Shooting Method Using Analytical Solutions for a Nonlinear System with Piecewise Linear Characteristics

Abstract

A kind of shooting method is presented for determining the periodic solutions with high accuracy of piecewise linear systems with strong nonlinearities. This method is composed of analytical solution of each linear equation of motion and Newton-Raphson method. The periodic solution obtained by this method correspond to exact solution. This method is applied to preloaded compliance system, two-degree-of-freedom gear rattling system and multi-degree-of-freedom system with nonlinear dynamic absorber. The results of this method and those of the ordinary shooting method which uses Runge-Kutta-Gill method as numerical integration method are compared with each other. The results obtained are summarized as follows : This method has high cost performance, namely it converges to highly accurate periodic solution in much shorter time than the ordinary shooting method. Moreover, its time difference becomes larger with increasing the degrees of freedom of the system. The complicate higher harmonic vibration which occurs in geared system is also obtainable by this method.