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Z. Naturforsch. 67a, 435 – 440
(2012)
doi:10.5560/ZNA.2012-0043
Dynamic Analysis of Nonlinear Oscillator Equation Arising in Double-Sided Driven Clamped Microbeam-Based Electromechanical Resonator
1 Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2 Department of Mechanical Engineering, Quchan Branch, Islamic Azad University, Quchan, Iran
Received February 1, 2011 / published online August 2, 2012
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yasirmath@yahoo.com
In this paper, three different analytical methods have been successfully used to study a nonlinear oscillator equation arising in the microbeam-based electromechanical resonator. These methods are: variational approach, Hamiltonian approach, and amplitude-frequency formulation. The governing equation is based on the Euler–Bernoulli hypothesis and the partial differential equation (PDE) is simplified into an ordinary differential equartion (ODE) by using the Galerkin method. A frequency analysis is carried out, and the relationship between the angular frequency and the initial amplitude is obtained in closed analytical form. A comparison of the present solutions is made with the existing solutions and excellent agreement is noted.
Key words: Microelectromechanical System; Nonlinear Oscillation; Analytical Methods; Periodic Solution.