Abstract The paper concerns coupling between longitudinal and transverse vibrations of tensioned Euler-Bernoulli beams with general linear boundary conditions of arbitrary elastic stiffness. The beams are assumed to be perfectly straight with symmetric boundary conditions, and excitation aligned with the longitudinal axis. Two types of excitation, harmonic and impact, are considered. A relatively simple approach is proposed to predict and qualitatively describe the coupling, allowing approximate explicit analytical expressions for the key parameters affecting the phenomenon. The beam model considered, with both ends supported by longitudinal, translational and rotational springs, can be used in particular to model tensioned bolts used in engineering. The effects of beam tension on the coupling phenomenon are revealed. A series of physical experiments is carried out to illustrate application of the obtained theoretical predictions. Numerical solution of the full nonlinear equations governing coupled transverse-longitudinal vibrations has been conducted to validate the theoretical predictions.

中文翻译：

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具有一般线性边界条件的张拉 Euler-Bernoulli 梁的纵向和横向耦合振动

摘要 本文涉及具有任意弹性刚度的一般线性边界条件的张拉欧拉-伯努利梁的纵向和横向振动之间的耦合。假设梁是完全笔直的，边界条件对称，激励与纵轴对齐。考虑了两种类型的激励，谐波和冲击。提出了一种相对简单的方法来预测和定性描述耦合，允许影响现象的关键参数的近似显式解析表达式。所考虑的梁模型，其两端由纵向、平移和旋转弹簧支撑，尤其可用于模拟工程中使用的受拉螺栓。揭示了梁张力对耦合现象的影响。进行了一系列物理实验来说明所获得的理论预测的应用。已经进行了控制横向-纵向耦合振动的全非线性方程的数值解，以验证理论预测。