Infinitesimal harmonic wave propagation in a homogeneously pre-strained idealised fibre-reinforced layer

Abstract

An investigation of harmonic wave propagation in an idealised fibre-reinforced layer is carried out in respect of the most general appropriate strain energy function and for propagation along a non-principal direction. The dispersion relation, giving phase speed as an implicit function of wave number, associated with incremental traction free boundary conditions is derived and decomposed into flexural and extensional motions. Some conditions for the existence of surface waves are derived, such a wave speed being the high wave number limit of both fundamental modes. As regards the harmonics, two distinct cases are observed numerically. For both cases asymptotic high wave number expansions are derived which offer an excellent approximation to the numerical solution in the moderate and high wave number region.