Strong nonlinear dynamics of MEMS and NEMS structures based on semi-analytical approaches

Sassi, Sarah Ben; Najar, Fehmi

doi:10.1016/j.cnsns.2018.01.022

Cited by 33 publications

(11 citation statements)

References 36 publications

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“…To solve the coupled fluid-structure equations, we follow Ben Sassi and Najar [31] in using a combination of Galerkin decomposition [32] and the differential quadrature method (DQM) [33]. First, we use DQM [34] to solve for the static deflection of the beam s w(x) under the polarization DC voltage.…”

Section: Solution Methodologymentioning

confidence: 99%

A square wave is the most efficient and reliable waveform for resonant actuation of micro switches

Sassi

Khater

Najar

et al. 2018

J. Micromech. Microeng.

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This paper investigates efficient actuation methods of shunt MEMS switches and other parallel-plate actuators. We start by formulating a multi-physics model of the micro switch, coupling the nonlinear Euler–Bernoulli beam theory with the nonlinear Reynolds equation to describe the structural and fluidic domains, respectively. The model takes into account fringing field effects as well as mid-plane stretching and squeeze film damping nonlinearities. Static analysis is undertaken using the differential quadrature method (DQM) to obtain the pull-in voltage, which is verified by means of the finite element model and validated experimentally. We develop a reduced order model employing the Galerkin method for the structural domain and DQM for the fluidic domain. The proposed waveforms are intended to be more suitable for integrated circuit standards. The dynamic response of the micro switch to harmonic, square and triangular waveforms are evaluated and compared experimentally and analytically. Low voltage actuation is obtained using dynamic pull-in with the proposed waveforms. In addition, global stability analysis carried out for the three signals shows advantages of employing the square signal as the actuation method in enhancing the performance of the micro switch in terms of actuation voltage, switching time, and sensitivity to initial conditions.

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Section: Solution Methodologymentioning

confidence: 99%

A square wave is the most efficient and reliable waveform for resonant actuation of micro switches

Sassi

Khater

Najar

et al. 2018

J. Micromech. Microeng.

Self Cite

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“…According to previous analyses, the convergence with DQM is obtained for a grid points number n = 13 [42,43]. The physical and geometrical properties of the arched microbeam are given in table 1.…”

Section: Static Analysismentioning

confidence: 99%

“…The first uses the differential quadrature method (DQM) to discretize the space domain and convert equations ( 16) and ( 17) into a set of ordinary differential equations (ODEs). The DQM model is used to compute the static response under a DC voltage and use the results to solve the damped eigenvalue problem and calculate the natural frequencies under the effect of the same DC voltage and the ambient pressure p a [42][43][44].…”

Section: Reduced-order Modelsmentioning

confidence: 99%

Parametric resonance of bi-directional axial loads shallow arch microresonators

Najar¹,

Ouakad²,

RAMINI³

et al. 2022

J. Micromech. Microeng.

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In this work, we investigate analytically and experimentally parametric resonances of an in-plane clamped-guided shallow arch microresonator. The arch is connected to a T-shaped moveable mass, which is sandwiched between two electrodes to electrostatically activate the device and to oﬀer bi-directional axial loads option. The device is tested under primary and secondary parametric resonances. In addition, an analytical model is presented taking into account the initial rise of the microbeam and the sliding motion at the guided side. The static and free vibration problems are solved using the Diﬀerential Quadrature Method, and the dynamic response is simulated using an assumed mode Galerkin approximation. The theoretical results of the static and dynamic behavior of the device are compared to experimental data showing good agreement. Moreover, we demonstrate the use of parametric excitation to signiﬁcantly amplify the axial motion. It is found that the second parametric resonance, corresponding to the fundamental mode of the arched microbeam, has a higher amplitude than the principal parametric case, due to the initial curvature of the beam. Thus, the proposed device can be a promising candidate for variety of sensing applications.

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“…The main reasons are that experimental techniques and MD simulations are difficult to perform and computationally costly, respectively. The majority of the size-dependent continuum models have been developed for nano/microbeams [8][9][10], nano/microshells [11] and nano/microplates [12,13] as they usually form the structural components of many NEMS-based devices [14][15][16]. Some important studies in this field are mentioned in the following.…”

Section: Introductionmentioning

confidence: 99%

Effect of flow pulsations on chaos in nanotubes using nonlocal strain gradient theory

Ghayesh

Farajpour

Farokhi

2020

Communications in Nonlinear Science and Numerical Simulation

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In this article, a chaos analysis is performed for the viscoelastic nonlinear coupled dynamics of perfectly straight nanotubes conveying pulsatile fluid for the first time. A size-dependent advanced elasticity model is developed with consideration of stress nonlocality as well as the gradient of strain components. After presenting the nonlinear motion equations using Hamilton's approach, they are numerically solved via application of a time-integration technique for a system with a large number of degrees of freedom. Chaos analysis is performed for the nanotube at both subcritical and supercritical flow regimes. Both mean fluid velocity and the amplitude of velocity pulsation are varied as the bifurcation parameter. The proposed size-dependent continuum modelling and numerical results would be useful in order to tailor the system parameters to avoid chaos in nanoelectromechanical devices using fluid-conveying nanotubes.

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Strong nonlinear dynamics of MEMS and NEMS structures based on semi-analytical approaches

Cited by 33 publications

References 36 publications

A square wave is the most efficient and reliable waveform for resonant actuation of micro switches

A square wave is the most efficient and reliable waveform for resonant actuation of micro switches

Parametric resonance of bi-directional axial loads shallow arch microresonators

Effect of flow pulsations on chaos in nanotubes using nonlocal strain gradient theory

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