Abstract In this study, a 2-D infinite flexible waveguide is considered. The waveguide carries a weakly nonlinear acoustic fluid. It is bounded on one side by a weakly nonlinear flexible membrane and the other side is rigid. The infinite waveguide is driven at the origin by a piston oscillating at a single frequency. However, we focus only on the positive side of the piston. As the coupled waves propagate in the membrane and the fluid, the modal interactions lead to resonances and beats which form the main focus of this work. A regular perturbation method is used to derive the linear and the quasilinear order equations which are then solved. At the linear order, the primary wavenumbers are solved for and the modes are found to be non-orthogonal because of the flexible membrane. Only the propagating waves are included in the analysis. Both self-mode and cross-mode interactions of the planar and the non-planar modes are considered. The novelty of this work lies in obtaining conditions and the closed form solutions for the resonances and beats along the spatial coordinate. It is found that the self-mode interactions lead to beats only. And in the self-mode interactions, the coupled planar mode plays an important role. On the other hand, the cross-mode interactions can lead to either resonances or beats.

中文翻译：

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流体填充柔性波导中的非线性声音和结构相互作用

摘要 在本研究中，考虑了二维无限柔性波导。波导承载弱非线性声学流体。它的一侧以弱非线性柔性膜为界，另一侧是刚性的。无限波导在原点由以单一频率振荡的活塞驱动。然而，我们只关注活塞的积极方面。当耦合波在膜和流体中传播时，模态相互作用导致共振和节拍，这构成了这项工作的主要焦点。使用常规微扰方法导出线性和拟线性阶方程，然后求解。在线性阶次上，主波数被求解，并且由于柔性膜，发现模式是非正交的。分析中仅包括传播波。考虑了平面和非平面模式的自模和交叉模相互作用。这项工作的新颖之处在于获得条件和沿空间坐标的共振和节拍的封闭形式解。发现自我模式交互仅导致节拍。而在自模相互作用中，耦合平面模起着重要作用。另一方面，交叉模式相互作用可能导致共振或节拍。