Study on Internal Resonance Existence Condition of Coupled RLC Circuit and Microbeam System

摘要

In order to study on internal resonance conditions of coupled RLC circuit and microbeam system, a mathematical model of coupled RLC circuit and microbeam system is established according to the Lagrange-Maxwell equation. By means of Galerkin's method the multiple modals vibration equations are obtained, and the necessary condition of the internal resonance is given. Two kinds of internal resonance are studied, including 2:1 type internal resonance and combined internal resonance. Theory analysis and numerical calculation results show that the double modals system does not satisfy the frequency condition under a certain parameters, and for three modals system that suits the frequency condition but does not have suitable coupled between modals. So the system could not occur the above two internal resonances.