Free Vibration of MDOF Systems with Nonperiodically Time-Varying Mass

Abstract

This paper deals with the free vibration response of MDOF mass-spring systems with time-variable mass and constant stiffness. To show the necessity of this study, a review on the related published articles is presented. After formulating the governing initial value problem which is a coupled system of differential equations with variable coefficients, the differential transform method (DTM) is employed to obtain an analytical solution. The proposed solutions are verified against exact results available in the literature. It is demonstrated that the effect of time-variable mass is equivalent to viscous damping. This viscous damping can be positive or negative depending on the sign of the mass change rate. This role is thoroughly investigated via numerical examples.