Abstract Modal interactions are studied in a weakly nonlinear structural-acoustic waveguide with a cylindrical geometry. The infinite cylindrical waveguide is driven by a flat piston at the center. Standard nonlinear equations are used for the shell and the fluid. The perturbation method separates the nonlinear equations into a linear set and a nonlinear set. At the linear order, only propagating modes are included. Due to the flat nature of the piston, these modes are axisymmetric. These linear order modes interact due to the nonlinearity and generate higher order modes. When a certain inverse relation between phase speeds gets satisfied, spatial resonance (weak shock) occurs, i.e., the solution grows in the propagation direction. Along the same lines, when this matching does not occur, the solution acquires a spatial beating nature that oscillates along the propagation direction. The responses, i.e., resonances or beats are further categorized as self-mode and cross-mode interactions. The conditions and the closed form solutions for resonances and beats are derived. Further, the effect of the boundary flexibility on the said resonances and beats is also presented. And it is seen that the nonlinear wave propagation is significantly different between a rigid and a flexible waveguide.

中文翻译：

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弱非线性结构声圆柱波导中的有限振幅模态相互作用

摘要 研究了具有圆柱几何形状的弱非线性结构声波波导中的模态相互作用。无限圆柱波导由中心的扁平活塞驱动。标准非线性方程用于壳和流体。微扰法将非线性方程分为线性组和非线性组。在线性顺序中，仅包括传播模式。由于活塞的扁平特性，这些模式是轴对称的。由于非线性，这些线性阶模相互作用并产生更高阶的模。当相位速度之间满足一定的反比关系时，就会发生空间共振（弱激波），即解沿传播方向增长。同样，当这种匹配不发生时，该解决方案获得了沿传播方向振荡的空间跳动性质。响应，即共振或节拍被进一步分类为自模式和交叉模式相互作用。推导出共振和节拍的条件和封闭形式解。此外，还呈现了边界柔性对所述共振和节拍的影响。并且可以看出，刚性波导和柔性波导之间的非线性波传播有显着差异。