轴压作用下自由-自由运动梁振动特性研究

针对轴向压力作用下的两端自由运动梁的振动问题,根据Timoshenko梁理论和Hamilton原理建立了梁的横向振动控制方程,通过解析法和微分求积法(DQM)求解了梁的振动特性,分析了轴向压力和运动效应以及轴向力导数和运动加速度对梁固有特性的影响,并对临界载荷、临界速度等的影响因素进行了比较研究。结果表明：轴向压力和运动效应都使得固有频率降低,压力和运动速度的特定组合会导致超临界现象和耦合模态颤振的出现;压力导数和加速度效应都会使得梁的基础频率产生不稳定性;梁的临界载荷随着运动速度增大而变小,临界速度随轴向压力增大而降低。

VIBRATION CHARACTERISTICS OF FREE-FREE MOVING BEAM UNDER AXIAL COMPRESSIVE LOADS

Based on Timoshenko beam theory and a Hamiltonian principle, the governing equation of transverse vibration of a free-free axially moving beam under an axial compressive load is established. The vibration characteristics of the beam are obtained by the analytical solution and Differential Quadrature Method (DQM). The effect of compressive load and axially moving speed along with a load derivative and an axial acceleration on natural frequencies is studied. The analyzing results show that the compressive load and the axially moving cause the natural frequency decreased. A supercritical phenomenon appears while the compressive load is high and the beam undergoes a coupled-mode flutter. The instability of the beam fundamental frequency happens under load derivative and acceleration effects; the critical load decreases as the moving speed increases, and the critical speed reduces with the increase of a compressive load.