Abstract

With the aid of a complete set of two scalar potential functions, the problem of transient wave propagation in transversely isotropic half-space, subjected to time dependent tractions applied on a finite patch at an arbitrary depth below the free surface of the half-space is investigated. With the use of the displacement–potential function relationships in a cylindrical coordinate system, the coupled equations of motion are uncoupled; resulting in two separate partial differential equations one of which is second order and the other is fourth order. These two partial differential equations are solved with the aid of both Fourier series expansion and joint Hankel–Laplace integral transforms. The solutions are also investigated in details for tractions varying with time as Heaviside step function, which may be used as a kernel in any integral based method for more complicated elastodynamic initial-boundary value problems. Moreover, some displacement Green's functions are numerically evaluated for a synthetic transversely isotropic material to graphically demonstrate the transient motion of the free surface of the half-space.