Effects of the electrode positions on the dynamical behaviour of electrostatically actuated MEMS resonators

2011 ◽  
Author(s):  
M. Pustan ◽  
S. Paquay ◽  
V. Rochus ◽  
J - C. Golinval
Keyword(s):  
Dynamical Behaviour ◽  
Electrostatically Actuated ◽  
Mems Resonators

ROM of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Second Order ◽  
Voltage Response ◽  
Order Model ◽  
Reduced Order ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Method Effects ◽  
Ground Plate

This paper deals with the voltage-amplitude response (or voltage response) of superharmonic resonance of second order of MEMS resonator sensors under electrostatic actuation. The system consists of a MEMS flexible cantilever above a parallel ground plate. The AC frequency of actuation is near one fourth the natural frequency. The voltage response of the superharmonic resonance of second order of the structure is investigated using the Reduced Order Model (ROM) method. Effects of voltage and damping voltage response are reported.

Electrostatically Actuated Coupled MEMS Resonators

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Nonlinear Response ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
System Structure ◽  
Lagrange Equations ◽  
Electrostatically Actuated ◽  
Beam System ◽  
Mems Resonators ◽  
The Mathematical Model ◽  
Steady State Solutions

This paper deals with the nonlinear response of an electrostatically actuated cantilever beam system composed of two micro beam resonators near natural frequency. The mathematical model of the system is obtained using Lagrange equations. The equations of motion are nondimensionalized and then the method of multiple scales is used to find steady state solutions. Both AC and DC actuation voltages of the first beam are considered, while the influence on the system of DC on the second beam is explored. Graphical representations of the influence of the detuning parameters are provided for a typical micro beam system structure.

An Analytical Study for Nonlinear Free and Forced Vibration of Electrostatically Actuated MEMS Resonators

2019 ◽  
Vol 19 (07) ◽  
pp. 1950072 ◽  
Author(s):  
S. K. Lai ◽  
X. Yang ◽  
C. Wang ◽  
W. J. Liu
Keyword(s):  
Free Vibration ◽  
Lower Order ◽  
Forced Vibration ◽  
Analytical Approximation ◽  
Beam Model ◽  
Decomposition Approach ◽  
Dc Voltage ◽  
Electrostatically Actuated ◽  
Mems Resonators ◽  
Resonance Response

This work aims to construct accurate and simple lower-order analytical approximation solutions for the free and forced vibration of electrostatically actuated micro-electro-mechanical system (MEMS) resonators, in which geometrical and material nonlinearities are induced by the mid-plane stretching, dynamic pull-in characteristics, electrostatic forces and other intrinsic properties. Due to the complexity of nonlinear MEMS systems, the quest of exact closed-form solutions for these problems is hardly obtained for system design and analysis, in particular for harmonically forced nonlinear systems. To examine the simplicity and effectiveness of the present analytical solutions, two illustrative cases are taken into consideration. First, the free vibration of a doubly clamped microbeam suspended on an electrode due to a suddenly applied DC voltage is considered. Based on the Euler–Bernoulli beam theory and the von Karman type nonlinear kinematics, the dynamic motion of the microbeam is further discretized by the Galerkin method to an autonomous system with general nonlinearity, which can be solved analytically by using the Newton harmonic balance method. In addition to large-amplitude free vibration, the primary resonance response of a doubly clamped microbeam driven by two symmetric electrodes is also investigated, in which the microbeam is actuated by a bias DC voltage and a harmonic AC voltage. Following the same decomposition approach, the governing equation of a harmonically forced beam model can be transformed to a nonautonomous system with odd nonlinearity only. Then, lower-order analytical approximation solutions are derived to analyze the steady-state resonance response of such a problem under a combination of various DC and AC voltage effects. Finally, the analytical approximation results of both cases are validated, and they are in good agreement with those obtained by the standard Runge–Kutta method.

Influence of Timestep and Mesh Sizes on Numerical Simulations of Boundary Value Problem Model of Electrostatically Actuated MEMS Resonators

2019 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Boundary Value Problem ◽  
Numerical Simulations ◽  
Multiple Scales ◽  
Boundary Value ◽  
Mesh Size ◽  
Problem Solver ◽  
Time Step ◽  
Problem Model ◽  
Electrostatically Actuated ◽  
Mems Resonators

Abstract This paper deals with the effects of mesh size and time step on the numerical simulations using bvp4c, a Matlab Boundary Value Problem solver, on the time response of electrostatically actuated MEMS resonators. These results are compared to the reduced order model as well as the method of multiple scales to test how accurate these results are at lower amplitudes. The refinement of mesh size leads to more accurate results to a certain extent, as it eventually reaches a convergence. It should be said that the larger the mesh size, the longer the calculations take. A similar result occurs with timestep size. The smaller the timestep the more accurate the results. However, the CPU time increases significantly. However, beyond a certain timestep, any smaller time step would not yield any noticeable differences. Thus it can be said convergence has been reached.

Simultaneous Resonance of Soft AC Doubly Actuated MEMS Resonators

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Natural Frequency ◽  
Phase Difference ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
The Other ◽  
Voltage Amplitude ◽  
Amplitude Response ◽  
Electrostatically Actuated ◽  
Mems Resonators ◽  
Voltage Phase

This paper deals with electrostatically actuated microelectromechanical (MEMS) cantilever resonators under soft AC double actuation. The cantilever is between two parallel ground plates. The two AC frequencies are one near half natural frequency, and the other near natural frequency. There is a phase difference between the two voltages. The system undergoes a simultaneous resonance. The voltage-amplitude response is investigated. The effects of the second voltage, phase difference between voltages, and frequency on the response are reported. The method of multiple scales is used in this paper.

Boundary Value Problem Method to Investigate Superharmonic Resonance of MEMS Resonators

2017 ◽  
Author(s):  
Julio Beatriz ◽  
Martin Botello ◽  
Christian Reyes ◽  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Equation Of Motion ◽  
The Other ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Amplitude Frequency Response ◽  
Problem Method ◽  
Mems Resonators

This paper deals with two different methods to analyze the amplitude frequency response of an electrostatically actuated micro resonator. The methods used in this paper are the method of multiple scales, which is an analytical method with one mode of vibration. The other method is based on system of odes which is derived using the partial differential equation of motion, as well as the boundary conditions. This system is then solved using a built in matlab function known as BVP4C. Results are then shown comparing the two methods, under a variety of parameters, including the influence of damping, voltage, and fringe.

Nonlinear Vibration of Electrostatically Actuated MEMS Resonators Under Parametric and External Excitations

2007 ◽  
Author(s):  
Wen-Ming Zhang ◽  
Guang Meng ◽  
Di Chen
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Squeeze Film ◽  
Electrostatically Actuated ◽  
Squeeze Film Damping ◽  
Mems Resonators ◽  
Nonlinear Dynamic Characteristics ◽  
Dynamical Parameters ◽  
Parametric And External Excitations ◽  
Significant Attention

Electrostatically actuated resonant MEMS (Micro-electromechanical Systems) have gotten significant attention due to their geometric simplicity and broad applicability. In this paper, analyses and simulations for the dynamics of electrostatically actuated MEM structures under parametric and external excitations are presented. The presented model and methodology enable simulation of the dynamics of the electrostatic MEM structure undergoing small motions. The numerical results showing the effects of varying the applied voltages and the squeeze film damping on the resonant frequencies and nonlinear dynamic characteristics are given in detail. Resonant frequency and peak amplitude are examined for variation of the dynamical parameters involved. It is demonstrated that the system goes through a complex nonlinear oscillation as the system parameters change. This investigation provides an understanding of the nonlinear dynamic characteristics of electrostatically actuated resonant MEMS.

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