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首页> 外文期刊>International Journal of Naval Architecture and Ocean Engineering >Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method
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Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method

机译：假定模式方法中使用特征正交多项式分析任意边约束矩形板的自由振动

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摘要

ABSTRACT An approximate method based on an assumed mode method has been presented for the free vibration analysis of a rectangular plate with arbitrary edge constraints. In the presented method, natural frequencies and their mode shapes of the plate are calculated by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. Characteristic orthogonal polynomials having the property of Timoshenko beam functions which satisfies edge constraints corresponding to those of the objective plate are used. In order to examine the accuracy of the proposed method, numerical examples of the rectangular plates with various thicknesses and edge constraints have been presented. The results have shown good agreement with those of other methods such as an analytic solution, an approximate solution, and a finite element analysis.
机译：摘要已经提出了一种基于假定模态方法的近似方法，用于对具有任意边缘约束的矩形板的自由振动进行分析。在提出的方法中，通过解决使用拉格朗日运动方程式导出的多自由度系统矩阵方程的特征值问题，计算板的固有频率及其模态形状。使用具有季莫申科束函数特性的特征正交多项式，该多项式满足与物镜的边缘约束相对应的边缘约束。为了检验该方法的准确性，给出了具有不同厚度和边缘约束的矩形板的数值示例。结果与解析解，近似解和有限元分析等其他方法具有很好的一致性。

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