Appearance of Coexistence Phenomenon in Stability Analysis of Plate-Moving Mass System

Dynamic behavior study of elastic structures under moving loads is one of the most famous problems in different engineering fields. In this study, dynamic stability of a simply supported rectangular plate under periodic passage of moving masses is investigated using Floquet theory and strained parameters method. Considering effects of all inertia components of the moving masses, the governing partial differential equation of motion is derived. The Galerkin’s method is applied to reduce the governing partial differential equation to a set of ordinary differential equations. The periodic loading across the plate results in a time-varying equation. Considering a straight path for passage of moving masses and applying the Floquet theory and strained parameters method, the dynamic instability of the plate and coexistence phenomenon are analyzed. In addition, defining a diagonal transition path of moving masses over the plate’s surface, the significance of the coexistence phenomenon and also sensitivity of plate instability to mass transition paths are investigated. Numerical simulations validate the accuracy of both methods results.