Forced Horizontal Vibration of Rigid Disc in Transversely Isotropic Trimaterial Full-Space

Abstract

A theoretical investigation is presented for the dynamic interaction of a rigid circular disc and its surrounding space, which is a trimaterial transversely isotropic full-space, and the disc is undergoing a prescribed horizontal harmonic vibration. Because the equations of motion form a system of coupled partial differential equations in a cylindrical coordinate system, a system of two scalar potential functions are used to decouple the equations of motion. This approach results in a set of two separated partial differential equations, which may be transformed to some ordinary differential equations by using Fourier series along the angular coordinate and the Hankel integral transformations with respect to the radial coordinate in a cylindrical coordinate system. After solving the ordinary differential equations, the unknown functions are determined by satisfying relaxed boundary conditions, which themselves are transformed to a set of four coupled integral equations. These coupled integral equations are reduced to two coupled Fredholm-Volterra integral equations of the second kind, which are numerically solved in this paper. The proposed solutions are applied for a transversely isotropic half-space, and the results showed the conformation of the existing solutions.