A new complete solution of the wave equations for istropic media

An isotropic material is considered in the sense of Green. A new complete solution in terms of potential functions for the wave equations is presented. The completeness is proved in view of the solution of the repeated wave equation in the isotropic media and the Boggio’s Theorem. In this paper we reduce the number of potential functions to only one, and we discuss the required conditions. As a special case, the torsionless and rotationally symmetric configuration with respect to an arbitrary axis is discussed. The limiting case of elastostatics is cited, where the solution is reduced to the Love strain function. The Lamb’s problem is solved with the new potential function. As expected , the solution is exactly equal to the one obtained by Lamb[5].

Keywords:

Potential function , Wave equation , Boggio's theorem , Lamb problem