This paper deals with analyzing the nonlinear vibration of an isotropic cracked plate interacting with an air cavity. A part-through surface crack with variable orientations and positions is considered and modeled using the modified line spring model. In the first step, based on the Von Karman theory, the governing equation of the nonlinear vibration related to the cracked plate–cavity is presented. Then, by employing the Euler equation along with the Galerkin method, the coupling effect between the fluid–solid media inside the enclosure is eliminated. In the next step, the variational iteration method (VIM) is introduced as an appropriate method for nonlinear analysis of the mentioned system. To this end, the convergence of the nonlinear coupled natural frequencies with high precision is proved by performing four iterations of VIM. Finally, the effect of the length, angle, and position corresponding to the crack as well as the cavity depth on the frequency ratio is inspected for various boundary conditions by plotting three and four-dimensional backbone curves. It is revealed that the crack angle is the most effective parameter on the frequency ratio.

中文翻译：

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裂纹板与流体介质相互作用的非线性动态响应的变分迭代法 (VIM)

本文涉及分析与气腔相互作用的各向同性裂纹板的非线性振动。使用修改后的线弹簧模型考虑和建模具有可变方向和位置的部分贯通表面裂纹。第一步，基于Von Karman理论，提出了与裂纹板腔相关的非线性振动控制方程。然后，通过采用欧拉方程和伽辽金方法，消除了外壳内流固介质之间的耦合效应。在下一步中，变分迭代法 (VIM) 被引入作为上述系统非线性分析的合适方法。为此，通过执行四次 VIM 迭代证明了非线性耦合固有频率的高精度收敛。最后，通过绘制 3 维和 4 维主干曲线，检查与裂纹对应的长度、角度和位置以及空腔深度对频率比的影响，以适应各种边界条件。结果表明，裂纹角度是影响频率比的最有效参数。