Abstract

Flexural waves are a prominent source of sound radiation in structural acoustics. A good understanding of such waves is paramount to the design of solid structures in order to minimise sound emissions. It is not yet fully understood how small inhomogeneities in solid structures affect the propagation of flexural waves.

The problem considered is of a thin elastic plate with a vertical crack acting as the inhomogeneity. With the assumption that the thickness of the plate is much smaller than the wavelength of the flexural waves, matched asymptotic expansions must be deployed in order to obtain the reflection and transmission coefficients arising from the crack.

The talk will focus on the inner problem, which turns out to be able to be formulated as a Wiener–Hopf problem. One aspect that distinguishes this particular problem from acoustic problems is that the governing equation is the fourth-order biharmonic equation for the Airy stress function, rather than the usual second-order Helmholtz equation. This introduces further complexity by dint of additional boundary conditions being required for a full solution.