Geometrical acoustics approximation for Rayleigh and Lamb waves

The present paper gives a brief review of the geometrical acoustics theory for Rayleigh and Lamb waves in inhomogeneous solids, based mainly on the original results of the present author. Initially, the propagation of Rayleigh waves along arbitrary curved surfaces is considered. The obtained results are applied to the explanation of the so-called smooth topographic waveguides for surface waves. Then, flexural waves in plates of variable thickness are considered. The results of this study are used for the development of the theory of the so-called ‘wedge acoustic waves’, i.e. guided ‘one-dimensional’ waves propagating along sharp edges of elastic wedges. Another important application of geometrical acoustics is the development of the theory of ‘acoustic black holes’ for flexural waves that can absorb almost all of the incident wave energy. Finally, the use of geometrical acoustic to describe waves in non-circular shells of arbitrary shape is considered, with applications to modelling structural vibrations of cars and aircraft.