自身波在厚度可变的粘弹性圆柱形面板中的传播

IF 0.8 Q2 MATHEMATICS
Ismoil Safarov, Bakhtiyor Nuriddinov, Zhavlon Nuriddinov
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引用次数: 0

摘要

摘要 本文研究了自然波在厚度可变的粘弹性圆柱板中的传播问题。针对厚度可变的粘弹性圆柱板中的波传播问题,提出了数学公式、求解技术和算法。为了推导壳方程,使用了可能位移原理(在基尔霍夫-洛夫假设的框架内)。利用变分方程和物理方程,得到了一个由八个微分方程组成的系统。经过一些变换后,为八个常微分方程系统构建了一个关于复参数的谱边界值问题,其形式为复变函数。得到了圆柱形面板的扩散关系、数值结果并进行了分析。结果表明,在楔形圆柱板的情况下,对于每种模式,都存在随着波数增加而增加的极限传播速度,其大小与零曲率楔形板中法线波的相应速度相吻合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Propagation of Own Waves in a Viscoelastic Cylindrical Panel of Variable Thickness

Propagation of Own Waves in a Viscoelastic Cylindrical Panel of Variable Thickness

Abstract

The paper considers the problem of propagation of natural waves in a viscoelastic cylindrical panel of variable thickness. A mathematical formulation, a solution technique and an algorithm for wave propagation problems in viscoelastic cylindrical panels of variable thickness are formulated. To derive the shell equations, the principle of possible displacements was used (within the framework of the Kirchhoff–Love hypotheses). Using the variational equation and physical equations, a system consisting of eight differential equations is obtained. After some transformations, a spectral boundary value problem on a complex parameter is constructed for a system of eight ordinary differential equations with respect to complex functions of the form. Dispersion relations for the cylindrical panel are obtained, numerical results are obtained and an analysis is made. It is established that in the case of a wedge-shaped cylindrical panel, for each mode, there are limiting propagation velocities with an increase in the wave number that coincide in magnitude with the corresponding velocities of normal waves in a wedge-shaped plate of zero curvature.

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来源期刊
CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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