Solitary waves and their existence conditions in microstructured solids

Abstract

By taking into account the macroscale nonlinear effect, quadratic and cubic microscale nonlinear effects, and microscale dispersion effect, a new model capable to describe the longitudinal wave propagation in one-dimensional microstructured solid is established based on the Mindlin theory. Using the qualitative analysis theory in the planar dynamical systems, we have analyzed the existence conditions and geometrical characteristics of solitary waves, and proved that the faces under the influence of quadratic microscale nonlinear effect, can form an asymmetric solitary wave in the microstructured solid; and under the influence of cubic microscale nonlinear effect, they can form a symmetric solitary wave in the microstructured solid, when the medium parameters and the propagation speeds of solitary waves satisfy certain appropriate conditions. Finally, the above results are further verified using a numerical method.