Exact Periodic Solutions for the Forced Oscillations of a Symmetric Nonlinear System with “Set-up Springs”

Abstract

This paper presents the exact periodic solutions for the forced oscillation of a symmetric nonlinear system with “set-up springs”. There exist many kinds of solutions, the “harmonic” solution, the subharmonic solution of odd order and the subharmonic solution of even order of equi-interval type and the “harmonic” and the even order subharmonic solution of non-equi-interval type. By “equi-interval” is meant that the time interval in which the solutions take positive or negative values in a cycle is a half of the fundamental period of the solution. The stability of the periodic solutions is investigated exactly with the aid of the Tsypkin's method used for the stability problems of relay control systems.