Asymmetric Vibrations of a Circular Elastic Plate on an Elastic Half Space

The asymmetric problem of a vibrating circular elastic plate in frictionless contact with an elastic half space is solved by an integral equation method, where the contact stress appears as the unknown function. By a trigonometric expansion, the problem is reduced to a number of uncoupled two-dimensional problems. The radial variations of contact stresses and surface displacements are represented by polynomials, the coefficients of which are directly related by an infinite matrix that is a function of the vibration frequency. The results include a parametric study of the power input as a function of the vibration frequency of various plate stiffnesses and the normal component of the surface displacement field for simple excitation of the plate and passage of a plane Rayleigh wave.