Slowly decaying strain solitons in nonlinear viscoelastic waveguides

IF 2.8 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2025-02-14 DOI:10.1016/j.ijnonlinmec.2025.105043

F.E. Garbuzov, Y.M. Beltukov

引用次数: 0

Abstract

This paper is devoted to the modeling of longitudinal strain waves in a rod composed of a nonlinear viscoelastic material characterized by frequency-dependent second- and third-order elastic constants. We demonstrate that long waves in such a material can be effectively described by a damped Boussinesq-type equation for the longitudinal strain, incorporating dissipation through retarded operators. Using the existing theory of solitary wave solutions in nearly integrable systems, we derive a slowly-decaying strain soliton solution to this equation. The derived soliton characteristics are shown to be in a good agreement with results from full 3D simulations. We demonstrate the importance of taking into account the frequency dependence of third-order elastic constants for the description of strain solitons.

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非线性粘弹性波导中的慢衰减应变孤子

本文研究了以频率相关的二阶和三阶弹性常数为特征的非线性粘弹性材料杆的纵向应变波模型。我们证明了这种材料中的长波可以用纵向应变的阻尼boussinesq型方程有效地描述，其中包含了通过延迟算子的耗散。利用现有的近可积系统的孤立波解理论，导出了该方程的慢衰减应变孤子解。推导出的孤子特性与全三维模拟结果很好地吻合。我们证明了考虑三阶弹性常数的频率依赖性对应变孤子描述的重要性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.