A fast estimation of the frequency property of the microelectromechanical system oscillator

Abstract

A nonlinear oscillator with zero initial conditions is considered, which makes some effective methods, for example, the variational iteration method and the homotopy perturbation method, invalid. To solve the bottleneck, this paper suggests a simple transform to convert the problem into a traditional case so that He’s frequency formulation can be effectively used to solve its approximate solution. An microelectromechanical system (MEMS) oscillator is used as example to show the solution process, and a good result is obtained.

An Efficient Analytical Approach for the Periodicity of Nano/Microelectromechanical Systems’ Oscillators

“…We depict the deflection of microbeam y obtained from LVIM (solid red lines) (equation ( 26)) with time t for four sets of parameter values (B, N, V, β) in the left side column of Figure 1 with the same yield by EBM (solid black lines) (equation (28)) and also obtained numerically by utilizing RK4 (solid blue line).…”

“…In the past decades, several techniques have been proposed to get the approximate analytic solution of N/ MEMS problems such as the homotopy perturbation method (HPM), higher-order HPM [8], Taylor series [9], energy balance technique [10], spreading residual harmonic balance method [11], higher-order Hamiltonian method [12], Adomian decomposition method (ADM) [13], Li-He modified HPM [14], modified ADM [15], variational approach [16], Galerkin decomposition method [17], and so on. It is also noted that, besides these methods, there are various analytical techniques for getting the approximate solution to the nonlinear equations, for example, the He-Laplace method [18], global residual harmonic balance method [19], integral transform-based methods [20][21][22], max-min approach [23], frequency-amplitude formulation method [24], Hamiltonian approach [25], and others [26][27][28][29]. Moreover, there have been several review articles that have appeared on the analytical methods for oscillatory problems during the past decade [30][31][32].…”

A Simple Frequency Formulation for the Tangent Oscillator

“…The fast development of nanotechnology and material science have led to skyrocketing interest in MEMS systems for the last decade [30][31][32]. We consider the following MEMS oscillator [33]…”