Further investigation of vibration induced by harmonic loadings applied at circular rigid plate on half-space medium

Abstract

This article is the further investigation of vibration induced by harmonic loadings applied at a circular rigid plate on a half-space medium as reported by Liou (Liou, G.S., 2009. Vibrations induced by harmonic loadings applied at circular rigid plate on half-space medium. Journal of Sound and Vibration, 323, 257-269). The main purposes of this article are (1) to give the semi-analytic solution for vibration at any specific location in half-space medium; (2) to calculate the total average energy flux over one period of vibration time from the surfaces of a cylindrical cavity. The reason to evaluate the total average energy flux is that the fluctuation phenomenon of vibration amplitude along the distance from the vibration source (circular rigid plate) has been observed by Liou (2009) and can be seen from the numerical results in this article. To calculate the total average energy flux from the surfaces, piecewise linear distribution of energy flux intensity along z-direction for cylindrical surface and r-direction for bottom surface of the cylindrical cavity is assumed. The results show that the total average energy flux from the surfaces attenuates as distance from vibration source increases. This is due to the material damping in the half-space medium. The attenuation of total average energy flux is faster as the damping in the half-space medium is higher.