">Figure 9
<p>Instantaneous flow field of a variant tail rigid model at different angles of attack.</p> Full article ">Figure 10
<p>Finite element model of tail wing structure.</p> Full article ">Figure 11
<p>Modal vibration mode of tail wing structure.</p> Full article ">Figure 12
<p>Generalized displacement response curves of variant tail wings at different angles of attack.</p> Full article ">Figure 13
<p>Displacement response curves of variant tail wing tips at different angles of attack.</p> Full article ">Figure 14
<p>Power spectral density of displacement response of variant tail wing tip.</p> Full article ">Figure 15
<p>Wing tip displacement response under different excitation forces based on velocity feedback method.</p> Full article ">Figure 16
<p>Power spectral density of wing tip displacement response.</p> Full article ">
24 pages, 5723 KiB  
Article
Stick–Slip Suppression in Drill String Systems Using a Novel Adaptive Sliding Mode Control Approach
by Fourat Zribi, Lilia Sidhom and Mohamed Gharib
Vibration 2024, 7(2), 479-502; https://doi.org/10.3390/vibration7020026 - 23 May 2024
Viewed by 636
Abstract
A novel control technique is presented in this paper, which is based on a first-order adaptive sliding mode that ensures convergence in a finite time without any prior information on the upper limits of the parametric uncertainties and/or external disturbances. Based on an [...] Read more.
A novel control technique is presented in this paper, which is based on a first-order adaptive sliding mode that ensures convergence in a finite time without any prior information on the upper limits of the parametric uncertainties and/or external disturbances. Based on an exponent reaching law, this controller uses two dynamically adaptive control gains. Once the sliding mode is reached, the dynamic gains decrease in order to loosen the system’s constraints, which guarantees minimal control effort. The proof of convergence was demonstrated according to Lyapunov’s criterion. The proposed algorithm was applied to a drill string system to evaluate its performance because such systems present variable operating conditions caused by, for example, the type of rock. The effectiveness of the proposed controller was evaluated by conducting a comparative study that involved comparing it against a commonly used sliding mode controller, as well as other recent adaptive sliding mode control techniques. The different mathematical performance measures included energy consumption. The proposed algorithm had the best performance measures with the lowest energy consumption and it was able to significantly improve the functioning of the drill string system. The results indicated that the proposed controller had 20% less chattering than the classic SM controller. Finally, the proposed controller was the most robust to uncertainties in system parameters and external disturbances, thus demonstrating the auto-adjustable features of the controller. Full article
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<p>Overall architecture of the proposed control scheme.</p> Full article ">Figure 2
<p>Schematic for the main parts of a drill string.</p> Full article ">Figure 3
<p>Effects of measurement noise on drill string bit velocities.</p> Full article ">Figure 4
<p>Effects of measurement noise on input signals; (<b>a</b>) global scale; and (<b>b</b>) local scale.</p> Full article ">Figure 5
<p>RMSD values of different controllers.</p> Full article ">Figure 6
<p>System responses of the CSMC with parametric uncertainty.</p> Full article ">Figure 7
<p>System responses of the MSMC with parametric uncertainty.</p> Full article ">Figure 8
<p>System responses of the ASMC with parametric uncertainty.</p> Full article ">Figure 9
<p>System responses of the proposed controller with parametric uncertainty.</p> Full article ">Figure 10
<p>Root mean square error (RMSE) of different controllers.</p> Full article ">Figure 11
<p>The ISE (integral square error) and IAE (integral absolute error) values for all controllers.</p> Full article ">Figure 12
<p>RMSD values with and without measurement noise for all controllers.</p> Full article ">
15 pages, 1853 KiB  
Article
Analytical Study of Nonlinear Flexural Vibration of a Beam with Geometric, Material and Combined Nonlinearities
by Yoganandh Madhuranthakam and Sunil Kishore Chakrapani
Vibration 2024, 7(2), 464-478; https://doi.org/10.3390/vibration7020025 - 13 May 2024
Viewed by 2860
Abstract
This article explores the nonlinear vibration of beams with different types of nonlinearities. The beam vibration was modeled using Hamilton’s principle, and the equation of motion was solved using method of multiple time scales. Three models were developed assuming (a) geometric nonlinearity, (b) [...] Read more.
This article explores the nonlinear vibration of beams with different types of nonlinearities. The beam vibration was modeled using Hamilton’s principle, and the equation of motion was solved using method of multiple time scales. Three models were developed assuming (a) geometric nonlinearity, (b) material nonlinearity and (c) combined geometric and material nonlinearity. The material nonlinearity also included both third and fourth nonlinear elasticity terms. The frequency response equation of these models were further evaluated quantitatively and qualitatively. The models capture the hardening effect, i.e., increase in resonant frequency as a function of forcing amplitude for geometric nonlinearity, and the softening effect, i.e., decrease in resonant frequency for material nonlinearity. The model is applied on the first three bending modes of the cantilever beam. The effect of the fourth-order material nonlinearity was smaller compared to the third-order term in the first mode, whereas it is significantly larger in second and third mode. The combined nonlinearity models shows a discontinuous frequency shift, which was resolved by utilizing a set of transition assumptions. This results in a smooth transition between the material and geometric zones in amplitude. These parametric models allow us to fine tune the nonlinear response of the system by changing the physical properties such as geometry, linear and nonlinear elastic properties. Full article
(This article belongs to the Special Issue Feature Papers in Vibration)
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<p>Schematic of 1D cantilever beam with nonlinear flexural vibrations.</p> Full article ">Figure 2
<p>Flowchart to calculate the nonlinear resonant frequency shift as a function of applied force for a vibrating beam.</p> Full article ">Figure 3
<p>Nonlinear shift in resonant frequency with change in applied force for a beam with only geometric nonlinearity observed in (<b>a</b>) 1st mode, (<b>b</b>) 2nd mode and (<b>c</b>) 3rd mode.</p> Full article ">Figure 4
<p>Change in resonant frequency shift with change in applied force in the beam with third-order (<math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) and fourth−order (<math display="inline"><semantics> <mrow> <mi>K</mi> <mo>≠</mo> <mn>0</mn> </mrow> </semantics></math>) material nonlinearity observed in (<b>a</b>) 1st mode, (<b>b</b>) 2nd mode and (<b>c</b>) 3rd mode.</p> Full article ">Figure 5
<p><math display="inline"><semantics> <mrow> <mi>H</mi> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </semantics></math> with change in beam deflection (<span class="html-italic">a</span>).</p> Full article ">Figure 6
<p>Change in resonant frequency shift with change in applied force in the beam with material and geometric nonlinearity using Model 1.</p> Full article ">Figure 7
<p>Change in resonant frequency shift with change in applied force in the beam with material and geometric nonlinearity using Model 2.</p> Full article ">
11 pages, 5155 KiB  
Article
Does the Workload Change When Using an Impact Wrench in Different Postures?—A Counter-Balanced Trial
by Nastaran Raffler, Thomas Wilzopolski, Christian Freitag and Elke Ochsmann
Vibration 2024, 7(2), 453-463; https://doi.org/10.3390/vibration7020024 - 9 May 2024
Viewed by 731
Abstract
Awkward hand-arm posture and overhead work increase the risk of musculoskeletal symptoms. These adverse health effects can also be caused by additional workloads such as hand-arm vibration exposure while carrying or holding a power tool. This pilot trial investigated posture and muscle activity [...] Read more.
Awkward hand-arm posture and overhead work increase the risk of musculoskeletal symptoms. These adverse health effects can also be caused by additional workloads such as hand-arm vibration exposure while carrying or holding a power tool. This pilot trial investigated posture and muscle activity of 11 subjects while using an impact wrench for three working directions: upwards, forwards and downwards. Although the vibration exposure did not show notable differences in the magnitude (4.8 m/s2 upwards, 4.4 m/s2 forwards and 4.7 m/s2 downwards), postural behavior and the muscle activity showed significantly higher workloads for working upwards compared to forwards direction. The muscle activity results for working downwards also showed elevated levels of muscle activity due to the awkward wrist posture. The results demonstrate that not only the working direction but also more importantly the arm, wrist and head posture need to be considered while investigating hand-arm vibration exposure. Full article
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<p>(<b>left</b>): Setup of the test for examining the three working directions while using an impact wrench; (<b>right</b>): Impact wrench with accelerometer.</p> Full article ">Figure 2
<p>Positioning of the sensors on the body to measure the angle of the body.</p> Full article ">Figure 3
<p>Location of the electromyography sensors on the skin.</p> Full article ">Figure 4
<p>Borg scale for subjective perception of the test subjects.</p> Full article ">Figure 5
<p>Posture analysis for three working directions while using an impact wrench; angles are given as boxplots (5th, 25th, 50th, 75th, 95th). The range of movements for each angle is given by the categories with respect to ISO TR 10,687 (green = neutral, yellow = moderate and red = awkward). (<b>a</b>): head inclination sagittal; (<b>b</b>): upper arm inclination right; (<b>c</b>): wrist flexion right; (<b>d</b>): wrist radial and ulnar deviation.</p> Full article ">Figure 6
<p>Electro muscle activity in three working directions; UF* = significance value &lt;0.05 between upwards and forwards, UD* = significance value &lt;0.05 between upwards and downwards and FD* = significance value &lt;0.05 between forwards and downwards. (<b>a</b>): trapezius descendens; (<b>b</b>): biceps brachii; (<b>c</b>): flexor carpi ulnaris; (<b>d</b>): extensor digitorum.</p> Full article ">Figure 7
<p>Subjective perception for the exposure of vibration and posture in three working directions.</p> Full article ">
21 pages, 5056 KiB  
Article
Effects of In-Wheel Suspension on Whole-Body Vibration and Comfort in Manual Wheelchair Users
by Ahlad Neti, Allison Brunswick, Logan Marsalko, Chloe Shearer and Alicia Koontz
Vibration 2024, 7(2), 432-452; https://doi.org/10.3390/vibration7020023 - 30 Apr 2024
Viewed by 1192
Abstract
Frequent and prolonged exposure to high levels of vibration and shock can cause neck and back pain and discomfort for many wheelchair users. Current methods to attenuate the vibration have shown to be ineffective and, in some cases, detrimental to health. Novel in-wheel [...] Read more.
Frequent and prolonged exposure to high levels of vibration and shock can cause neck and back pain and discomfort for many wheelchair users. Current methods to attenuate the vibration have shown to be ineffective and, in some cases, detrimental to health. Novel in-wheel suspension systems claim to offer a solution by replacing traditional spokes of the rear wheels with dampening elements or springs. The objective of this study was to investigate the effects of in-wheel suspension on reducing vibration and shock and improving comfort in manual wheelchair users. Twenty-four manual wheelchair users were propelled over nine different surfaces using a standard spoked wheel, a Spinergy CLX, and Loopwheels while accelerometry data was collected at the footrest, seat, and backrest. Loopwheels lowered vibrations by 10% at the backrest compared to the standard and CLX wheels (p-value < 0.001) and by 7% at the footrest compared to the CLX (p-value < 0.05). They also reduced shocks by 7% at the backrest compared to the standard wheel and CLX (p-value < 0.001). No significant differences were found in comfort between the wheels. Results indicate that Loopwheels is effective at reducing vibration and shock, but more long-term testing is required to determine effects on health. Full article
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<p>The diagram above shows how the in-wheel suspension system works when it encounters an obstacle. As shown, the axle hub of the wheel is able to deflect relative to the rim of the wheel and stay level relative to the ground. The dashed line represents the level of the axle, and the blue region represents the surface.</p> Full article ">Figure 2
<p>The surfaces, obstacles, and course layout used for this study. The course was split into three intensity regions and three surfaces/obstacles in each region. These regions were physically marked off with tape on the floor.</p> Full article ">Figure 3
<p>The three different wheel types used in this study.</p> Full article ">Figure 4
<p>The diagram above shows the approximate locations of where the Shimmer3 sensors were placed on the wheelchair along with the respective coordinate system.</p> Full article ">Figure 5
<p>The image above shows differences in sensor position between two different manual wheelchairs, a ROGUE (1) and a PantheraX (2). Overall (<b>A1</b>,<b>A2</b>), footrest (<b>B1</b>,<b>B2</b>), seat panel (<b>C1</b>,<b>C2</b>), and back rest (<b>D1</b>,<b>D2</b>) differences are shown along with sensor orientation.</p> Full article ">Figure 6
<p>Average RMS values over all participants for each wheel, sensor location, and intensity region. Error bars show standard deviation.</p> Full article ">Figure 7
<p>Average VDV over all participants for each wheel, sensor location, and intensity region. Error bars show standard deviation.</p> Full article ">Figure 8
<p>RMS mean values calculated for each wheel type at each sensor location. Error bars signify the standard deviation, and statistically significant differences are reported by * and ** (<span class="html-italic">p</span>-value &lt; 0.05 and 0.001, respectively). (ST: standard, CX: CLX, and LW: Loopwheels).</p> Full article ">Figure 9
<p>The VDV mean values calculated for each wheel type at each sensor location. Error bars show the standard deviation, and statistically significant differences are reported by ** (<span class="html-italic">p</span>-value &lt; 0.001). (ST: standard, CX: CLX, and LW: Loopwheels).</p> Full article ">Figure 10
<p>Mean self-reported comfort scores for each surface and wheel type.</p> Full article ">Figure A1
<p>The plots above show the raw and rotated acceleration data from the first second of a static position. Original coordinate system is shown by x, y, and z, and the rotated system is x’, y’, and z’. As shown, in the rotated system, gravity is only applied in the z’ direction.</p> Full article ">Figure A2
<p>The plot above shows the raw and filtered vertical acceleration from two seconds of a trial.</p> Full article ">Figure A3
<p>The plot above shows the acceleration measured by a sensor for the whole obstacle course. The intensity regions are defined by their start (green line) and their end (red line). Only data within each region was used to calculate WBV values.</p> Full article ">
13 pages, 864 KiB  
Article
Assessing Ride Motion Discomfort Measurement Formulas
by Louis T Klauder Jr
Vibration 2024, 7(2), 419-431; https://doi.org/10.3390/vibration7020022 - 30 Apr 2024
Viewed by 740
Abstract
This article is about a framework for determining the degree of realism of any given passenger ride motion discomfort measurement formula. After providing some context and reviewing evidence of deficiency in currently popular ride motion discomfort measurement formulas, the article outlines the research [...] Read more.
This article is about a framework for determining the degree of realism of any given passenger ride motion discomfort measurement formula. After providing some context and reviewing evidence of deficiency in currently popular ride motion discomfort measurement formulas, the article outlines the research program that needs to be carried out in order to establish such a framework. The research begins with gathering recordings of uncomfortable ride motion episodes encountered in a chosen type of passenger transport service. It then has test subjects compare the episodes via a ride motion simulator and adjust their amplitudes pair wise until they cause equal discomfort. It explains how to take the pair wise amplitude adjustments and determine amplitude adjustments that bring all of the motion episode recordings to a common level of discomfort so that they form a normalized set. Then, the lower the scatter of the scores assigned by any given discomfort measurement formula to the members of that set, the more realistic that formula will be for the chosen service. Full article
(This article belongs to the Special Issue Whole-Body Vibration and Hand-Arm Vibration Related to ISO-TC108-SC4 Published Standards)
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<p>Flow charts depicting steps of proposed research program.</p> Full article ">
12 pages, 11017 KiB  
Article
Exploring the Effects of Additional Vibration on the Perceived Quality of an Electric Cello
by Hanna Järveläinen, Stefano Papetti and Eric Larrieux
Vibration 2024, 7(2), 407-418; https://doi.org/10.3390/vibration7020021 - 30 Apr 2024
Viewed by 805
Abstract
Haptic feedback holds the potential to enhance the engagement and expressivity of future digital and electric musical instruments. This study investigates the impact of artificial vibration on the perceived quality of a silent electric cello. We developed a haptic cello prototype capable of [...] Read more.
Haptic feedback holds the potential to enhance the engagement and expressivity of future digital and electric musical instruments. This study investigates the impact of artificial vibration on the perceived quality of a silent electric cello. We developed a haptic cello prototype capable of rendering vibration signals of varying degree of congruence with the produced sound. Experienced cellists participated in an experiment comparing setups with and without vibrotactile feedback, rating them on preference, perceived power, liveliness, and feel. Results show nuanced effects, with added vibrations moderately enhancing feel and liveliness, and significantly increasing perceived power when using vibrations obtained from the pickup at the cello’s bridge. High uncertainty in our statistical model parameters underscores substantial individual differences in the participants responses, as commonly found in qualitative assessments, and highlights the importance of consistent feedback in the vibrotactile and auditory channels. Our findings contribute valuable insights to the intersection of haptics and music technology, paving the way for creating richer and more engaging experiences with future musical instruments. Full article
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<p>A Tactile Labs Haptuator BM3C vibrotactile transducer attached to the scroll of the instrument.</p> Full article ">Figure 2
<p>Accelerometer attached at various locations on the acoustic cello, each typically in contact with the player’s body. (<b>a</b>) Neck: left-hand grip (for right-handed players). (<b>b</b>) Top back: chest contact. (<b>c</b>) Side: inner thigh contact.</p> Full article ">Figure 3
<p>Accelerometer attached at various locations on the haptic cello, each corresponding to those on the acoustic instrument. (<b>a</b>) Neck: left-hand grip (for right-handed players). (<b>b</b>) Top back: chest contact. (<b>c</b>) Side: inner thigh contact.</p> Full article ">Figure 4
<p>The experimental setting, and a close-up of the GUI for rating the qualitative attribute <span class="html-italic">liveliness</span>.</p> Full article ">Figure 5
<p>Raw data: smoothed density plots (solid lines) and sample means (dashed lines) of rating responses by attribute and vibration type. Vertical lines at x = 0.5 mark the point of perceived equality between the test and reference setups. Each plot represents data of three repeated measurements taken from N = 11 participants.</p> Full article ">Figure 6
<p>Estimated mean ratings and 95% CI of the response distribution for all response variables.</p> Full article ">
19 pages, 5391 KiB  
Article
The Development of a High-Static Low-Dynamic Cushion for a Seat Containing Large Amounts of Friction
by Janik Habegger, Megan E. Govers, Marwan Hassan and Michele L. Oliver
Vibration 2024, 7(2), 388-406; https://doi.org/10.3390/vibration7020020 - 25 Apr 2024
Viewed by 823
Abstract
Exposure to whole-body vibration (WBV) has been shown to result in lower-back pain, sciatica, and other forms of discomfort for operators of heavy equipment. While WBV is defined to be between 0.5 and 80 Hz, humans are most sensitive to vertical vibrations between [...] Read more.
Exposure to whole-body vibration (WBV) has been shown to result in lower-back pain, sciatica, and other forms of discomfort for operators of heavy equipment. While WBV is defined to be between 0.5 and 80 Hz, humans are most sensitive to vertical vibrations between 5 and 10 Hz. To reduce WBV exposure, a novel seat cushion is proposed that optimally tunes a High-Static Low-Dynamic (HSLD) stiffness isolator. Experimental and numerical results indicate that the cushion can drastically increase the size of the attenuation region compared to a stock foam cushion. When placed on top of a universal tractor seat, the cushion is capable of mitigating vibrations at frequencies higher than 1.1 Hz. For comparison, the universal tractor seat with a stock foam cushion isolates vibrations between 3.4 and 4.1 Hz, as well as frequencies larger than 4.8 Hz. Friction within the universal seat is accurately modeled using the Force Balance Friction Model (FBFM), and an analysis is conducted to show why friction hinders overall seat performance. Finally, the cushion is shown to be robust against changes in mass, assuming accurate tuning of the preload is possible. Full article
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<p>The model of a two-degree-of-freedom system consisting of nonlinear stiffness elements.</p> Full article ">Figure 2
<p>The stiffness of a High-Static Low-Dynamic (HSLD) system when tuned to have localized positive, negative, and quasi-zero stiffness (QZS).</p> Full article ">Figure 3
<p>Negative stiffness oblique spring mechanism.</p> Full article ">Figure 4
<p>Overall experimental setup of universal tractor seat with quasi-zero stiffness cushion on top.</p> Full article ">Figure 5
<p>The internal mechanism of the novel quasi-zero stiffness cushion with a foam pad on top.</p> Full article ">Figure 6
<p>A force–displacement plot of the universal tractor seat as a single-degree-of-freedom system. (<b>a</b>) The Instron applies its force near the front of the seat; (<b>b</b>) the Instron applies its force near the back of the seat. In each plot, the green line is fit to the preload portion of the plot and the purple line to the main stroke of the seat. When a mass is placed on the seat, the seat vibrates entirely within the ”Seat Stroke” region.</p> Full article ">Figure 7
<p>Diagram of stock universal tractor seat, containing two potential degrees of freedom.</p> Full article ">Figure 8
<p>Spring stiffness of springs within quasi-zero stiffness cushion. (<b>a</b>) Spring stiffness of vertical springs approximated by line of best fit; (<b>b</b>) Spring stiffness of ten oblique springs in parallel approximated by line of best fit.</p> Full article ">Figure 9
<p>The experimental dynamic response of the universal tractor seat compared to the expected linear response and the numerical simulation with the Force Balance Friction Model. In all cases, <span class="html-italic">m</span> = 81.9 kg, <span class="html-italic">ζ</span> = 0.4, <span class="html-italic">k</span> = 3420 m/N, and <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>o</mi> </msub> </mrow> </semantics></math> = 0.001 m/s.</p> Full article ">Figure 10
<p>Universal tractor seat with quasi-zero stiffness and foam cushion on top of it.</p> Full article ">Figure 11
<p>Comparison of the experimental, analytical, and numerical results for the quasi-zero stiffness (QZS) cushion. The analytical response of a similar linear system is included for reference. For all plots, the mass, vertical stiffness, and damping are identical. In the case of the QZS system, tuned oblique springs are added.</p> Full article ">Figure 12
<p>The response of the overall universal seat with a regular cushion and the quasi-zero stiffness (QZS) cushion.</p> Full article ">Figure 13
<p>Dynamic response of the one-inch polyurethane foam pad used on the quasi-zero stiffness (QZS) cushion between 0.5 and 9 Hz.</p> Full article ">Figure 14
<p>Effect of increasing viscous damping (ζ) within quasi-zero stiffness cushion.</p> Full article ">Figure 15
<p>Theoretical response of universal seat and quasi-zero stiffness (QZS) cushion with and without friction.</p> Full article ">Figure 16
<p>Mass 2 transmissibility within the universal seat in combination with the quasi-zero stiffness (QZS) cushion.</p> Full article ">Figure 17
<p>The effects of changing mass on the universal seat with the quasi-zero stiffness (QZS) cushion, assuming that the cushion is tuned to the point of lowest stiffness.</p> Full article ">
14 pages, 2130 KiB  
Article
Alterations in Step Width and Reaction Times in Walking Subjects Exposed to Mediolateral Foot-Transmitted Vibration
by Flavia Marrone, Stefano Marelli, Filippo Bertozzi, Alessandra Goggi, Enrico Marchetti, Manuela Galli and Marco Tarabini
Vibration 2024, 7(2), 374-387; https://doi.org/10.3390/vibration7020019 - 14 Apr 2024
Cited by 1 | Viewed by 1181
Abstract
This study explores how low-frequency foot-transmitted vibration (FTV) affects both gait parameters and cognitive performance. Twenty healthy male participants experienced harmonic mediolateral FTV (1.25 Hz, 1 m/s2) while either standing or walking on a treadmill. We assessed participants’ reaction times to [...] Read more.
This study explores how low-frequency foot-transmitted vibration (FTV) affects both gait parameters and cognitive performance. Twenty healthy male participants experienced harmonic mediolateral FTV (1.25 Hz, 1 m/s2) while either standing or walking on a treadmill. We assessed participants’ reaction times to visual stimuli using a psychomotor vigilance task (PVT) test under five conditions, including (i) baseline (standing still without vibration), (ii) vibration (standing still with vibration), (iii) walking (walking without vibration), (iv) walking with vibration, and (v) post-test (standing still without vibration after the tests). Additionally, the step width (SW) was measured with a camera system in conditions (iii) and (iv), i.e., when participants were walking with and without vibration and during PVT execution. The results showed that the average vigilance decreased, and the step width increased while walking and/or with vibration exposure. These findings suggest a potential connection between decreased vigilance, increased step width, and the need for enhanced stability, focusing on balance maintenance and a wider base of support. Implications for future standard revisions are presented and discussed. Full article
(This article belongs to the Special Issue Whole-Body Vibration and Hand-Arm Vibration Related to ISO-TC108-SC4 Published Standards)
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<p>(<b>a</b>) Pictorial view of the setup: the vibrating platform and the PVT device; (<b>b</b>) PVT device: the subject waits a random amount of time (2–9 s) for the green LED to light up and then presses the button as quickly as possible to record the reaction time; (<b>c</b>) The patches on the feet to measure step width: a round shape on the right, and a square shape on the left.</p> Full article ">Figure 2
<p>Temporal schemes of the baseline (<span class="html-italic">B</span>) and post-test (<span class="html-italic">P</span>), vibration (<span class="html-italic">V</span>), walking (<span class="html-italic">W</span>), and walking with vibration (<span class="html-italic">W+V</span>) trials for the PVT execution, and unperturbed gait (<span class="html-italic">U</span>), unperturbed gait with PVT (<span class="html-italic">U-PVT</span>), perturbed gait (<span class="html-italic">P</span>), and perturbed gait with PVT (<span class="html-italic">P-PVT</span>) for the step width recording.</p> Full article ">Figure 3
<p>Mean and standard deviation for the PVT trial conditions (<span class="html-italic">B</span>: baseline, <span class="html-italic">V</span>: vibration, <span class="html-italic">W</span>: walking, <span class="html-italic">W+V</span>: walking with vibration, <span class="html-italic">P</span>: post-test) of all the PVT metrics: (<b>a</b>) mean RT, (<b>b</b>) fastest RT, (<b>c</b>) slowest RT, and (<b>d</b>) lapses.</p> Full article ">Figure 4
<p>Mean, standard deviation, and regression line of RTs for each minute in all the PVT trials: (<b>a</b>) <span class="html-italic">B</span>: baseline, (<b>b</b>) <span class="html-italic">V</span>: vibration, (<b>c</b>) <span class="html-italic">W</span>: walking, (<b>d</b>) <span class="html-italic">W+V</span>: walking with vibration, and (<b>e</b>) <span class="html-italic">P</span>: post-test.</p> Full article ">Figure 5
<p><span class="html-italic">SW</span> (<b>a</b>) and <span class="html-italic">sw</span> (<b>b</b>) as a function of the gait condition (<span class="html-italic">U</span>: unperturbed, <span class="html-italic">P</span>: perturbed, <span class="html-italic">U-PVT</span>: unperturbed with PVT, <span class="html-italic">P-PVT</span>: perturbed with PVT).</p> Full article ">
12 pages, 929 KiB  
Article
Optimal and Quasi-Optimal Automatic Tuning of Vibration Neutralizers
by Emiliano Rustighi
Vibration 2024, 7(2), 362-373; https://doi.org/10.3390/vibration7020018 - 29 Mar 2024
Cited by 1 | Viewed by 955
Abstract
Vibration neutralizers are single-degree-of-freedom devices affixed to vibrating structures in order to reduce the response at a specific troublesome harmonic excitation frequency. As this frequency may vary over time, it becomes imperative to track and adjust the neutralizer to maintain the optimal performance. [...] Read more.
Vibration neutralizers are single-degree-of-freedom devices affixed to vibrating structures in order to reduce the response at a specific troublesome harmonic excitation frequency. As this frequency may vary over time, it becomes imperative to track and adjust the neutralizer to maintain the optimal performance. Recent years have witnessed the emergence of adaptive tunable vibration neutralizers, offering real-time adjustment capabilities through external actions. Thanks to real-time control algorithms, these devices enable the automatic mitigation of vibration levels in mechanical structures. A particularly successful algorithm for the automatic tuning of these devices leverages the phase angle between the base acceleration and the neutralizer’s mass. This study critically examines the justification for employing such an algorithm and scrutinizes its optimal applicability limits, particularly in the context of viscous and structurally damped systems. The findings reveal that this algorithm accurately approximates optimum tuning for systems with low damping. Moreover, from an engineering perspective, the algorithm remains acceptable even for heavily damped structures. Through a focused and comprehensive analysis, this paper provides valuable insights into the efficacy and limitations of the phase-angle-based tuning algorithm, contributing to the advancement of adaptive vibration control strategies in smart structures. Full article
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<p>(<b>a</b>) A single-degree-of-freedom host structure with viscous damping; (<b>b</b>) an ATVN with viscous damping; (<b>c</b>) Host structure and ATVN with viscous damping; (<b>d</b>) Host structure and ATVN with hysteretic damping.</p> Full article ">Figure 2
<p>Receptance of a single-degree-of-freedom host structure with viscous damping (continuous blue line) and receptance of the host structure with an ATVN tuned at the natural frequency of the host structure (continuous black line) and twenty percent below and above the natural frequency of the host structure (dotted and dashed black lines).</p> Full article ">Figure 3
<p>Reduction levels <span class="html-italic">D</span> as function of <math display="inline"><semantics> <mi>γ</mi> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> for viscous (<b>a</b>,<b>c</b>,<b>e</b>) and structural (<b>b</b>,<b>d</b>,<b>f</b>) damping: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ζ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ζ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ζ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>. The continuous black line shows the reduction levels obtained with the optimal tuning strategy. The dashed line presents the reduction levels obtained with quasi-optimal damping.</p> Full article ">Figure 4
<p>Optimal, quasi-optimal, and approximated tuning <math display="inline"><semantics> <mi>γ</mi> </semantics></math> as a function of the damping for viscous (<b>a</b>,<b>c</b>,<b>e</b>) and structural (<b>b</b>,<b>d</b>,<b>f</b>) damping (<math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>): (<b>a</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ζ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ζ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ζ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>Difference between the reduction levels <span class="html-italic">D</span> obtained with the quasi-optimal and the optimal strategies expressed in dBs: (<b>a</b>) viscous damping with <math display="inline"><semantics> <mrow> <msub> <mi>ζ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) structural damping with <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>.</p> Full article ">
11 pages, 2479 KiB  
Article
Antihistamine Medication Blunts Localized-Vibration-Induced Increases in Popliteal Blood Flow
by Devin Needs, Jonathan Blotter, Gilbert W. Fellingham, Glenn Cruse, Jayson R. Gifford, Aaron Wayne Johnson and Jeffrey Brent Feland
Vibration 2024, 7(2), 351-361; https://doi.org/10.3390/vibration7020017 - 29 Mar 2024
Viewed by 1215
Abstract
Localized vibration (LV) of the lower leg increases arterial blood flow (BF). However, it is unclear how LV causes this increase. Understanding the mechanisms of this response could lead to the optimized future use of LV as a therapy. One possible mechanism of [...] Read more.
Localized vibration (LV) of the lower leg increases arterial blood flow (BF). However, it is unclear how LV causes this increase. Understanding the mechanisms of this response could lead to the optimized future use of LV as a therapy. One possible mechanism of LV-mediated BF is through histamine release by mechanosensitive mast cells. The purpose of this study was to measure the BF response of 21 recreationally active young adults (11 male, 10 female, mean age 22.1 years) after 47 Hz and 10 min LV to the calf, with and without antihistamine medication (180 mg Fexofenadine). Each participant received both control (no antihistamine) and antihistamine (treatment) conditions separated by at least 24 h. BF ultrasound measurements (mean and peak blood velocity, volume flow, popliteal diameter, and heart rate) were taken before LV therapy and periodically for 19 min post LV. Using a cell means mixed model, we found that LV significantly increased the control mean blood velocity immediately post LV but did not significantly increase the antihistamine mean blood velocity immediately post LV. Therefore, we hypothesize that a primary mechanism of LV increase in BF is histamine release from mechano-sensing mast cells, and that this response is force-dependent. Full article
(This article belongs to the Special Issue Feature Papers in Vibration)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Illustration of the timing of blood flow measurements with respect to LV therapy.</p> Full article ">Figure 2
<p>(<b>A</b>) Immediately post-LV mean velocity difference from baseline distributions for control and antihistamine conditions. Statistical outliers of the distributions are shown with an “+”. (<b>B</b>) Distributions for mean velocity difference all times post-LV, averaged for both conditions.</p> Full article ">Figure 3
<p>Mean velocity difference from baseline for control and antihistamine conditions with raw standard deviations.</p> Full article ">Figure 4
<p>Volume flow difference from baseline for control and antihistamine conditions with raw standard deviations.</p> Full article ">Figure 5
<p>Plot of the average velocity difference from baseline for two trials of 47 Hz 10 min LV.</p> Full article ">Figure 6
<p>Plot of the average volume flow difference from baseline for two trials of 47 Hz 10 min LV.</p> Full article ">
25 pages, 2122 KiB  
Article
Railway Bridge Runability Safety Analysis in a Vessel Collision Event
by Lorenzo Bernardini, Andrea Collina and Gianluca Soldavini
Vibration 2024, 7(2), 326-350; https://doi.org/10.3390/vibration7020016 - 25 Mar 2024
Viewed by 1231
Abstract
Bridges connecting islands close to the coast and crossing the sea have been attracting the attention of several researchers working in the field of train–bridge interactions. A runability analysis of a bridge during the event of a ship impact with a pier is [...] Read more.
Bridges connecting islands close to the coast and crossing the sea have been attracting the attention of several researchers working in the field of train–bridge interactions. A runability analysis of a bridge during the event of a ship impact with a pier is one of the most interesting and challenging scenarios to simulate. The objective of the present paper is to study the impact on the running safety of a train crossing a sea bridge as a function of different operational factors, such as the train travelling speed, the type of impacting ship, and the impact force magnitude. Considering train–bridge interactions, a focus is also placed on wheel–rail geometrical contact profiles, considering new and worn wheel–rail profiles. This work is developed considering a representative continuous deck bridge with pier foundations located on the sea bed composed of six spans of 80 m. Time-domain simulations of trains running on the bridge during ship impact events were carried out to quantify the effect of different operating parameters on the train running safety. For this purpose, derailment and unloading coefficients, according to railway standards, were calculated from wheel–rail vertical and lateral contact forces. Maps of the safety coefficients were finally built to assess the combined effect of the impact force magnitude and train speed. The present investigation also showed that new wheel–rail contact geometrical profiles represent the most critical case compared to moderately worn wheel–rail profiles. Full article
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Figure 1

Figure 1
<p>Occurrence of peak collision forces in the examined literature [<a href="#B12-vibration-07-00016" class="html-bibr">12</a>,<a href="#B13-vibration-07-00016" class="html-bibr">13</a>,<a href="#B14-vibration-07-00016" class="html-bibr">14</a>,<a href="#B15-vibration-07-00016" class="html-bibr">15</a>,<a href="#B16-vibration-07-00016" class="html-bibr">16</a>,<a href="#B17-vibration-07-00016" class="html-bibr">17</a>,<a href="#B19-vibration-07-00016" class="html-bibr">19</a>,<a href="#B33-vibration-07-00016" class="html-bibr">33</a>,<a href="#B35-vibration-07-00016" class="html-bibr">35</a>,<a href="#B37-vibration-07-00016" class="html-bibr">37</a>,<a href="#B38-vibration-07-00016" class="html-bibr">38</a>,<a href="#B39-vibration-07-00016" class="html-bibr">39</a>,<a href="#B40-vibration-07-00016" class="html-bibr">40</a>,<a href="#B41-vibration-07-00016" class="html-bibr">41</a>,<a href="#B42-vibration-07-00016" class="html-bibr">42</a>,<a href="#B43-vibration-07-00016" class="html-bibr">43</a>,<a href="#B44-vibration-07-00016" class="html-bibr">44</a>,<a href="#B45-vibration-07-00016" class="html-bibr">45</a>,<a href="#B46-vibration-07-00016" class="html-bibr">46</a>,<a href="#B47-vibration-07-00016" class="html-bibr">47</a>,<a href="#B48-vibration-07-00016" class="html-bibr">48</a>]. Most authors focus on investigating impact in a range from 5 to 40 MN as the maximum peak force.</p> Full article ">Figure 2
<p>Occurrence of vessel mass (DWT, ton) in the examined literature [<a href="#B12-vibration-07-00016" class="html-bibr">12</a>,<a href="#B13-vibration-07-00016" class="html-bibr">13</a>,<a href="#B14-vibration-07-00016" class="html-bibr">14</a>,<a href="#B15-vibration-07-00016" class="html-bibr">15</a>,<a href="#B16-vibration-07-00016" class="html-bibr">16</a>,<a href="#B17-vibration-07-00016" class="html-bibr">17</a>,<a href="#B19-vibration-07-00016" class="html-bibr">19</a>,<a href="#B33-vibration-07-00016" class="html-bibr">33</a>,<a href="#B35-vibration-07-00016" class="html-bibr">35</a>,<a href="#B37-vibration-07-00016" class="html-bibr">37</a>,<a href="#B38-vibration-07-00016" class="html-bibr">38</a>,<a href="#B39-vibration-07-00016" class="html-bibr">39</a>,<a href="#B40-vibration-07-00016" class="html-bibr">40</a>,<a href="#B41-vibration-07-00016" class="html-bibr">41</a>,<a href="#B42-vibration-07-00016" class="html-bibr">42</a>,<a href="#B43-vibration-07-00016" class="html-bibr">43</a>,<a href="#B44-vibration-07-00016" class="html-bibr">44</a>,<a href="#B45-vibration-07-00016" class="html-bibr">45</a>,<a href="#B46-vibration-07-00016" class="html-bibr">46</a>,<a href="#B47-vibration-07-00016" class="html-bibr">47</a>,<a href="#B48-vibration-07-00016" class="html-bibr">48</a>]. Most authors focused on investigating vessels below 15,000 DWT (a vessel of this size can reach 150 m in overall length).</p> Full article ">Figure 3
<p>Impacts involving bulb vessels in the literature with a “double-peak”-shaped time force [<a href="#B37-vibration-07-00016" class="html-bibr">37</a>,<a href="#B39-vibration-07-00016" class="html-bibr">39</a>,<a href="#B42-vibration-07-00016" class="html-bibr">42</a>]. The red line represents the average curve, while the light blue region represents the distribution of force plots around the mean value curve. These impact forces are obtained from an FEM numerical experiment that models an impact between a vessel and a bridge pier.</p> Full article ">Figure 4
<p>Impact forces involving barges from the literature considering a single-peak-shaped force [<a href="#B41-vibration-07-00016" class="html-bibr">41</a>,<a href="#B44-vibration-07-00016" class="html-bibr">44</a>]. The red line represents the average curve, while the light blue region represents the scatter of force plots around their mean value curve. These impact forces are obtained from an FEM experiment that models an impact between a vessel and a bridge pier.</p> Full article ">Figure 5
<p>The time trend of the impact force due to a barge impact. This impact shows single-peak behavior [<a href="#B41-vibration-07-00016" class="html-bibr">41</a>,<a href="#B44-vibration-07-00016" class="html-bibr">44</a>]. The maximum peak force module is around 5 MN.</p> Full article ">Figure 6
<p>Bulb vessel collision force [<a href="#B39-vibration-07-00016" class="html-bibr">39</a>], rescaled, with a peak around 40 MN.</p> Full article ">Figure 7
<p>Lateral view of the unifilar FE model of the considered sea bridge. Impact occurs at pier N. 3.</p> Full article ">Figure 8
<p>Bridge deck cross-section adopted in the present analysis.</p> Full article ">Figure 9
<p>Bridge main lateral eigenfrequencies and associated mode shapes involved in the dynamical response to a vessel collision.</p> Full article ">Figure 10
<p>Track irregularity profile components computed according to [<a href="#B49-vibration-07-00016" class="html-bibr">49</a>].</p> Full article ">Figure 11
<p>Thirty-five-degree-of-freedom scheme model of a rail coach. The degrees of freedom and the connections by means of springs and dampers between the rigid bodies are highlighted in the figure.</p> Full article ">Figure 12
<p>(<b>a</b>) Wheel–rail vertical and lateral contact force conventions (on left wheel) in the case when only one point of contact is active. (<b>b</b>) Bumpstop force reported as a function of the lateral relative displacement between the car body and the bogie.</p> Full article ">Figure 13
<p>Rolling radius variation for left and right wheels as a function of the relative lateral displacement between the wheel and rail. Scenario with new profiles, with an equivalent conicity of 0.05. The right wheel corresponds to negative values of lateral displacement; the left wheel corresponds to positive ones.</p> Full article ">Figure 14
<p>Location of the possible contact point on the wheel profile (new wheel and rail profiles).</p> Full article ">Figure 15
<p>Rolling radius variation for left and right wheels as a function of the relative lateral displacement between the wheel and rail. Scenario with moderately worn profiles, with an equivalent conicity of 0.15. The right wheel corresponds to negative values of lateral displacement; the left wheel corresponds to positive ones.</p> Full article ">Figure 16
<p>Numerical time domain integration procedure. The red box identifies the <span class="html-italic">m-th</span> iteration within the <span class="html-italic">i-th</span> time step. The blue box indicates the first approximation of state vectors at the beginning of the <span class="html-italic">i-th</span> time step. <math display="inline"><semantics> <msub> <mi>N</mi> <mi>k</mi> </msub> </semantics></math> refers to the normal contact forces and <math display="inline"><semantics> <msub> <mi>F</mi> <mrow> <mi>l</mi> <mi>k</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>F</mi> <mrow> <mi>t</mi> <mi>k</mi> </mrow> </msub> </semantics></math> stand for the longitudinal and tangential contact forces in the local contact plane for the <span class="html-italic">k-th</span> wheel.</p> Full article ">Figure 17
<p>Displacements and accelerations in the y direction at the impacted pier in the case of a barge impact, scaled to 40 MN, and relative spectra.</p> Full article ">Figure 18
<p>Displacements and accelerations in the y direction at the deck level in the case of a barge impact, scaled at 40 MN, and relative spectra.</p> Full article ">Figure 19
<p>Displacements and accelerations in the y direction at the affected pier in the case of bulb vessel impact, scaled at 40 MN, and relative spectra.</p> Full article ">Figure 20
<p>Displacements and accelerations in the y direction at the deck level in the case of bulb vessel impact, scaled at 40 MN, and relative spectra.</p> Full article ">Figure 21
<p>Schematic representation of the procedure followed to determine the presented coefficients maps.</p> Full article ">Figure 22
<p>Vertical (Q) and lateral (Y) contact forces for wheel set N. 18 of the adopted train in the case of a barge impact with a 40 MN peak value and a travelling speed of 150 km/h.</p> Full article ">Figure 23
<p>Derailment and unloading coefficients plotted as a function of the wheel position for wheel set N. 18 in the case of a barge impact with a 40 MN peak value and a travelling speed of 150 km/h.</p> Full article ">Figure 24
<p>Train running coefficient comparison for each wheel set. The train speed is 150 km/h and the barge impact force is 40 MN.</p> Full article ">Figure 25
<p>Distribution of running safety coefficients for the double-deck train in the case of a barge impact. Safety coefficients associated with the new wheel–rail profile are reported on the left (derailment: top and unloading: bottom). The analogous distributions related to the moderately worn profile are illustrated on the right.</p> Full article ">Figure 26
<p>Distribution of running safety coefficients for the double-deck train in the case of a bulb vessel impact. Safety coefficients associated with the new wheel–rail profile are reported on the left (derailment: top and unloading: bottom). The analogous distributions related to the moderately worn profile are illustrated on the right.</p> Full article ">
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