Nonlinear acoustodiagnostics of viscoelastic media

Abstract

One-dimensional finite longitudinal pulses propagating according to the Voigt. Maxwell, standard, and Volterra-Rabotnov hereditary type linear and nonlinear mathematical models are considered. For the linear case the exact and asymptotic solutions are derived with the aid of Laplace integral transforms. Further, making use of an iterative method, asymptotic solutions are obtained which take into consideration weak nonlinear effects. The distortion of the finite pulse's form due to viscosity and nonlinearity of the medium is analysed. Conclusions are made about how experimental data on this distortion might be used for solving the inverse problem of finding the proper mathematical model of the given nonlinear viscoelastic medium and the physical constants which describe it.