轴向运动梁在轴向载荷作用下的动力学特性研究

摘要

研究了轴向运动 Timoshenko 梁在轴向载荷作用下的振动特性。首先通过考虑轴向拉压载荷作用，根据Timoshenko 梁理论和 Hamilton 原理建立了梁的横向振动控制微分方程，推导了简支－简支边界条件下的梁的无量纲频率随轴向载荷的变化关系，采用新的无量纲化形式消除了无载荷作用下控制方程的奇异性。通过微分求积法进行数值求解并对结果进行验证，分析结果表明：无载荷作用下，长细比越大，越易达到失稳状态；在相同运动速度下，受压状态时比受拉状态下更易达到失稳；临界速度随着轴向载荷的绝对值的增大而减小。通过研究探索了影响临界速度和临界载荷的因素以及两者的关系，对于轴向受载运动系统设计具有一定指导意义。%The effects of axial load on vibration characteristics of an axially moving Timoshenko beam were investigated.The governing differential equation for transverse vibration of the axially moving beam under axial load was established based on Timoshenko beam theory and Hamilton's principle.The dynamic characteristics of the beam under axial load and pinned-pinned boundary conditions were investigated.The dimensionless frequencies of the beam versus axial load were calculated numerically using the differential quadrature method (DQM),and they were compared with the analytical solutions for verification.The results showed that under the condition of no load,the larger the slendness ratio of the beam,the easier the beam reaches unstable state;the beam reaches unstable state easier under compressive load than it does under tensile load;the critical speed of the beam decreases with increase in the absolute value of axial load. Through studying the influence factors and the relationship between the critical speed and the critical load of the beam,the results provided a guid for the design of axially moving systems under axial load.