On the propagation of solitary waves in Mindlin-type microstructured solids

Abstract

The Mindlin-Engelbrecht-Pastrone model is applied to simulating 1D wave propagation in microstructured solids. The model takes into account the nonlinearity in micro-and macroscale. Numerical solutions are found for the full system of equations (FSE) and the hierarchical equation (HE). The latter is derived from the FSE by making use of the slaving principle. Analysis of results demonstrates good agreement between the solutions of the FSE and HE in the considered domain of parameters. For numerical integration the pseudospectral method is used.

Periodic Waves in Microstructured Solids and Inverse Problems

“…Existence of solitary waves in the one-dimensional case was proved both for the Boussinesq-type approximation and an original Mindlin's coupled system [12,14]. Numerical simulations [2,17,21] and physical observations [18,19] support the theoretical results. Solitary waves can be used to reconstruct material parameters [8,12].…”

“…Rigorous mathematical proof of the stability is a complicated task, 612 I. Sertakov and J. Janno because the system (2.1) is not integrable. The stability can be seen from numerical simulations [17,21,22]. Moreover, physical solitary waves are observed in some microstructured materials [18,19].…”