Abstract The vibration characteristics of irregular elastic coupled plate systems are studied by Chebyshev-Ritz method in this paper, including dynamics and power flow control. Firstly, the accurate geometric model is established, and the coupling conditions and boundary conditions are simulated by artificial virtual springs. In order to facilitate integral operations, the irregular integral area is mapped into the regular integral area by a special coordinate transformation. Then all energy equations of the coupled system are established according to the first order shear deformation theory. The Chebyshev polynomial is used as the allowable displacement functions. Finally, the unknown coefficients in the allowable displacement functions are determined by the Rayleigh-Ritz technique. On the basis of the free vibration study, the dynamic behavior is studied by applying the external load to the system surface, including the forced response, the admittance and the power flow. While deriving the method, some modal verification experiments about coupled plate systems are designed. The innovation of the study is the establishment of the vibration analysis model of irregular elastic coupled plate systems based on the elastic theory, the coordinate transformation criterion and the two-dimensional Chebyshev-Ritz principle. The mechanism and control of energy transfers of the coupled plate system are studied by the power flow intensity analysis. The numerical results show that both the coupling condition and the boundary condition are important parameters in the vibration. This study provides some new insights into the vibration characteristics and energy transfer of the irregular elastic coupled plate system.

中文翻译：

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不规则弹性耦合板系统的动力学和潮流控制：精确建模和实验验证

摘要 本文采用Chebyshev-Ritz方法研究了不规则弹性耦合板系统的振动特性，包括动力学和潮流控制。首先建立精确的几何模型，通过人工虚拟弹簧对耦合条件和边界条件进行模拟。为了方便积分运算，不规则积分区域通过特殊的坐标变换映射到规则积分区域。然后根据一阶剪切变形理论建立耦合系统的所有能量方程。Chebyshev 多项式用作允许位移函数。最后，允许位移函数中的未知系数由 Rayleigh-Ritz 技术确定。在自由振动研究的基础上，通过将外部负载施加到系统表面来研究动态行为，包括强制响应、导纳和功率流。在推导该方法的同时，设计了耦合板系统的模态验证实验。研究的创新点是基于弹性理论、坐标变换准则和二维切比雪夫-里兹原理，建立了不规则弹性耦合板系统的振动分析模型。通过潮流强度分析研究了耦合板系统能量传递的机理和控制。数值结果表明，耦合条件和边界条件都是振动的重要参数。