Dynamic Response of Elastic Plates on Viscoelastic Half Space

Abstract

The time‐harmonic vertical vibratios of an elastic annular plate resting in smooth contact with a homogeneous isotropic viscoelastic half space is considered. The plate is subjected to a vertical distributed loading, or it may be excited by specified displacements or stress resultants applied along the plate edges. The response of the plate is goverried by classical thin‐plate theory and its vertical displacement is represented by an admissible function containing a set of generalized coordinates. A representation for contact stresses is obtained through the solution of a flexibility equation based on an exact displacement Green's function of the half space. The equation of motion of the plate in terms of generalized coordinates are established through the application of Lagrange's equation of motion. The plate edge boundary conditions are incorporated into the plate Lagrangian function as constraint terms through a set of Lagrange multipliers. Selected numerical results for displacement and contact stresses of annular elastic plates are presented.