黏弹性阻尼作用下轴向运动Timoshenko梁振动特性的研究

黏弹性阻尼一直是轴向运动系统的研究热点之一.以往研究轴向运动系统大都没有考虑黏弹性阻尼的影响.但在工程实际中, 存在黏弹性阻尼的轴向运动体系更为普遍.本文研究了黏弹性阻尼作用下轴向运动Timoshenko梁的振动特性.首先, 采用广义Hamilton原理给出了轴向运动黏弹性Timoshenko梁的动力学方程组和相应的简支边界条件.其次, 应用直接多尺度法得到了轴速和相关参数的对应关系, 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似解析解.最后, 采用微分求积法分析了在有无黏弹性作用下前两阶固有频率和衰减系数随轴速的变化; 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似数值解, 验证了近似解析解的有效性.结果表明: 随着轴速的增大, 梁的固有频率逐渐减小.梁的固有频率和衰减系数随着黏弹性系数的增大而逐渐减小, 其中衰减系数与黏弹性系数成正比关系, 黏弹性系数对第一阶衰减系数和固有频率的影响很小, 对第二阶衰减系数和固有频率的影响较大. 

VIBRATION CHARACTERISTICS OF AXIALLY MOVING TIMOSHENKO BEAM UNDER VISCOELASTIC DAMPING 1)

Viscoelastic damping has always been one of the research hotspots of axial motion system. The influence of viscoelastic damping has not been considered in most previous researches on axial motion systems. In the present paper, the vibration characteristics of the axially moving Timoshenko beam with viscoelastic damping are studied. The dynamic equations of Timoshenko beams with axial viscoelastic motion and the corresponding boundary conditions of simply supported beams are obtained using the generalized Hamilton principle. The method of direct multiple scales is used to show the corresponding relationship between axial speed and parameters. The approximate analytical solutions of the first two natural frequency and attenuation coefficient are obtained. The differential quadrature method is applied to analyze the variation of the first two natural frequencies and attenuation coefficients with the axial speed under the presence or absence of viscoelasticity. The approximate numerical solutions of the first two natural frequencies and attenuation coefficients under viscoelastic action are given and the validity of approximate analytic solution is verified. It is shown that the natural frequency of the beam decreases gradually with the increasing axial speed. The natural frequency and attenuation coefficient of the beam decrease with the increasing viscoelastic coefficient. The attenuation coefficient is proportional to the viscoelastic coefficient. The viscoelastic coefficient has little effect on the first order attenuation coefficient and natural frequency. But it has a greater influence on the second-order attenuation coefficient and natural frequency.