Pseudo analytical solution to time periodic stiffness systems  

作　　者：王延忠 周元子 

机构地区：[1]School of Mechanical Engineering and Automation,Beihang University

出　　处：《Chinese Physics B》2011年第4期97-102,共6页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 50875009);the Defense Industrial Technology Development Program of China (Grant No. B0620060424);the Aviation Science Foundation of China (Grant No. 20090451009)

摘　　要：An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudoclosed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudoclosed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.

关 键 词：parametric excitation time periodic stiffness STABILITY RESPONSE 

分 类 号：O322[理学—一般力学与力学基础]