Due to the performance requirements, structural discontinuities are inevitable in engineering structures. Free vibration of an elastically connected annular plate system with discontinuities has not yet been reported in the literature. In this study, an analytical method is developed for the free vibration of an annular plate system with discontinuities along its radius. The annular plates are connected continuously using an elastic layer. The coupled vibration equations of the annular plate system were decoupled into a series of uncoupled general “vibration” equations which are then transferred into a symplectic dual system. The general “vibration” state can then be analytically described in terms of waves utilizing the elastic wave theory. Using the analytical wave modes and satisfying the compatibility and boundary conditions at the discontinuities, a frequency equation can be obtained analytically. In numerical examples, the free vibrations of systems consist of two and three annular plates were investigated. The accuracy of the proposed method is verified by comparison with literature and finite element method (FEM).

中文翻译：

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不连续弹性连接环形板系统自由横向振动的解析解

工程结构由于性能要求，结构不连续性是不可避免的。具有不连续性的弹性连接环形板系统的自由振动尚未在文献中报道。在这项研究中，开发了一种分析方法，用于分析沿其半径具有不连续性的环形板系统的自由振动。环形板使用弹性层连续连接。环形板系统的耦合振动方程被解耦为一系列非耦合一般“振动”方程，然后转移到辛对偶系统中。然后可以利用弹性波理论用波来分析描述一般的“振动”状态。使用解析波模并满足不连续点处的兼容性和边界条件，可以解析地获得频率方程。在数值算例中，研究了由两个和三个环形板组成的系统的自由振动。通过与文献和有限元法（FEM）的比较，验证了该方法的准确性。