承受移动均布质量的简支梁振动反应分析

VIBRATION ANALYSIS OF A SIMPLY SUPPORTED BEAM TRAVERSED BY UNIFORM DISTRIBUTED MOVING MASS

考虑磁浮交通等工程背景下,研究了大于简支梁跨度的质量在简支梁上移动时,简支梁的竖向振动情况,建立了简支梁向振动分析的移动均布荷载模型,通过使用荷载移动状态函数得到了简化形式的简支梁振动方程组,并用振型叠加和Wilson-θ法求出了简支梁的振动反应。文中比较和研究了移动荷载作用下简支梁跨中位移和加速度与梁的跨度、荷载移动速度以及移动质量与桥梁质量比之间的关系。结果表明梁的自振频率,荷载的行驶频率和荷载与梁质量比对梁的振动都起着重要的作用。

Considering the engineering background of some transportation systems like maglev and so on, vertical vibration of the simply supported beam is investigated. The length of the vehicle is assumed to be longer than the beam span. The model of moving distributed load with constant speed is established. The beam is considered as Euler-Brnoulli beam and the right side of the control equation is simplified by using a moving status function. The solution of the beam's dynamic behavior including its deflection and acceleration is obtained by using Wilson-θ numerical integral and mode superposition method. The results from different parameters such as the span of beam, velocity of moving mass and ratio of moving unit mass to beam unit mass are compared. All results show that the beam dynamic behavior is tied up with these factors: frequency of beam, moving frequency of the load and the ratio of vehicle unit mass to beam unit mass.