Abstract This paper presents a theoretical study on the modelling and active control of bending waves propagating in an orthotropic rectangular panel. The main objectives are to clarify the characteristics of the wave dynamics of an orthotropic rectangular panel and to propose the feedforward control of wave propagation based on a transfer matrix method. As a result of the numerical investigation of the wave dynamics, it is found that there are two types of cut-on frequency in the orthotropic rectangular panel, and the type of bending waves are categorised into progressive, evanescent, and amplitude-varying progressive waves. Next, after the reflected wave absorbing control (RWAC) and the transmitted wave eliminating control (TWEC) laws are derived, numerical simulations on an active wave control system are performed. It is clarified that if the number of control forces is same as that of target mode groups, the RWAC enables the inactivation of vibration modes, and the TWEC enables the vibration-free state in the orthotropic rectangular panel. Moreover, it is concluded that if the number of control forces is lower than that of target mode group, the optimal position of the control force is around the nodal line of the non-targeted mode group which is closer to the disturbance force.

中文翻译：

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基于传递矩阵法的正交各向异性矩形面板波传播建模与前馈控制

摘要 本文对正交各向异性矩形面板中传播的弯曲波的建模和主动控制进行了理论研究。主要目的是阐明正交各向异性矩形面板的波动力学特性，并提出基于传递矩阵方法的波传播前馈控制。通过波动力学数值研究发现正交各向异性矩形面板的截止频率有两种类型，弯曲波的类型分为渐进波、渐逝波和变幅渐进波. 接着，在推导出反射波吸收控制（RWAC）和透射波消除控制（TWEC）规律后，对主动波控制系统进行数值模拟。明确了如果控制力的数量与目标模态组的数量相同，则RWAC使振动模态失活，TWEC使正交各向异性矩形面板中的无振动状态成为可能。此外，得出结论，如果控制力的数量小于目标模式组的数量，则控制力的最佳位置在非目标模式组的节点线附近，该节点更接近扰动力。