An asymptotic analysis of the dispersion relation of a prestressed incompressible elastic plate
The interest in the wave propagation in prestressed incompressible elastic plates has been growing with the advent of fibre-reinforced composites. This paper gives an analysis of the asymptotic behaviour of the dispersion relation (i.e. an algebraic relation involving the wave speed, the wave number, and a parameter characterizing the prestress) for such structures. Some important conclusions are derived: a) the fundamental modes (both symmetric and antisymmetric) tend to the associated Rayleigh surface mode; b) while the lower modes are very sensitive to prestress changes, the higher harmonics are very little affected; c) in the linear theory (the present one being such) an instability phenomenon can appear. The last effect provides an exponential growth, so that future studies in this area have to be corrected by taking into account the inherent nonlinearity of the elastic field for finite amplitude displacements. We think the paper brings a basic contribution to the area of wave propagation in prestressed plates.
scientific article; zbMATH DE number 923807
scientific article