The influence of a primary stress upon the propagation of small-amplitude elastic disturbances.

This thesis considers three problems in the field of elastodynamics. The first concerns small-amplitude elastic disturbances in an infinite cylinder, a problem first investigated by Pochhammer [1] and Chree [2]. Our approach extends the results of Pochhammer and Chree by utilising a method of successive approximation through which the governing equations are solved to produce dispersion relations. The second investigation, recently considered by Eringen and Suhubi [3], is of the propagation of elastic waves in a prestressed body, with particular reference to the circular cylinder and the half-space. The governing equations are again solved via successive approximation to give new and detailed results describing the wave motion. The final investigation is of a compressible strain-energy function which is an extension of the Ko model. The model is examined in the light of various a priori inequalities, and is then used to obtain solutions to the problem of vibrations in a stressed plate. [1] POCHHAMMER, L., J. Reine Angew. Math., 81, (1876). [2] CHREE, C., Trans. Camb. Phil. Soc., 14, (1889). [3] ERINGEN, A.C. and SUHUBI, E.S., Elastodynamics, Vol. I Finite Motions, (Academic Press, New York), (1974).