Computation of propagating and non-propagating guided modes in nonuniformly stressed plates using spectral methods

This paper presents a numerical approach based on spectral methods for the computation of guided ultrasonic wave modes (i.e., Lamb and shear horizontal) in nonuniformly stressed plates. In particular, anisotropic elastic plates subjected to a normal stress profile, which varies nonuniformly over their thickness, are considered. The proposed approach computes the modeshapes and the full three-dimensional dispersion spectrum (i.e., real frequency, complex wavenumber). It therefore includes both propagating (real wavenumber) and non-propagating (complex wavenumber) modes. Furthermore, an approach for robustly post-processing the dispersion spectra in order to compute the group velocity of propagating modes is presented, which is based on a spectral quadrature method. Numerical results are presented for two case studies: (1) a bending profile in a fiber-reinforced graphite/epoxy plate, and (2) an exponential profile in a silver plate. The results show the computational efficiency (i.e., spectral convergence) of the proposed method compared to other existing approaches such as the sublayering and finite element methods. (C) 2018 Acoustical Society of America.