A new exact approach for analyzing free vibration of SDOF systems with nonperiodically time varying parameters

A new exact approach for analyzing free vibration of single degree of freedom (SDOF) systems with nonperiodically time varying parameters is presented in this paper. The function for describing the variation of mass of a SDQF system with time is an arbitrary continuous real-valued function, and the variation of stiffness with time is expressed as a functional relation with the variation of mass and vice versa. Using appropriate functional transformation, the governing differential equations for free vibration of SDOF systems with nonperiodically time varying parameters are reduced to Bessel's equations or ordinary differential equations with constant coefficients for several cases, and the corresponding exact analytical solutions are thus obtained. A numerical example shows that the results obtained by the derived exact approach are in good agreement with those calculated by numerical methods, illustrating that the proposed approach is an efficient and exact method.