Steady Vibration of Flexible Circular Plate on an Elastic Half Space

The steady vibration of a flexible circular plate with finite rigidity resting on an elastic half space and subjected to harmonic vertical loads on the surface of the plate is studied in the present paper. The contact between the plate and the half space is assumed to be frictionless. Three types of load are considered: 1. the load uniformly distributed over the entire surface of the plate, 2. the load uniformly distributed over a ring zone of the surface of the plate, 3. the concentrated load applied at the center of the plate. By expanding the distribution of the contact stress between the plate and the half space into a series of the Jacobi polynomials, the problem is reduced to solve a system of simultaneous algebraic equations. The numerical results show that: when the rigidity of the plate is rat her large, the plate behaves like a rigid one, on the other hand, when the flexibility of the plate is rather large, the dynamic behavior of the plate is dependent of the type of the applied load.