Frequency Spectra of Nonlinear Elastic Pulse-Mode Waves

Abraham Kadish, James TenCate, and Paul Johnsona

Earth and Environmental Sciences Division, Mail Stop D443, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

a) also at Université Pierre et Marie Curie, Bureau des Mécaniques, Tour 22, 4, Place Jussieu, 75252 Paris Cedex 05


The frequency spectrum of simple waves is used to derive a closed form analytical representation for the frequency spectrum of damped nonlinear pulses in elastic materials. The damping modification of simple wave theory provides an efficient numerical method for calculating propagating waveforms. The spectral representation, which is neither pulse length nor amplitude limited, is used to obtain estimates for parameters of the nonlinear state relation for a sandstone sample from published experimental data, and the results are compared with those of other theories. The method should have broad application to many solids.