Longitudinal Waves in Two Coaxial Elastic Shells with Hard Cubic Nonlinearity and Filled with a Viscous Incompressible Fluid

Abstract

This article investigates the influence of fluid motion on the amplitude and velocity of longitudinal deformation waves in physically nonlinear coaxial cylindrical elastic shells. The shells contain a viscous incompressible fluid as between them, as in the inner one. The model of deformation waves (used to transmit the information) is studied by using the numerical method. This work is carried out by using the difference scheme similar to the Crank-Nicholson one. The numerical experiment showed that in the absence of the fluid in the inner shell the velocity and amplitude in the shells do not change. The movement of the waves takes place in the positive direction. This means that the waves’ velocity is supersonic. It is equivalent to the behavior of the exact solutions. Therefore, the difference scheme and the system of generalized modified Korteweg-de Vries equations are adequate. The inertia of the fluid motion in the inner shell leads to a decrease in the strain wave velocity, while the influence of the fluid viscosity in the inner shell leads to a decrease in the wave amplitudes.