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首页> 外文期刊>Journal of Fluids and Structures >Free vibration analysis of cantilever plate partially submerged into a fluid
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Free vibration analysis of cantilever plate partially submerged into a fluid

机译：部分浸入流体中的悬臂板的自由振动分析

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摘要

The free flexural vibration of a cantilever plate partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The virtual mass matrix is derived by solving the boundary-value problem related to the fluid motion using elliptical coordinates. The introduction of the elliptical coordinates naturally leads to the use of the Mathieu function. Hence, the virtual mass matrix which reflects the effect of the fluid on the natural vibration characteristics is expressed in analytical form in terms of the Mathieu functions. The virtual mass matrix is then combined with the dynamic model of a thin rectangular plate obtained by using the Rayleigh-Ritz method. This combination is used to analyze the natural vibration characteristics of a partially submerged cantilever plate qualitatively. Also, the non-dimensionalized added virtual mass incremental factors for a partially submerged cantilever plate are presented to facilitate the easy estimation of natural frequencies of a partially submerged cantilever plate. It is found that the numerical results are in good agreement with the previous results, thus validating the proposed approach.
机译：研究了部分浸入流体中的悬臂板的自由挠曲振动。假定流体不粘稠且无旋流。通过使用椭圆坐标求解与流体运动有关的边界值问题，可以得出虚拟质量矩阵。椭圆坐标的引入自然会导致使用Mathieu函数。因此，根据Mathieu函数，以解析形式表示反映流体对自然振动特性影响的虚拟质量矩阵。然后，将虚拟质量矩阵与通过使用Rayleigh-Ritz方法获得的矩形薄板的动力学模型组合。该组合用于定性分析部分浸入式悬臂板的固有振动特性。而且，提出了部分浸没悬臂板的无量纲增加的虚拟质量增量因子，以便于容易地估计部分浸没悬臂板的固有频率。发现数值结果与先前的结果非常吻合，从而验证了所提出的方法。

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