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.

中文翻译：

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自身波在厚度可变的粘弹性圆柱板中的传播

 抽象的

本文考虑了自然波在可变厚度的粘弹性圆柱板中的传播问题。制定了可变厚度粘弹性圆柱板中波传播问题的数学公式、求解技术和算法。为了推导壳方程，使用了可能位移的原理（在基尔霍夫-洛夫假设的框架内）。利用变分方程和物理方程，得到由八个微分方程组成的系统。经过一些变换后，针对八个常微分方程组构造了关于复参数的谱边值问题，其形式为复函数。获得了圆柱形面板的色散关系，获得了数值结果并进行了分析。可以确定，在楔形圆柱形板的情况下，对于每种模式，随着波数的增加，存在极限传播速度，其幅度与零楔形板中法向波的相应速度一致曲率。