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Nonlinear Vibration of the Double-Beams Assembly Subjected to A.C. Electrostatic Force

Shueei-Muh Lin1
Mechanical Engineering Department, Kun Shan University, Tainan, Taiwan 710-03, Republic of China. E-Mail: {

Computer Modeling in Engineering & Sciences 2010, 60(1), 95-114.


In this study, the mathematical model of double-beams assembly subjected to the a.c. electrostatic force is established. This is helpful for designing sensors and actuators. The boundary condition of this system is nonlinear and time-dependent. Obviously, this system is very complicated. A new solution method is here developed to derive the analytical solution. Because the a.c. electrostatic force includes the static and harmonic forces, the system is divided into the nonlinear static and dynamic subsystems. The exact static solution is presented. In the other hand, the boundary conditions of the dynamic subsystem are nonlinear and time-dependent. First, using the balanced method the system with time-dependent coefficients is transformed into one with time-independent coefficients. Further, the analytical solution of the transformed dynamic subsystem is derived. It is found that there exists great difference between the linear and nonlinear spectrums. Moreover, the effects of several geometry and material parameters on the frequency spectrums of this system are significant.


nonlinear, coupled beam, analytical solution, vibration, electrostatic force

Cite This Article

Lin, S. (2010). Nonlinear Vibration of the Double-Beams Assembly Subjected to A.C. Electrostatic Force. CMES-Computer Modeling in Engineering & Sciences, 60(1), 95–114.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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