On the parametric and external resonances of rectangular plates on an elastic foundation traversed by sequential masses

Elastodynamic behavior analysis of structures under moving loads is of great interest in most engineering fields. In this study, dynamic instability due to parametric and external resonances of simply supported thin rectangular plates on an elastic foundation under successive moving masses is investigated as a linear time-periodic problem. Effects of all components of moving mass inertia are considered in the analysis. The governing partial differential equation of motion is transformed to a set of ordinary differential equations using the Galerkin method. A comprehensive study of resonance conditions is carried out for two cases: (1) the masses move on a rectilinear path parallel to the longitudinal edges of the plate, and (2) a sequence of moving masses along the diagonal of the plate. Homotopy perturbation method (HPM) is employed as a semi-analytical method to obtain stable and unstable zones in a parameters space in additions to external resonance curves. In order to validate the HPM results, Floquet theory is applied to the state-space equations. A good agreement between two methods is observed. The results of this study are useful for the design of road pavements resting on foundation soil, slab-type bridges, airport pavements, and decks of ships on which aircrafts land.