求解周期性分段线性系统动态响应的高效数值方法

Abstract

An efficient method based on the parametric variational principle (PVP) was proposed for computing the dynamic responses of periodic piecewise linear systems with multiple gap-activated springs. Through description of gap-activated springs with the PVP, the complex nonlinear dynamic problem was transformed to a standard linear complementary problem. This method can avoid iterations and updating the stiffness matrix in the computing process and can accurately determine the states of the gap-activated springs. Based on the periodicity of the system and the precise integration method (PIM), an efficient numerical time-integration method was developed to obtain the dynamic responses of the system. This method indicates that there are a large number of identical elements and zero elements in the matrix exponents of a periodic structure, and saves computation load and computer storage by avoiding repeated calculation and storage of these elements. Numerical results validate the proposed method. The dynamic behaviors of a 5-DOF piecewise linear system under harmonic excitations were analyzed, including the stable periodic motion, the quasi-periodic motion and the chaotic motion. In comparison with the Runge-Kutta method, the proposed method has satisfactory correctness and efficiency.