Parametric resonance analysis of rectangular plates subjected to moving inertial loads via IHB method

This paper deals with the induced instability due to parametric resonance of rectangular plates traversed by inertial loads and lying on elastic foundations. The extended Hamilton's principle is employed to derive the partial differential equation associated with the transverse motion of the plate. Subsequently, this equation is transformed into a set of ordinary differential equations by the Galerkin method. Including vertical, centripetal and Coriolis acceleration terms related to the moving mass transition in the analysis leads to governing equations with time-varying mass, damping and stiffness coefficients. Particularly, the intermittent passage of masses along rectilinear paths, or the motion of an individual mass along an orbiting path, permits to subcategorize the problem as a parametrically excited system with periodic coefficients. By applying the incremental harmonic balance (IHB) method, the stability of the induced plate vibrations is investigated, revealing an emersion of instability tongues in the parameters plane. Semi-analytical results are provided for various boundary conditions of the plate which got verified through direct numerical simulations and other results reported in the literature.