Evanescent and propagating waves in prestretched hyperelastic plates

A detailed spectral analysis is presented for dynamic eigenfields generated by time harmonic edge perturbations applied to a semi-infinite prestrained plate. Formulation is exact within continuum elasticity theory and frequency maps are provided over a range of prestrain, material (hyperelastic) properties, boundary conditions and frequency of applied disturbance. We concentrate mainly on numerical findings for the complex wave numbers associated with evanescent waves. Asymptotic expansions, at the limit of low frequency and near cut-off frequencies are given. An appreciable depth of penetration of evanescent waves is found to characterize frequencies just below any cut-off frequency. Cut-off frequencies, independent of boundary conditions, are highly sensitive to material properties and their explicit dependence on prestrain level has been exposed. Asymptotic solutions of the frequency equations, for the propagating modes in the long wavelength region, are added to enhance and to support the numerical results. The influence of symmetric boundary conditions over the long faces (free, clamped, sliding and inextensional) on the wave behaviour is highlighted. Application of the results to non-symmetric boundary conditions is suggested. (C) 2004 Elsevier Ltd. All rights reserved.