Vibrations induced by harmonic loadings applied at circular rigid plate on half-space medium

Abstract

The paper presents a systematic scheme to calculate the vibration at any specific location on a half-space medium due to harmonic vibrations of a circular rigid plate on the medium. In the scheme, the analytic solutions of 3D wave equations in cylindrical coordinates are employed. The vibration at any specific location on half-space medium is obtained analytically by a semi-infinite integration with respect to wave number k from 0 to ∞. Because of decaying nature of integrand with respect to wave number k, the numerical integration can only be performed up to a certain upper limit k u instead of ∞ without loosing accuracy. The choosing of the integration upper limit k u is dependent upon the factors of nondimensional vibration frequency and nondimensional distance between vibration source and receiving location. From the numerical results, one finds that some components of vibration on the surface may not attenuate monotonically along the distance from source. Some verification for the accuracy of the presented scheme will be made, and selected numerical results will be shown and discussed. Comments on the presented scheme will be given, and the presented scheme is proved to be effective and efficient for accurately predicting the vibrations on the surface induced by harmonic loadings applied at rigid circular plate.