A tractable transfer matrix method based on the classical beam theory is developed and is subsequently used to investigate the effects of the axial tensile load and moving speed on the natural frequencies of axially moving beams under three different end conditions. The differential equation for the proposed method is solved in a closed analytical form. The transfer matrix method is derived from the relationship between displacements and forces specified at both ends of the axially moving beam. The accuracy of the method is validated through a comparison between the predicted results and those of previous studies. The critical speed for the fundamental frequency of an axially moving beam is analyzed by investigating the moving speed value in the vicinity of divergence instability. The numerical results for the end conditions considered provide useful information for capturing the divergence instability.

提出了一种基于经典梁理论的束缚传递矩阵方法，并随后用于研究轴向拉力和移动速度对三种不同端部条件下轴向移动梁固有频率的影响。拟议方法的微分方程以封闭解析形式求解。传递矩阵法是根据位移和轴向移动梁两端指定的力之间的关系得出的。通过将预测结果与先前研究的结果进行比较，验证了该方法的准确性。通过研究发散不稳定性附近的运动速度值，分析了轴向运动的梁的基本频率的临界速度。