Forced vibrations of single-degree-of-freedom systems with nonperiodically time-varying parameters

A new exact approach for forced vibration analysis of single-degree-of-freedom (SDOF) systems with nonperiodically time-varying parameters (mass and stiffness) is presented. In this paper, the variations of mass and stiffness, relative to time, are described by the selection of suitable expressions such as power functions and exponential functions. More general cases, such as the variation of mass is described by an arbitrary continuous real-valued function and the variation of stiffness is expressed as a functional relation with the variation of mass and vice versa, are also considered in this study. Using appropriate functional transformation, the governing differential equations for vibrations of SDOF systems with nonperiodically time-varying parameters are reduced to Bessel's equations or other solvable equations for several important cases. Thus, classes of exact solutions for the free and forced vibrations of SDOF systems with arbitrarily time-varying parameters (mass and stiffness) are obtained. Numerical examples show that the proposed procedure is a simple, efficient, and exact method.