单向加筋板低频振动的简化建模精度影响因素研究
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中国舰船研究设计中心

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Research on Influencing Factors of Simplified Modeling Accuracy for Low Frequency Vibration of Unidirectional Stiffened Plate
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China Ship Development and Design Center

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    摘要:

    为研究加筋板结构在低频振动中的模型简化,基于小挠度薄板弯曲理论,通过质量等效与刚度等效,得到将加筋板等效为正交各向异性板的密度与弯曲刚度计算公式。以单向加筋矩形板为研究对象,通过计算加筋板固有频率有限元解和等效正交异性板固有频率解析解的误差,证明了等效方法的有效性,并讨论了质量等效、刚度等效以及结构参数对等效方法精度的影响。结果表明:刚度等效是等效方法精度的主要影响因素,质量等效的影响可以忽略不计;筋条截面高度、筋条数量和基板厚度对等效方法精度均有一定的影响。最后,通过定义无量纲参数附加弯曲刚度比,对三项结构参数进行定量比较分析。结果表明:筋条数量是影响等效方法精度最显著的结构参数,附加弯曲刚度比在10的二次方量级以内可以保证等效方法的准确性。

    Abstract:

    In order to study the model simplification of stiffened plate structure in low frequency vibration, based on the small deflection thin plate bending theory, through mass equivalent and stiffness equivalent, the density formulation and the bending stiffness formulation of stiffened plate equivalent to orthotropic plate are obtained in this paper. Taking the unidirectional stiffened rectangular plate as the research object, the validity of the equivalent method is proved by calculating the error of the finite element solution of the natural frequency of the stiffened plate and the analytical solution of the natural frequency of the equivalent orthotropic plate. The influence of mass equivalence, stiffness equivalence and structural parameters on the accuracy of the equivalent method is discussed. The results show that stiffness equivalence is the main factor affecting the accuracy of the equivalent method, and the effect of quality equivalence can be ignored. The height of beam section, the number of beams and the thickness of plate all have a certain impact on the accuracy of the equivalent method. Finally, this paper makes a quantitative comparison and analysis of the three structural parameters by defining dimensionless parameters. The results show that the number of beams is the most significant structural parameter that affects the accuracy of the equivalent method, and the additional bending stiffness ratio within the quadratic order of 10 can ensure the accuracy of the equivalent method.

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  • 收稿日期:2021-04-15
  • 最后修改日期:2021-04-15
  • 录用日期:2021-05-18
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