An Electrostatically Actuated MEMS Arch Band-Pass Filter

Ouakad, Hassen M.

doi:10.1155/2013/819398

Cited by 34 publications

(24 citation statements)

References 26 publications

(55 reference statements)

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“…Figure 2 shows the nonlinear responses of the microbeam at the primary resonance; the following parameters are selected: f 1 ¼ 1.15 and A 0 ¼ 0.2, giving x 1 ¼ 12.3518, where x 1 is the first linear natural frequency of the transverse motion; moreover, the modal damping ratio is set to f ¼ 0.009 for all generalized coordinate throughout the numerical simulation. As seen in the figure, the system displays a hardening-type nonlinear behavior with two limit-point bifurcations at X ¼ 1.0935x 1 and X ¼ 1.0305x 1 . A comparison between subfigures (a) and (c) reveals that the longitudinal displacement is much smaller than the transverse displacement; however, this does not mean that the effect of the longitudinal displacement is negligible.…”

Section: Coupled Nonlinear Dynamical Behavior Of the Systemmentioning

confidence: 93%

“…9; the excitation frequency is set to X ¼ 0.9650x 1 . It is seen that the number of limit-point bifurcations are increased to four, due to increased amplitude of initial imperfection.…”

Section: Coupled Nonlinear Dynamical Behavior Of the Systemmentioning

confidence: 99%

“…Continuous microsystems are present in many engineering devices and micromachines [1,2], for example, in micro energy harvesters, airbag accelerometers, biosensors, biomechanical organs, microactuators, microswitches, MEMS resonators, and vibration shock sensors [3][4][5][6][7][8]; due to their widespread application, many researchers have investigated the dynamical behavior of these systems in recent years. An important issue in the theoretical modeling of microscale continuous systems is to use a continuum theory which is capable of capturing small-size effects; the dependence on size was first found out experimentally [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams

Ghayesh

Farokhi

2015

Journal of Computational and Nonlinear Dynamics

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This paper aims at analyzing the coupled nonlinear dynamical behavior of geometrically imperfect shear deformable extensible microbeams based on the third-order shear deformation and modified couple stress theories. Using Hamilton's principle and taking into account extensibility, the three nonlinear coupled continuous expressions are obtained for an initially slightly curved (i.e., a geometrically imperfect) microbeam, describing the longitudinal, transverse, and rotational motions. A high-dimensional Galerkin scheme is employed, together with an assumed-mode technique, in order to truncate the continuous system with an infinite number of degrees of freedom into a discretized model with sufficient degrees of freedom. This high-dimensional discretized model is solved by means of the pseudo-arclength continuation technique for the system at the primary resonance, and also by direct time-integration to characterize the dynamic response at a fixed forcing amplitude and frequency; stability analysis is conducted via the Floquet theory. Apart from analyzing the nonlinear resonant response, the linear natural frequencies are obtained via an eigenvalue analysis. Results are shown through frequency-response curves, force-response curves, time traces, phase-plane portraits, and fast Fourier transforms (FFTs). The effect of taking into account the length-scale parameter on the coupled nonlinear dynamic response of the system is also highlighted. Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible MicrobeamsThis paper aims at analyzing the coupled nonlinear dynamical behavior of geometrically imperfect shear deformable extensible microbeams based on the third-order shear deformation and modified couple stress theories. Using Hamilton's principle and taking into account extensibility, the three nonlinear coupled continuous expressions are obtained for an initially slightly curved (i.e., a geometrically imperfect) microbeam, describing the longitudinal, transverse, and rotational motions. A high-dimensional Galerkin scheme is employed, together with an assumed-mode technique, in order to truncate the continuous system with an infinite number of degrees of freedom into a discretized model with sufficient degrees of freedom. This high-dimensional discretized model is solved by means of the pseudo-arclength continuation technique for the system at the primary resonance, and also by direct time-integration to characterize the dynamic response at a fixed forcing amplitude and frequency; stability analysis is conducted via the Floquet theory. Apart from analyzing the nonlinear resonant response, the linear natural frequencies are obtained via an eigenvalue analysis. Results are shown through frequency-response curves, force-response curves, time traces, phase-plane portraits, and fast Fourier transforms (FFTs). The effect of taking into account the length-scale parameter on the coupled nonlinear dynamic response of the system is also highlighted.

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Section: Coupled Nonlinear Dynamical Behavior Of the Systemmentioning

confidence: 93%

“…9; the excitation frequency is set to X ¼ 0.9650x 1 . It is seen that the number of limit-point bifurcations are increased to four, due to increased amplitude of initial imperfection.…”

Section: Coupled Nonlinear Dynamical Behavior Of the Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams

Ghayesh

Farokhi

2015

Journal of Computational and Nonlinear Dynamics

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“…Microstructures [1][2][3][4][5] are widely used in many micromachines, e.g. in biosensors [1,2], microactuators, accelerometers, microresonators [1], microswitches, micro-electro-mechanical systems (MEMS) [2][3][4][5][6], vibration shock sensors, and mass flow sensors.…”

Section: Introductionmentioning

confidence: 99%

On the nonlinear resonant dynamics of Timoshenko microbeams: effects of axial load and geometric imperfection

et al. 2015

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The nonlinear size-dependent dynamics of a geometrically imperfect Timoshenko microbeam subject to an axial load is investigated numerically based on the modified couple stress theory. Increasing the compressive axial load leads to an increase in the deflection (bending) amplitude of the microbeam. A distributed harmonic excitation load in the transverse direction is then applied to the microbeam and the nonlinear dynamics over the new deflection is analyzed. More specifically, the kinetic energy of the system, the size-dependent strain potential energy, and the works due to the external excitations and damping are constructed as functions of the displacement field. These expressions are then inserted in Hamilton's principle, a variational energy technique, in order to obtain the nonlinear partial differential equations of motion. The Galerkin scheme is then applied to the resultant equations, yielding a set of second-order nonlinear ordinary differential equations. These equations are solved numerically via a direct time integration method as well as a continuation technique. Results are plotted in the form of deflectionaxial load diagrams, frequency-responses, forceresponses, time traces, phase-plane portraits, and fast Fourier transforms. The importance of taking into account small-size effects, through use of the modified couple stress theory, is highlighted.

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“…Ansari et al [38] examined the nonlinear bending and postbuckling of functionally graded Mindlin rectangular plates based on the modified couple stress theory. There have been several studies on the dynamical behavior of initially curved microbeams (MEMS microarches), for example, by Das and Batra [39], who examined the pull-in and snap-through instabilities in MEMS shallow arches under dynamic loading; Ouakad and Younis [40,41] and Ouakad [42], who analyzed the dynamic behavior of an arch resonator and its application as a band-pass filter; Mohammad and Ouakad [43], who performed a bifurcation analysis of electrostatically actuated MEMS arches; and Medina et al [44][45][46], who performed theoretical and experimental investigations on the static behavior of electrostatically actuated initially curved microbeams. However, the literature regarding the dynamical behavior of initially curved microplates is limited [15].…”

Section: Introductionmentioning

confidence: 99%

Internal Energy Transfer in Dynamical Behavior of Slightly Curved Shear Deformable Microplates

Ghayesh

Farokhi

Alici

2015

Journal of Computational and Nonlinear Dynamics

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This paper investigates the internal energy transfer and modal interactions in the dynamical behavior of slightly curved microplates. Employing the third-order shear deformation theory, the microplate model is developed taking into account geometric nonlinearities as well as the modified couple stress theory; the initial curvature is modeled by an initial imperfection in the out-of-plane direction. The in-plane displacements and inertia are retained, and the coupled out-of-plane, rotational, and in-plane motion characteristics are analyzed. Specifically, continuous models are developed for kinetic and potential energies as well as damping and external works; these are balanced and reduced via Lagrange's equations along with an assumed-mode technique. The reduced-order model is then solved numerically by means of a continuation technique; stability analysis is performed by means of the Floquet theory. The possibility of the occurrence of modal interactions and internal energy transfers is verified via a linear analysis on different natural frequencies of the system. The nonlinear resonant response of the system is obtained for the cases with internal energy transfer, and energy transfer mechanisms are analyzed; as we shall see, the presence of an initial curvature affects the system dynamics substantially. The importance of taking into account small-size effects is also shown by discovering this fact that both the linear and nonlinear internal energy transfer mechanisms are shifted substantially if this effect is ignored. This paper investigates the internal energy transfer and modal interactions in the dynamical behavior of slightly curved microplates. Employing the third-order shear deformation theory, the microplate model is developed taking into account geometric nonlinearities as well as the modified couple stress theory; the initial curvature is modeled by an initial imperfection in the out-of-plane direction. The in-plane displacements and inertia are retained, and the coupled out-of-plane, rotational, and in-plane motion characteristics are analyzed. Specifically, continuous models are developed for kinetic and potential energies as well as damping and external works; these are balanced and reduced via Lagrange's equations along with an assumed-mode technique. The reduced-order model is then solved numerically by means of a continuation technique; stability analysis is performed by means of the Floquet theory. The possibility of the occurrence of modal interactions and internal energy transfers is verified via a linear analysis on different natural frequencies of the system. The nonlinear resonant response of the system is obtained for the cases with internal energy transfer, and energy transfer mechanisms are analyzed; as we shall see, the presence of an initial curvature affects the system dynamics substantially. The importance of taking into account small-size effects is also shown by discovering this fact that both the linear and nonlinear internal energy transfer mechanisms are shifted subst...

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An Electrostatically Actuated MEMS Arch Band-Pass Filter

Cited by 34 publications

References 26 publications

Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams

Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams

On the nonlinear resonant dynamics of Timoshenko microbeams: effects of axial load and geometric imperfection

Internal Energy Transfer in Dynamical Behavior of Slightly Curved Shear Deformable Microplates

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