Abstract In this paper, we present a statement of the axisymmetric problem on steady-state oscillations of an inhomogeneous elastic cylinder on the basis of the general relations of the linear theory of elasticity. The material parameters and density are considered to be variable along the radial coordinate. The oscillations are caused by a distributed load applied to the outer part of the cylinder boundary. We reduce the direct problem on determination of the radial and longitudinal displacement components to the numerical solution of a number of canonical systems of differential equations with variable coefficients. On the basis of the solution obtained, we carry out the computational experiments to analyze the influence of the variable Lame parameters on the displacement field components, the stress tensor components, the amplitude-frequency characteristics and the values of resonant frequencies.

中文翻译：

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材料不均匀性对功能梯度空心圆柱体特性的影响

摘要 在本文中，我们基于线性弹性理论的一般关系，提出了关于非均匀弹性圆柱稳态振荡的轴对称问题的陈述。材料参数和密度被认为沿径向坐标是可变的。振动是由施加到圆柱边界外部的分布载荷引起的。我们将确定径向和纵向位移分量的直接问题简化为许多具有可变系数的微分方程正则系统的数值解。在得到的解的基础上，我们进行了计算实验，分析了变 Lame 参数对位移场分量、应力张量分量、