The existence of surface waves in piezoelectric half-spaces and of edge waves in elastic laminated plates

• Main Author: Brookes, David William
• Published: Keele University 2005
• Subjects: 620.11897
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.425970

This thesis is concerned with determining the possibility of the existence of subsonic free surface waves in piezoelectric half-spaces, and of subsonic free edge waves in elastic laminated semi-infinite plates, where the material constants are not presumed to possess any particular special form of symmetry. By means of an introduction, standard analytical results are presented for the existence and uniqueness of surface waves and edge waves in isotropic elastic half-spaces and semi-infinite plates respectively, together with analytical expressions for the wave speeds. A re-analysis of the problem of determining the existence of surface waves in piezoelectric half-spaces is then presented. Lothe and Barnet [30] solved this problem using ideas from the Stroh formalism, whereas the work presented here arrives at the same conclusions by using different analytical methods. For the electrically open boundary condition it is shown that at most one surface wave may exist, and when the boundary condition is not electrically open then at least one and at most two surface waves may exist. A computer program was used to calculate the surface wave speeds for a variety of boundary conditions. The numerical results obtained are shown to be in agreement with the theory. Original theoretical work is then presented regarding the existence of waves propagating along the edge of an elastic laminated plate. The problem is resolved using an octet formalism, and it is shown that when a normal transonic state is present then at least one and at most two edge waves may exist. In the case where there is an exceptional transonic state, then it is possible that zero, one or two edge waves may exist. Numerical results relating to edge wave speeds are then obtained using another computer program, and are found not to conflict with the theory.