Abstract—

Exact solution of axisymmetric wave propagation problem in radially and functionally graded circular cylinder made from combination of isotropic and transversely isotropic materials is obtained. This solution is based on exact relationships derived by C. Chree and exact continuity and boundary conditions formulated for the problem with arbitrary number of concentric circular layers. The solutions are obtained for dilatational and shear waves. Frequency spectra of travelling and evanescent waves are plotted for dilatational modes of vibration of two- and three-layered cylinders. Phase velocities are calculated and plotted for the travelling dilatational waves. Peculiarities of wave propagation in the functionally graded cylinders are discussed.

中文翻译：

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具有各向同性和横向各向同性层的功能级圆柱中的轴对称波传播

摘要-

获得了由各向同性和横向各向同性材料组合制成的径向和功能梯度圆柱中轴对称波传播问题的精确解。该解决方案基于 C. Chree 导出的精确关系以及为具有任意数量同心圆层的问题制定的精确连续性和边界条件。得到了膨胀波和剪切波的解。绘制了两层和三层圆柱体的膨胀振动模式的行波和渐逝波的频谱。计算并绘制膨胀波的相速度。讨论了功能梯度圆柱中波传播的特性。