Subharmonic Solutions of Governed MEMS System Subjected to Parametric and External Excitations
A. M. El-Naggar
Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt.
K. M. Khalil
Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt.
A. M. Omran *
Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt.
*Author to whom correspondence should be addressed.
Abstract
Subharmonic periodic solutions of order (1/2 ,1/4) to a weakly second order ordinary differential equation which governed the motion of a micro-dynamical system are studied analytically. Applying the method of multiple scales, we derive the modulation equation in the amplitude and the phase of each type of periodic solutions. Determine the steady-state solutions (fixed-points of the modulation equation). Obtained the frequency-response equation (The relation between the amplitude and the detuning parameter and other parameter in the differential equation). Stability analysis of the steady-state solutions is given. Numerical study of the frequency-response equation are carried out. The results are presented in a group of Figures in which solid (dashed) curves indicated stable (unstable) preiodic solutions.
Keywords: MEMS, Multiple scales method, parametric excitation and external excitation