Abstract—

The axisymmetric wave propagation is investigated in coaxially layered isotropic functionally graded cylinders with different mass and stiffness properties of the layers. Exact solutions of the governing equations of the wave propagation in the cylinders exist only for isotropic, transversely isotropic and piezoelectric transversely isotropic cylinders. In the case of the functionally graded cylinders exact solutions are not known. The authors developed a method of exact solution of the problem, which is based on matching of continuity and boundary conditions on junctions of the layers. The continuity and boundary conditions are formulated in terms of exact solutions for displacements and stresses in the layers obtained in Bessel functions. The spectral diagrams of the dispersion curves of frequencies versus wave numbers are plotted for both propagating and evanescent waves and graphs of the phase and group velocities are obtained from these diagrams.

中文翻译：

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各向同性同心层功能梯度圆柱中的轴对称波传播

摘要-

在具有不同质量和刚度层的同轴分层各向同性功能梯度圆柱中研究轴对称波的传播。仅对于各向同性，横向各向同性和压电横向各向同性的圆柱，才存在圆柱中波传播的控制方程的精确解。在功能梯度气缸的情况下，确切的解决方案是未知的。作者开发了一种精确解决该问题的方法，该方法基于连续性和各层交界处的边界条件的匹配。连续性和边界条件是根据在Bessel函数中获得的层中位移和应力的精确解制定的。