Euler-Bernoull梁模态公式的修正

MODIFICATION OF THE MODE SHAPE EXPRESSIONS FOR EULER-BERNOULL BEAMS

  • 摘要: 在机械振动教科书给出Euler-Bernoull梁的模态表达式中,除了简支梁,一般只能计算前12阶模态。主要原因是由于模态表达式中存在双曲正弦和双曲余弦函数,双曲函数随模态阶数呈指数增加,由此引起的舍入误差导致数值计算时模态形状失真。本文提出对传统的模态表达式进行修正,从而可以精确计算至少前200阶模态。

     

    Abstract: In most vibration text books, the expressions for mode shape functions of Euler–Bernoulli beams in numerical evaluation can only accurate up to the first 12 modes except simply-supported boundary condition. The main reason is that these expressions involve the hyperbolic sine and cosine functions, which are exponential increasing as mode index increasing. The mode shapes in numerical calculation will distort due to the round-off errors. In this paper, these functions are modified in a different form. With proposed modified expressions, the modes for vibrating beam can be calculated up to at least the 200th mode accurately.

     

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