Dynamic Instability Analysis of Rectangular Plates under Periodic Passage of Oscillating Rigid Bodies

In this paper, the dynamic stability of a thin rectangular plate under the periodic passage of oscillating rigid bodies is studied. Each of the two ends of a rigid body is connected to a wheel through a suspension system. Using the assumed-mode method, the governing equations are derived. The periodic passing of moving objects along a straight path on the surface of the plate results in a dynamic system with periodic coefficients. The Floquet theory is employed as a numerical method to obtained stable and unstable zones of parameters plane. Considering the point moving object model, the effect of moving object modeling on the stability analysis results is also investigated. The results indicate that the stiffness and damping of the suspension system, the mass ratio of the wheels to the whole rigid body, the rigid body’s length and the moving object modeling method are very effective on domains stability and instability of the system. Numerical simulations of the plate middle point verify the accuracy of the obtained results