Strain solitary waves in an elastic rod embedded in another elastic external medium with sliding

Abstract

The propagation of nonlinear elastic longitudinal strain solitary waves (i.e., strain solitons) in a cylindrical rod being in sliding contact with an external elastic medium is considered. The waves have phase velocity in an interval, determined by the elastic properties of the external medium. Furthermore, it is shown that relative to the free rod case the external medium may alter the type of strain soliton. The theory developed can formally be used to estimate the surface-tension-like effects resulting from imperfections of the rod's lateral surface. Finally, from the results obtained an approach is suggested for the possible experimental determination of the Murnaghan third-order isotropic elastic moduli.