Geometrical acoustics of Lamb waves

In the present work, an overview of the developments of the geometrical acoustics (GA) theory of Lamb waves in plates of variable thickness is given, based mainly on the original results of the present author. The main attention is paid to the lowest order Lamb modes in plates of variable thickness, i.e. flexural and quasi-longitudinal plate waves. It is shown that the GA approach is an ideal tool to describe propagation of ultrasonic Lamb waves in complex plate-like and wedge-like structures. In particular, it is demonstrated that the developed GA theory involving both lowest order Lamb modes can be used for theoretical description of the classical problem of Rayleigh surface wave reflection from the tip of an elastic wedge of arbitrary angle, both at normal and at oblique incidence. The GA approach operating with flexural waves alone can be used for the development of the theory of localised waves propagating along sharp edges of different wedge-like structures. Another important application of GA is the development of the theory of ‘acoustic black holes’ for flexural waves that can absorb almost all of the incident wave energy. The obtained theoretical results are illustrated by recent experiments.