Some boundary effects in continuum mechanics

• Main Author: Wickham, G. R.
• Published: University of Surrey 1970
• Subjects: 530.15
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.477193

This thesis is concerned with the estimation of the effects of an external boundary on some dynamical system of continuum mechanics which have previously been analysed for infinite media. The problems considered are:- (i) The forced torsional oscillations of a rigid spheroidal inclusion in a bounded axisymmetric elastic solid. (ii) The diffraction of torsional stress waves travelling along the axis of an infinite elastic cylinder by a) a fixed rigid inclusion and b) a penny shaped crack. (iii) The diffraction of harmonic sound waves in a circular tube by a) a soft spheroidal obstacle and b) a rigid disc. (iv) The steady swirling flow of an inviscid fluid past a rigid spheroidal body in a coaxial tube (v) The forced torsional oscillations of a) a rigid sphere and b) a rigid disc in an axisymmetric container of viscous fluid. These are particular examples of a general class of boundary value problems for the reduced wave equations which may be formulated by means of Green's theorem and appropriate Green's functions as Fredholm integral equations of the first kind. By perturbing on the static solution low frequency" approximations for quantities of physical interest exhibiting explicitly the first order effects of the external boundaries are obtained. The advantage of this procedure is that it may be used in a large variety of situations where the geometry of the problem prohibits the use of exact processes such as the method of separation of variables. Integral equation formulations may also facilitate the use of a direct boundary perturbation on the infinite medium solution; this technique is used here in a few particular examples.