ABSTRACT This study investigates the small scale effect on the nonlinear static and dynamic respo... more ABSTRACT This study investigates the small scale effect on the nonlinear static and dynamic response of a capacitive nanoactuator subjected to a DC voltage. The nanoactuator is modeled as a Euler-Bernoulli beam cantilever beam and beam clamped at its both ends. The model accounts for residual stresses, initial deflection, the von Kármán nonlinear strains, and the electrostatic forcing. The intermolecular forces, such as the Casimir and von der Waals forces, are also included in the model. Hamilton’s principle is used to derive the governing equations and boundary conditions for the nonlinear Euler–Bernoulli beam with Eringen’s nonlocal elasticity model. The differential quadrature method (DQM) is used to solve the governing equations. First, the static response to an applied DC voltage is determined to investigate the influence of scale effect on the maximum stable deflection and pull-in voltage of the device. Next, the dynamic response is investigated by examining the small scale effect on the natural frequencies of the system.
In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the con... more In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differenti...
The modeling and dynamics of microbeam-based electrostatic microactuators are the focal points of... more The modeling and dynamics of microbeam-based electrostatic microactuators are the focal points of this book. In order to analyze the static, transient, and steady-state behaviors of a microactuator, a reduced order models is used by discretizing the space and time derivatives using the Differential Quadrature and the Finite Difference Methods, respectively. The obtained models are convergent, numerically stable, and do not suffer from stiffness and sensitivity to initial conditions. The microactuator behavior near primary and secondary resonances is deeply investigated thanks to the derived model. Results show that superharmonic and subharmonic resonances of the first mode can lead to dynamic pull-in. Increasing the amplitude of the AC voltage was found to erode the basin of attraction of bounded motions with fractal tongues incursions. This leads to high sensitivity of the microactuator response to initial conditions. Modeling and simulation of variable-geometry microactuators was ...
This study investigates the use of dynamic pull-in instability to actuate a capacitive microswitc... more This study investigates the use of dynamic pull-in instability to actuate a capacitive microswitch. Using a reducedorder model based on the Differential Quadrature Method, which fully incorporate the electrostatic force nonlinearities, we solve for static, transient and limit-cycle solutions. We show that using only nine grid points give relatively accurate results when compared to those obtained using ANSYS. Then we examine the dynamic behavior of the MEMS switch under different electrical actuation waveforms and obtain results indicating that subsequent reduction can be obtained in actuation voltage and switching time.
In this paper, a computational model for large amplitude vibrations of a parametrically excited c... more In this paper, a computational model for large amplitude vibrations of a parametrically excited carbon nanotube (CNT) is developed. The continuous model includes geometric and electrostatic nonlinearities. The Galerkin discretization is used to transform the nonlinear partial differential equation to a finite degrees of freedom system which is numerically solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). The influence of higher modes on the nonlinear dynamics of the considered resonator is investigated in order to retain the number of modes which will be used by the HBM+ANM procedure. It is shown that at least two modes are required in order to predict accurately the CNT frequency responses.
ABSTRACT This study investigates the small scale effect on the nonlinear static and dynamic respo... more ABSTRACT This study investigates the small scale effect on the nonlinear static and dynamic response of a capacitive nanoactuator subjected to a DC voltage. The nanoactuator is modeled as a Euler-Bernoulli beam cantilever beam and beam clamped at its both ends. The model accounts for residual stresses, initial deflection, the von Kármán nonlinear strains, and the electrostatic forcing. The intermolecular forces, such as the Casimir and von der Waals forces, are also included in the model. Hamilton’s principle is used to derive the governing equations and boundary conditions for the nonlinear Euler–Bernoulli beam with Eringen’s nonlocal elasticity model. The differential quadrature method (DQM) is used to solve the governing equations. First, the static response to an applied DC voltage is determined to investigate the influence of scale effect on the maximum stable deflection and pull-in voltage of the device. Next, the dynamic response is investigated by examining the small scale effect on the natural frequencies of the system.
In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the con... more In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differenti...
The modeling and dynamics of microbeam-based electrostatic microactuators are the focal points of... more The modeling and dynamics of microbeam-based electrostatic microactuators are the focal points of this book. In order to analyze the static, transient, and steady-state behaviors of a microactuator, a reduced order models is used by discretizing the space and time derivatives using the Differential Quadrature and the Finite Difference Methods, respectively. The obtained models are convergent, numerically stable, and do not suffer from stiffness and sensitivity to initial conditions. The microactuator behavior near primary and secondary resonances is deeply investigated thanks to the derived model. Results show that superharmonic and subharmonic resonances of the first mode can lead to dynamic pull-in. Increasing the amplitude of the AC voltage was found to erode the basin of attraction of bounded motions with fractal tongues incursions. This leads to high sensitivity of the microactuator response to initial conditions. Modeling and simulation of variable-geometry microactuators was ...
This study investigates the use of dynamic pull-in instability to actuate a capacitive microswitc... more This study investigates the use of dynamic pull-in instability to actuate a capacitive microswitch. Using a reducedorder model based on the Differential Quadrature Method, which fully incorporate the electrostatic force nonlinearities, we solve for static, transient and limit-cycle solutions. We show that using only nine grid points give relatively accurate results when compared to those obtained using ANSYS. Then we examine the dynamic behavior of the MEMS switch under different electrical actuation waveforms and obtain results indicating that subsequent reduction can be obtained in actuation voltage and switching time.
In this paper, a computational model for large amplitude vibrations of a parametrically excited c... more In this paper, a computational model for large amplitude vibrations of a parametrically excited carbon nanotube (CNT) is developed. The continuous model includes geometric and electrostatic nonlinearities. The Galerkin discretization is used to transform the nonlinear partial differential equation to a finite degrees of freedom system which is numerically solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). The influence of higher modes on the nonlinear dynamics of the considered resonator is investigated in order to retain the number of modes which will be used by the HBM+ANM procedure. It is shown that at least two modes are required in order to predict accurately the CNT frequency responses.
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