Periodic Solutions of the Free Vibration of a Two Degree-of-Freedom Nonlinear Spring-Mass System

Abstract

This is a fundamental analysis of periodic solutions of the free vibration of a two degree-of-freedom nonlinear spring-mass system. After transforming the differential equation under consideration into a canonical form, the relation between the initial values which yield periodic solutions and the period has been established. It has been proved that, by the perturbation method, the periodic solution and the period can actually be determined uniquely as powers of a small parameter. The condition that two masses vibrate in phase with each other has been ascertained. The calculation for a case with nonlinear terms of a cubic expression has been executed yielding the result that there holds the same relation between the amplitude and the period as in the case of a single degree-of-freedom nonlinear spring-mass system, if all of the three springs are either hard springs or soft ones.