Some Mixed Boundary-Value Problems in Elastodynamics and Acoustics.

In this thesis a variety of mixed boundary-value problems, taken from the fields of elastodynamics, magnetohydrodynamics and acoustics are investigated. The work is divided into two main parts. In each part a different method is employed to solve the integral equations governing the particular problems under consideration. Numerical results are obtained and whenever possible comparisons made with results taken from other works. Part I deals with the solution of a class of Fredholm integral equations of the second kind by means of a kernel approximation technique. Starting from a typical mixed boundary-value problem an analysis is presented in such a way as to indicate the theoretical basis of the method. The exact kernel of the integral equation is replaced by an approximate kernel, derived from a Pade approximation, which permits the solution of the equation in closed form. Numerical comparisons between exact and approximate quantities are presented. The method is applied to transient elasto-dynamic problems of the Reissner-Sagoci and Boussinesq types and to the case of a disc rotating in a conducting fluid. Finally an extension of the approximation leading to improved accuracy is discussed. The far field pattern produced by a vibrating circular piston set in an infinite, plane, non-rigid baffle is investigated in the second part of the work. An approximation to the solution of the problem, depending upon the solution of an integral equation which arises in the problem of diffraction of a normally incidented plane wave by a rigid disc, is found by following a complicated asymptotic analysis. Because of the ranges of certain parameters three sets of solutions are found. These are combined to form composite graphs of the radiation pattern function for various values of the baffle impedence