Abstract This paper presents a closed-form frequency equation that predicts the modal coupling between the adjacent axial and bending modes of a beam with a transverse open crack. The final form of the proposed frequency equation is simply expressed in terms of the uncoupled frequency equations of intact and cracked beams for any type of support condition of the beam by introducing an axial–bending modal coupling factor. The validity of the proposed frequency equation is demonstrated through a comparison with the numerical results from a finite element analysis and with experimental data. For relatively deep cracks, the overall effect of axial–bending modal coupling on the axial modal frequencies is more significant than that on the bending modal frequencies.

中文翻译：

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考虑轴弯模态耦合的横向开裂任意支撑梁的闭式频率方程

摘要 本文提出了一个闭式频率方程，用于预测具有横向开裂梁的相邻轴向和弯曲模态之间的模态耦合。通过引入轴向弯曲模态耦合因子，对于梁的任何类型的支撑条件，所提出的频率方程的最终形式可以简单地表示为完整梁和有裂纹梁的非耦合频率方程。通过与有限元分析的数值结果和实验数据的比较，证明了所提出的频率方程的有效性。对于较深的裂纹，轴向-弯曲模态耦合对轴向模态频率的整体影响比对弯曲模态频率的影响更显着。