非线性粘弹性波导中的慢衰减应变孤子
Slowly decaying strain solitons in nonlinear viscoelastic waveguides
AI总结：
针对非线性粘弹性材料杆中纵向应变波建模问题，提出含延迟算子耗散的阻尼Boussinesq型方程，推导出慢衰减应变孤子解，验证了其与三维模拟的一致性，强调三阶弹性常数频率依赖性的重要性。
摘要：
本文致力于研究由非线性粘弹性材料构成的杆中纵向应变波的建模，该材料的特征是二阶和三阶弹性常数具有频率依赖性。我们证明，此类材料中的长波可通过含阻尼的Boussinesq型方程有效描述纵向应变，该方程通过延迟算子引入耗散机制。利用近可积系统中孤波解的现有理论，我们推导出该方程的一个慢衰减应变孤子解。结果表明，推导得到的孤子特性与全三维模拟结果吻合良好。我们还证明了在描述应变孤子时，考虑三阶弹性常数的频率依赖性具有重要意义。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
