Solution schemes for hyperbolic wave problems, with application to the mechanics of brain injury

Partial differential equations that arise in the study of mechanical waves are studied through analytical and numerical techniques. A new method of finding the solution to such equations is presented. The method involves an algebraic series that provides an approximation to the inverse Laplace Transform of a solution. The partial differential equations describing the small strain deformation of a Maxwell viscoelastic cylinder are solved using a variety of techniques. An analytical solution is derived for the cases of sinusoidal boundary conditions, which is shown to be singular due to the discontinuity introduced by the boundary condition in the problem. The peak strains resulting from transient and steady state solutions to sinusoidal boundary conditions are studied through analytical and numerical techniques.