Reduced-order modelling of wave propagation in an elastic layer of constant curvature and thickness

This paper is concerned with reduced-order modelling of wave propagation in an elastic layer of constant curvature and thickness by means of the generalised Galerkin method with Legendre polynomials used as coordinate functions. A new family of polynomial approximations to the dispersion relation and corresponding approximations to the field variables are obtained. These approximations have high accuracy, particularly in resolving the surface waves which are dominant features of the solution. The convergence rate is assessed by alternative accuracy measures and shown to be exponentially fast while the order of polynomials increases at a slow and regular rate. Detailed analysis of displacements and stresses in (frequency, wavenumber) space is performed. This novel modelling should facilitate studies of mode conversion around bends, where short waves are involved, for example in soft materials.