Qs. Li et al., Exact solutions for free vibration of single-degree-of-freedom systems with nonperiodically varying parameters, J VIB CONTR, 6(3), 2000, pp. 449-462
An analysis of free vibration of single-degree-of-freedom (SDoF) systems wi
th nonperiodically varying parameters, such as variable mass and stiffness,
is presented and discussed in this paper. The variations, relative to time
, of mass and stiffness are expressed by the selection of suitable expressi
ons such as power functions and exponential functions, and the general gove
rning differential equation for free vibration of SDoF systems with nonperi
odically varying parameters is established. The exact solutions for free vi
bration of such time-varying systems are derived. The obtained solutions de
monstrate that free vibration of several undamped systems with nonperiodica
lly varying parameters cannot be induced by an initial disturbance.