基于等效板模型发展了一种适用于导弹翼面的动力学和颤振分析方法。在等效板建模过程中,使用简单多项式定义翼面的几何、结构和位移,利用人工弹簧近似边界条件,通过全局Ritz法得到刚度和质量矩阵的解析表达形式,通过特征值问题的求解得到翼面的固有频率和振型。通过频率和模态的初步比较发现,利用该方法得到的弹翼动力学特性与通过有限元方法得到的结果一致。然后利用这两组模态进行弹翼的颤振分析,通过对比发现,两种方法的颤振分析结果吻合,这也进一步验证了等效板方法在弹翼动力学分析方面的准确性。等效板方法为弹翼初步设计阶段的快速建模提供了一种有效工具。
A method based on an equivalent plate model for the dynamic and flutter analysis of a missile wing is developed. In the process of equivalent plate modeling, simple polynomials are used to describe the geometry, structure and displacement of the missile wing, and artificial springs are used to approximate the boundary conditions. The analytical expressions for the matrices of stiffness and mass are obtained by the global Ritz method. The natural frequencies and modes of the missile wing are obtained by solving the eigenvalue problem. Preliminary comparison between the frequencies and the modes from the new method and the finite element method indicates that the two methods are consistent. Then the two sets of modes are used to perform a flutter analysis and the results agree well, which further validates the accuracy of the equivalent plate method for analyzing the dynamic characteristics of a missile wing. The equivalent plate model provides an efficient tool for quick modeling of missile wings in the early design stage.
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