轴向运动简支梁振动响应分析

轴向运动系统广泛存在于诸如火炮发射系统、动力传送带、带锯、空中缆车索道等工程领域，理论上可将其抽象为轴向运动弦线和梁的力学模型，具有重要理论意义和工程应用价值。基于Euler-Bernoulli梁理论，建立了移动质量作用下轴向运动简支梁振动方程，利用Galerkin法对方程进行离散，采用Newmark-β法对方程进行数值求解。计算了移动质量对轴向运动梁动态响应的影响，结果表明：相比轴向运动梁的自由振动，移动质量的作用使轴向运动梁更多的模态被激起；移动质量速度越小，频域成分越丰富；在移动质量作用前半阶段，梁的振动频率较低，在后半阶段振动频率较高。

Vibration Analysis of Axially Moving Simply-Supported Beam

Axially moving systems are widely used in engineering,such as gun launching system,power transmission band,belt saws,aerial cable tramways,etc. If the bending stiffness is concern,this kind of systems can be modeled as axially moving beams and has important theoretical significance and engineering application value. A partial-differential equation governing the transverse vibration of an axially moving simply supported beam with lumped mass was derived from Euler-Bernoulli beam model. The governing equation was resolved to a set of second order ordinary differential equations using the Galerkin method. Then the equations were calculated based on Newmark-β method. The effect of the moving mass on the dynamic response of the axially moving beam was studied. The results show that the lumped mass arouses more vibration modes of the simply supported moving beam than that of free vibration. Further,it is found that the decrease of the moving speed of the mass along the beam increases the frequency components of the bean vibration. In addition,the vibration frequencies of the beam increase when the lumped mass moves toward the end point. The beam vibration frequency is low,and the vibration frequency is higher in the second half of the beam.