具有分数和二次物理非线性并在环形壳内间隙中含有流体的同轴壳中的孤立应变波

IF 0.8 4区 地球科学 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC Radiophysics and Quantum Electronics Pub Date : 2024-09-30 DOI:10.1007/s11141-024-10333-8
L. I. Mogilevich, E. V. Popova
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引用次数: 0

摘要

我们研究了在环形壳间隙中含有粘性不可压缩流体的同轴壳中的纵向非线性孤应变波。我们考虑了壳体材料具有分数和二次非线性的情况。我们定义了所考虑的环形通道的水弹性问题,并使用扰动法对其进行了渐近分析,从而得到了一个由两个演化方程组成的系统,该系统概括了 Schamel-Korteweg-de Vries 方程。在没有流体影响的情况下,该系统分解为两个独立的方程,它们都有一个精确的孤子解。利用新获得的有限差分方案(类似于热方程的 Crank-Nicolson 方案)对同轴壳中孤子波的演变进行了数值研究。差分方案与在每个壳体中指定相同速度和振幅的孤子波的精确特定解进行了验证。结果表明,在波速的线性近似值(即声速)上发现的非线性附加值加快了孤波的速度,使其成为超音速波。此外,数值实验表明,在外壳中激发的孤波在一段时间内保持其速度和振幅,并发生弹性相互作用,即这些波是孤子。
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Solitary Strain Waves in Coaxial Shells with Fractional and Quadratic Physical Nonlinearity and with a Fluid Contained in the Annular Intershell Gap

We study the longitudinal nonlinear solitary strain waves in coaxial shells containing a viscous incompressible fluid in the annular intershell gap. The case is considered where the shell material has fractional and quadratic nonlinearity. We define the hydroelasticity problem for the annular channel under consideration and analyze it asymptotically using the perturbation method, which allows us to obtain a system of two evolution equations that generalize the Schamel–Korteweg–de Vries equations. Without the effect of the fluid, the system decomposes into two separate equations, which have an exact soliton solution. The evolution of soliton waves in coaxial shells is studied numerically with the newly obtained finite-difference scheme similar to the Crank–Nicolson scheme for the heat equation. The difference scheme is verified with the exact particular solution found for the case where a solitary wave of the same velocity and amplitude is specified in each of the shells. It is determined that the found nonlinear addition to the linear approximation for wave velocities, i.e., to the velocity of sound, speeds up the solitary waves, and they become supersonic. Moreover, the numerical experiments show that the solitary waves excited in the shells maintain their speeds and amplitudes over time and interact elastically, i.e., these waves are solitons.

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来源期刊
Radiophysics and Quantum Electronics
Radiophysics and Quantum Electronics ENGINEERING, ELECTRICAL & ELECTRONIC-PHYSICS, APPLIED
CiteScore
1.10
自引率
12.50%
发文量
60
审稿时长
6-12 weeks
期刊介绍: Radiophysics and Quantum Electronics contains the most recent and best Russian research on topics such as: Radio astronomy; Plasma astrophysics; Ionospheric, atmospheric and oceanic physics; Radiowave propagation; Quantum radiophysics; Pphysics of oscillations and waves; Physics of plasmas; Statistical radiophysics; Electrodynamics; Vacuum and plasma electronics; Acoustics; Solid-state electronics. Radiophysics and Quantum Electronics is a translation of the Russian journal Izvestiya VUZ. Radiofizika, published by the Radiophysical Research Institute and N.I. Lobachevsky State University at Nizhnii Novgorod, Russia. The Russian volume-year is published in English beginning in April. All articles are peer-reviewed.
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