| publication name | Sub-Harmonic Solutions of Even Order (1/2,1/4), To A Weakly Non-Linear Second Order Differential Equation Governed the Motion (MEMS) |
|---|---|
| Authors | A. M. Elnaggar, A. F. El-Bassiouny, A. M. Omran |
| year | 2015 |
| keywords | MEMS, Weakly non-linear differential equation, Multiple scales method, Stability and Parametric Excitation. |
| journal | International Journal of Basic and Applied Science, |
| volume | 3 |
| issue | Not Available |
| pages | Not Available |
| publisher | Not Available |
| Local/International | International |
| Paper Link | Not Available |
| Full paper | download |
| Supplementary materials | Not Available |
Abstract
Sub-harmonic periodic solutions of even order ( 1 2 , 1 4 ) to a weakly nonlinear second order differential equations which governed the motion of a microelectro mechanical system (MEMS) (Bandpass Filter) are investigated analytically. The method of multiple scales is used to determine the modulation equations in the amplitude and the phase, steady state solutions. The frequency-response equation and stability analysis of the steady state solutions are obtained. Numerical study of the frequency-response equations and stability equations are given for different values of the parameters. Results are plotted in group of Figures, on which solid (dashed) curves are stable (unstable) solutions. Finally discussion and conclusion are given.