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Longitudinal-strain soliton focusing in a narrowing nonlinearly elastic rod

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TLDR
In this article, the evolution of a longitudinal-strain solitary wave (a soliton) was studied theoretically and in experiments in a nonlinearly elastic tapered rod with decreasing cross-section.
Abstract
The evolution of a longitudinal-strain solitary wave (a soliton) is studied theoretically and in experiments in a nonlinearly elastic tapered rod. Amplification (focusing) of the soliton is predicted and observed in the rod with decreasing cross section. An asymmetric soliton deformation when focused is observed. An approach is developed to obtain analytical relationships between longitudinal and shear nonlinear strains, and an asymptotic solution to the problem is found, accurately satisfying the boundary conditions on the lateral rod's surface. The explicit relationship is obtained for the soliton amplitude dependence upon the cross section radius' variations of the nonlinearly elastic rod. An allowed interval of soliton velocities is shown to exist that is dependent on elasticity. It was proved in experiments that the elastic strain soliton is not absorbed even at distances much greater than the typical linear dissipation length for linear waves in polystyrene.

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Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods

TL;DR: In this paper, the Navier-Bernoulli hypothesis was used to derive the KdV equation for elastic rods in the far field, which is consistent with the lateral boundary conditions.
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Asmptoticaliy Approximate Model Equations for Weakly Nonlinear Long Waves in Compressible Elastic Rods and their Comparisons with Other Simplified Model Equations

TL;DR: Weakly nonlinear long waves in a cylindrical elastic rod composed of a compressible Murnaghan material are studied in this paper, and four types of model equations describing nonlinear dispersive waves are derived, two of which can satisfy the lateral boundary conditions asymptotically.
Journal ArticleDOI

Solitary waves in an inhomogeneous rod composed of a general hyperelastic material

TL;DR: In this paper, the development of a soliton propagating along a circular rod composed of a general compressible hyperelastic material with variable cross-sections and variable material density was analyzed.
Journal ArticleDOI

Splitting induced generation of soliton trains in layered waveguides

TL;DR: In this article, the splitting induced generation of a soliton train from a single incident strain soliton in two-and three-layered elastic waveguides was reported, based on a weakly nonlinear solution for the doubly dispersive (Boussinesq type) equation with piecewise constant coefficients for the waveguide made of a piecewise isotropic nonlinearly elastic material.
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