Exact Solutions for Free Vibration of Single-Degree-of-Freedom Systems with Nonperiodically Varying Parameters

Abstract

An analysis of free vibration of single-degree-of-freedom (SDoF) systems with nonperiodically varying parameters, such as variable mass and stiffness, is presented and discussed in this paper The vari ations, relative to time, of mass and stiffness are expressed by the selection of suitable expressions such as power functions and exponential functions, and the general governing differential equation for free vi bration of SDoF systems with nonperiodically varying parameters is established. The exact solutions for free vibration of such time-varying systems are derived. The obtained solutions demonstrate that free vibra tion of several undamped systems with nonperiodically varying parameters cannot be induced by an initial disturbance.