Nonlinear flexural waves in fluid–filled elastic channels

Finite Element Approximations of Nonlinear Elastic Waves

In this paper we study finite element methods for a class of problems of nonlinear elastodynamics. We discretize the equations in space using Galerkin methods. For the temporal discretization, the construction of our schemes is based on rational approximations of cosx and ex . We analyze semidiscrete as well as secondand fourth-order accurate in time fully discrete methods for the approximation...

Degenerate weakly nonlinear elastic plane waves

Weakly nonlinear plane waves are considered in hyperelastic crystals. Evolution equations are derived at a quadratically nonlinear level for the amplitudes of quasi-longitudinal and quasi-transverse waves propagating in arbitrary anisotropic media. The form of the equations obtained depends upon the direction of propagation relative to the crystal axes. A single equation is found for all propag...

Interactions of Nonlinear Waves in Fluid-Filled Elastic Tubes

In this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincaré-Lighthill-Kuo) perturbation method. The results show that up to O(k3), where k is the wave number, the head-on collision of two soli...

Nonlinear Bulk Elastic Waves in Layered Solid Wave Guides

During the last decade we have performed theoretical investigations and successful experimental research demonstrating the existence and main properties of bulk strain solitary waves in nonlinearly elastic solid wave guides. Following the topic we present preliminary results on strain soliton propagation in layered wave guides made of PMMA. The obvious physical relevance of data on strain solit...

Nonlinear waves and wave scattering in layered elastic waveguides