Stability analysis of transverse vibrations of rectangular plates under periodic passage of moving masses

In this study, stability of transverse vibrations of a simply supported rectangular thin plate under periodic passage of equally-spaced moving masses, by considering all components of the mass inertia in the analysis, is examined. The periodical traverse of masses across the plate results to a linear time-periodic problem. Using Galerkin procedure, the partial differential equation of transverse vibration is transformed to a set of ordinary differential equations. In this study, The Floquet theory is implemented as a numerical method to obtain stable and unstable zones of parameters plane. Applying the strained parameters method as a semi-analytical method, not only certifies the stable and unstable zones resulted by Floquet theory but also clarify the coexistence phenomenon for plate-moving mass system. Numerical simulations of the plate mid-span displacement show the validity of the analytical results obtained by two methods.