Dynamic Analysis of Multilayers Based MEMS Resonators

Ouakad, Hassen M.; Alofi, Abdulrahman; Nayfeh, Ali H.

doi:10.1155/2017/1262650

Cited by 7 publications

(7 citation statements)

References 22 publications

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“…Perturbation methods are applied to obtain the modulation equations that govern the amplitude and phase response of the resonator. Examples of these studies can be found in microbeams [107,166,217,[261][262][263][264][265][266][267][268][269][270][271][272][273][274][275][276][277][278][279], torsional mirrors [280,281], self-excited resonators [282][283][284][285], PZT based MEMS models [286][287][288], MEMS filters [171], MEMS arch resonators [169,289], carbon Nanotubes [290], and coupled oscillators [291]. The influence of secondary-resonance excitations on MEMS has been also studied.…”

Section: Nonlinear Response Of Mems Resonators Using Perturbation Methodsmentioning

confidence: 99%

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Hajjaj

Jaber

Ilyas

et al. 2020

International Journal of Non-Linear Mechanics

117

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Micro and nanoelectromechanical systems M/NEMS have been extensively investigated and exploited in the past few decades for various applications and for probing fundamental physical phenomena. Understanding the linear and nonlinear dynamical behaviors of the movable structures in these systems is crucial for their successful implementation in various novel technologies and to meet the long list of new sophisticated requirements. This paper presents a review for some of the recent topics pertaining to the dynamical behaviors, linear and nonlinear, of M/NEMS resonating structures. First, an overview is presented of the various used dynamical approaches to enhance the sensitivity of resonators for sensing applications. Then a summary is presented of the recent works on the linear and nonlinear mode coupling in M/NEMS resonator. Next, recent research is reviewed on coupled M/NEMS resonators, mechanically and electrically, leading to collective behaviors like mode localization. The final part of the paper discusses analytical approaches that have been developed to better understand and investigate the dynamical behavior of M/NEMS resonators focusing on the perturbation method the multiple time scales.

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Section: Nonlinear Response Of Mems Resonators Using Perturbation Methodsmentioning

confidence: 99%

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Hajjaj

Jaber

Ilyas

et al. 2020

International Journal of Non-Linear Mechanics

117

View full text Add to dashboard Cite

show abstract

“…An excellent match is noticed between the MTS solution and the numerical solution of the truncated Eq. (31). The frequency response curves of Fig.…”

Section: Resultsmentioning

confidence: 99%

“…To understand the nonlinear dynamical behavior of MEMS/NEMS resonators, it is important to develop analytical models that predict the resonator's behavior under different excitation conditions. Commonly, to treat the complex parallel-plate electrostatic forcing term in the equation of motion, the forcing term is expanded in Taylor series, where some significant terms are retained and higher-order terms are dropped [19,21,24,[31][32][33][34]. This is done in order to obtain a simpler equation to carry out further analysis such as bifurcation studies, stability analysis, and analytical solutions using perturbation techniques.…”

Section: Introductionmentioning

confidence: 99%

On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators

Ilyas

Alfosail

Younis

2019

Journal of Computational and Nonlinear Dynamics

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We investigate modeling the dynamics of an electrostatically actuated resonator using the perturbation method of multiple time scales (MTS). First, we discuss two approaches to treat the nonlinear parallel-plate electrostatic force in the equation of motion and their impact on the application of MTS: expanding the force in Taylor series and multiplying both sides of the equation with the denominator of the forcing term. Considering a spring–mass–damper system excited electrostatically near primary resonance, it is concluded that, with consistent truncation of higher-order terms, both techniques yield same modulation equations. Then, we consider the problem of an electrostatically actuated resonator under simultaneous superharmonic and primary resonance excitation and derive a comprehensive analytical solution using MTS. The results of the analytical solution are compared against the numerical results obtained by long-time integration of the equation of motion. It is demonstrated that along with the direct excitation components at the excitation frequency and twice of that, higher-order parametric terms should also be included. Finally, the contributions of primary and superharmonic resonance toward the overall response of the resonator are examined.

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“…With the rapid development and extensive application of micro-/nano-technology [3], the material micro-deformation is also common in micro-structures and even nano-structures and devices because of the complexity of external loadings in such as micro-/nano-electromechanical systems, micro-switches, micro-resonators, micro-sensors, and microoscillators [4][5][6][7][8]. For beams with a macroscopic length, the classical mechanics of materials and elasticity theory are enough to characterize and explain the mechanical behaviors [9,10].…”

Section: Introductionmentioning

confidence: 99%

On Nonlocal Vertical and Horizontal Bending of a Micro-Beam

Zhu

Chen

Zhao

et al. 2022

Mathematical Problems in Engineering

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The vertical and horizontal bending of micro-beams subjected to axial compressive and transverse concentrated loadings is a common lateral deformation in micro-/nano-engineering that plays a significant role in the design and optimization of micro-/nano-devices. The present study aims to investigate it using the nonlocal theory. For this purpose, the simplified mathematical model is developed, and the nonlocal differential constitutive equation is applied. Since the mechanical properties of micro-beams are different from those of macro-beams, the non-classical nonlocal bending moment is introduced to improve the classical bending formulation in order to adapt to the vertical and horizontal bending of micro-beams. The effects of the external load, external size, structural stiffness, and internal characteristic scale on the vertical and horizontal bending deformation including the midpoint deflection and critical compression are presented. The present analytical model and results are validated by the finite element method. It is shown that the critical compression decreases with increasing the internal characteristic scale. Moreover, the midpoint deflection varies remarkably with respect to the axial and transverse loadings, structural stiffness, internal characteristic scale, and external size. An obvious nonlocal scale effect is found, in which the internal characteristic scale cannot be neglected compared with the external size. Besides, a threshold value of the structural stiffness is determined, and the connotation of the nonlocal interaction requires that the structural stiffness shall not be lower than that threshold. A mutual restriction between structural stiffness and external loadings is observed in the vertical and horizontal bending. In particular, it is further proved that the classical continuum mechanics can not be used in micro-/nano-scaled mechanics through a strange phenomenon that is contrary to mechanical common sense in the calculation example. The study is expected to be beneficial to the design and application of micro-beams subjected to the vertical and horizontal bending.

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Dynamic Analysis of Multilayers Based MEMS Resonators

Cited by 7 publications

References 22 publications

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators

On Nonlocal Vertical and Horizontal Bending of a Micro-Beam

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