Viscous damping

Stime dello smorzamento nelle strutture civili pongono un serio problema nella dinamica strutturale. Vi sono serie difficoltà di fornire misure accurate di smorzamento a partire da test dinamici. In presenza di azioni sismiche, gli spostamenti e le sollecitazioni in una struttura sono influenzati in maniera rilevante dalla sua capacità dissipativa e quindi nasce l’esigenza di una valutazione accurata dei coefficienti di smorzamento per una progettazione ottimale degli elementi strutturali. Il presente lavoro ha analizzato e studiato il comportamento dello smorzamento viscoso proporzionale in presenza di danno nei sistemi strutturali. Le conseguenze derivanti dalla modellazione dei vari modelli delle forze dissipative adottati sono state ricavate mediante la realizzazione di algoritmi in ambiente Matlab applicate su di un caso studio: telaio in c.a. deformabile a cinque livelli (5 gradi di libertà traslazionali). E’ stato dimostrato che utilizzando un modello di smorzamento proporzionale alla rigidezza tangente e con i coefficienti di proporzionalità basati sulle frequenze aggiornate non vengono prodotte forze dissipative artificiali a differenza invece di modelli basati su rigidezza iniziale e coefficienti di proporzionalità basati sulle frequenze non aggiornate. Va sottolineato che, soprattutto nelle strutture aventi parti strutturali a elevata rigidezza, l’utilizzo di un modello di smorzamento rispetto ad un altro comporta una progettazione in molti casi differente. Allo scopo di ridurre i sovra smorzamenti artificiali, è stato realizzato uno studio della variazione della funzione smorzamento modale rispetto ad un valore prestabilito in fase progettuale. Selezionando una quantità desiderata di smorzamento e un range di frequenze tali da coprire i modi di vibrare di interesse, viene computata la deviazione dell’effettivo smorzamento rispetto al valore mirato prima dell’analisi. In definitiva, è possibile controllare la variabile coefficiente di smorzamento modale e ridurre i sovra smorzamenti artificiali che si sviluppano durante l’analisi con modelli di smorzamento proporzionali alla rigidezza iniziale e rigidezza tangente.

Construction technology advancements in the last couple of decades have led to the use of lightweight and high-strength materials in structural systems. Although longer spans and lighter materials result in floor systems with less mass, stiffness, and damping , the trend toward a paperless office decreases damping and the amount of live load on the floors even more. Consequently, structures have become more vulnerable to annoying vibrations, and vibration serviceability has become an area of serviceability concern. For vibration serviceability calculations, the damping value of the structural systems is a critical parameter. Damping in structures has proved to be dependent on the amplitude of the applied force on the structure. This condition is referred to as nonlinear damping, or amplitude-dependent damping. Although damping is constant at low and high amplitudes, for in-between amplitudes, the damping value increases with the levels of excitation amplitude. For wind and earthquake excitations, the amplitude-dependent characteristics of damping have been studied extensively in the literature. For floor vibration serviceability applications, even though the nonlinear behavior of damping has been accepted to exist and mentioned in some publications, it is not closely looked at or discussed in detail. The floor vibration serviceability calculations are very sensitive to damping values, but vibration serviceability researchers and practicing engineers are often uncomfortable with assigning a specific number as a damping ratio for a specific mode because of the inconsistency of damping values obtained from different methods. This paper presents a closer look at the amplitude-dependent damping in vibration serviceability and focuses on a laboratory footbridge with experimental and analytical studies. The laboratory footbridge was studied extensively with static and dynamic tests. Three-dimensional finite-element (FE) models were developed, updated, and fine-tuned for two bottom chord extension configurations for both static and dynamic tests. The amplitude-dependent damping behavior of the laboratory footbridge is shown for different amplitudes of sinusoidal excitations. The amplitude-dependent damping ratio values obtained from effective mass calculations proved to be correct with the FE model acceleration predictions. The FE model predictions successfully matched the test results with the nonlinear characteristic introduced for modal damping. One of the most difficult tasks in vibration serv-iceability research is matching the measured acceleration responses with the FE models, and the success of this paper in matching the acceleration responses for various levels of excitations (with corresponding amplitude-dependent damping values) with the FE model is unique. Successful verification and clarification of the amplitude-dependent phenomenon and FE model matching of measured acceleration responses reinforce the confidence in the FE models in vibration serviceability research by showing that the FE models are reliable not only for natural frequency predictions but also for acceleration response predictions.

Nonlinear response history analysis, contributing to seismic performance assessment, is a constructive tool for evaluating buildings' behavior and damages due to the earthquake. Applying an accurate viscous damping model constitutes a crucial part in this regard. The seismic response and performance of two reinforced concrete moment frames considering various damping modeling techniques and nonlinear elements are investigated. Two basic approaches to consider nonlinearity are selected: distributed and concentrated plasticity, using force and displacement-based fiber elements and elements that contain two end springs and elastic parts to which zero and modified initial stiffness proportional damping are allocated respectively. Rayleigh damping with mass and four different stiffness matrices are applied in fiber elements. The results of Incremental Dynamic Analysis and loss estimation, considering performance-based earthquake engineering methodology, indicate that Rayleigh damping with mass and initial stiffness overestimates collapse capacity and underestimates performance parameters , while, the model with mass and tangent stiffness with updated proportionality terms shows the opposite trend. In concentrated plasticity models, the more flexible the springs, the more conservative the evaluation of building performance.

The damping characterization is important in making accurate predictions of the seismic response of the hybrid structures dominated by different damping mechanisms. Different damping characteristics arise from the construction of the tower with different materials: steel for the upper part; reinforced concrete for the lower main part and interaction with supporting soil. The process of modeling damping matrices and experimental verification is challenging because damping cannot be determined via static tests as mass and stiffness can be. The assumption of classical damping is not appropriate if the system to be analyzed consists of two or more parts with significantly different levels of damping. The dynamic response of structures is critically determined by the damping mechanisms, and its value is very important for the design and analysis of vibrating structures. An analytical approach that is capable of evaluating the equivalent modal damping ratio from structural components is desirable for improving seismic design. Two approaches are considered to define and investigate dynamic characteristics of a composite tower of cable-stayed bridges: The first approach makes use of a simplified approximation of two lumped masses to investigate the structure irregularity effects including damping of different material, mass ratio, frequency ratio on dynamic characteristics and modal damping. The second approach employs a detailed numerical step-by-step integration procedure.

The hysteretic behaviour of RC columns has been object of many experimental studies over the past years. However, the majority of these studies are focused on unidirectional loading. An experimental program was carried out where 24 columns were tested for different loading histories, under uniaxial and biaxial conditions. The experimental results are presented in this paper and are discussed in terms of global column behaviour, and particularly with regards to energy dissipation and damping capacity. The energy dissipation capacity of the columns was evaluated in terms of cumulative dissipated energy, comparing uniaxial and biaxial test results, and individual cycle dissipated energy. Ultimately, an equation relating the normalised dissipated energy with the displacement ductility is proposed. The equivalent viscous damping was analysed by comparing the uniaxial with biaxial test results, demonstrating the high influence of the load path in the biaxial response of RC columns. Proposals for estimating the equivalent viscous damping given by other authors are compared with the experimental results. Finally, simplified expressions are proposed to estimate equivalent viscous damping in RC columns under biaxial loading.

Seismic response of multi-storied base-isolated building on various isolation systems connected using viscous dampers to an adjacent dissimilar base-isolated or fixed-base building is investigated. The multi-storied buildings are modeled as a shear type structures with lateral degree-of-freedom at each floor, which are connected at different floor levels by the viscous dampers. Performance of this novel combination is studied by deriving the governing equations of motion and solving it in the incremental form using Newmark's step by-step method of integration. The variation of top floor absolute acceleration and bearing displacement under different real earthquake ground motions is computed to study the behavior and effectiveness of the connected systems. It is concluded that connecting the two adjacent base-isolated buildings with the viscous dampers is helpful in controlling large bearing displacement in the base-isolated structures; thereby, eliminating isolator damages arisi...

The hysteretic behaviour of RC columns has been object of many experimental studies over the past years. However, the majority of these studies are focused on unidirectional loading. An experimental program was carried out where 24 columns were tested for different loading histories, under uniaxial and biaxial conditions. The experimental results are presented in this paper and are discussed in terms of global column behaviour, and particularly with regards to energy dissipation and damping capacity. The energy ...

Performance-based optimization of energy dissipation devices in structures necessitates massive and repetitive dynamic ‎analyses. In the endurance time method known as a rather fast dynamic analysis procedure, structures are subjected to ‎intensifying dynamic excitations and their response at multiple intensity levels is estimated by a minimal number of analyses. ‎So, this method significantly reduces computational endeavors. In this paper, the endurance time method is employed to determine the optimal placement of viscous dampers in a weak structure to achieve the desired performance at various hazard levels, simultaneously. The viscous damper is one of the energy dissipation systems which can dissipate a large amount of seismic input energy to the ‎structure. To this end, hysteretic energy compatible endurance time ‎ ‎excitation functions are used and the validity of the results is investigated by comparing them with the results obtained from a suite of ground motions. To optimize the placement of the dampers, the genetic algorithm is used. The damping coefficients of the dampers are considered as design variables in the optimization procedure and determined ‎in such a way that the sum of them has a minimum value. The behavior of the weak structure before and after rehabilitation is also investigated using endurance ‎time and nonlinear time history analysis procedures in different hazard levels.‎

The influence of isolator characteristics on the seismic response of multi-story base-isolated structure is investigated. The isolated building is modeled as a shear type structure with lateral degree-of-freedom at each floor. The isolators are modeled by using two different mathematical models depicted by bi-linear hysteretic and equivalent linear elastic–viscous behaviors. The coupled differential equations of motion for the isolated system

One of the important measures to decrease the seismic forces on the structure is by damping. The basic principle of seismic modification is to modify the response of the building to permit the dissipation of vibration energy. The present study demonstrates the effect of different percentages of damping on a multistorey building with shear wall, we will get a clear idea how the damping affects on base shear, storey displacements and storey drifts. For the present study we have analyzed the building on Etabs 9.7.0, and the building is having a shear wall. The study has been carried out for the Zone V and on soft soil and for different percentages of damping as specified in IS 1893-2002.

In this paper, modal responses of the Brezina concrete arch dam, Algeria, are determined using the finite elements commercial packages ANSYS. To study the effects of the foundation soil, three 3D models have been created, the dam alone without soil, the dam-massless soil and the dam-soil with soil mass model. Moreover, a parametric study of the viscous damping, in Raleigh form, has been conducted. It is found that the natural frequencies of either undamped or damped modes obtained from the dam-soil with soil mass model are drastically lower compared to that of the dam alone model, and are markedly lower than those obtained from the dam-massless soil model. Likewise, similar comparisons have been observed for the damping quantities, in absolute values, between the three models. An in-depth review of the literature reveals that the study carried out herein constitutes several elements of originality as only very few similar work have been undertaken.

The mechanical response of a circularly driven disk in a dissipative medium is considered. We focus on the
role played by viscous friction in the spinning motion of the disk, especially on the effect called reverse rotation,
where the intrinsic and orbital rotations are antiparallel. Contrary to what happens in the frictionless case, where
steady reverse rotations are possible, we find that this dynamical behavior may exist only as a transient when
dissipation is considered. Whether or not reverse rotations in fact occur depends on the initial conditions and on
two parameters, one related to dragging, inertia, and driving, the other associated with the geometric configuration
of the system. The critical value of this geometric parameter (separating the regions where reverse rotation is
possible from those where it is forbidden) as a function of viscosity is well adjusted by a q-exponential function.

This paper deals with the dynamic analysis of primary-secondary combined systems. The problem of selecting the vibrational modes to be retained in analysis is first addressed, for the case of secondary substructures which may possess numerous low frequency modes with negligible mass, and a dynamic mode acceleration method (DyMAM) is adopted in view of the application for seismic analysis. The influence of
various approaches to build the viscous damping matrix of the primary-secondary assembly is then investigated, and a novel technique based on modal damping superposition is proposed. The results of a parametric study for a representative staircase system multi-connected to a two-dimensional multi-storey frame reveal that the DyMAM correction is capable of increasing the response accuracy with a reduced number of modes compared to the classical MAM (modal acceleration method). Furthermore, a new technique is proposed for assembling the damping matrix, which is shown to be a convenient alternative for modelling the dissipative forces in composite systems. Indeed, while mass and stiffness matrices can unambiguously be defined, various assumptions can be made for the damping matrix, inducing considerable variation in the predicted seismic response.