Strain solitary waves in a thin-walled waveguide

Abstract

A mathematical model is proposed to describe bulk longitudinal waves in a nonlinearly elastic thin-walled cylindrical shell. The equation of motion for the longitudinal displacement is derived. In case of the homogeneous shell, this equation is reduced to the doubly dispersive equation for the linear longitudinal strain component and provides a solitary wave solution. Results of the first experimental observation of the bulk strain soliton in a duct-like shell are presented, and both the wave amplitude and velocity are estimated.