移动荷载下有限深度Winkler地基上梁的动力响应研究

Dynamic response of beam on Winkler foundation with finite depth under moving load

基于考虑有限深度土体运动的Winkler地基梁理论,建立移动荷载作用下弹性地基上有限长梁的横向运动方程。利用模态叠加法求得移动荷载作用下有限长梁动力响应的解析解,进而以移动荷载离开时梁的响应为初值,采用分离变量法求得有限长梁自由振动的一阶近似解;通过数值计算和参数分析,揭示了移动荷载作用下有限深度Winkler地基上简支边界梁的动力学特性,分析地基深度、地基黏滞阻尼系数和荷载移动速度等对有限长梁受迫振动阶段和自由振动阶段动力响应的影响,全面揭示有限深度土体运动对临界速度的作用效应。结果表明:地基深度显著降低了临界速度,且弹性地基黏滞阻尼明显延长了自由振动衰减时间;荷载移动速度加剧了有限深度弹性地基与其支承梁的相互作用效应,系统振动的幅值和响应周期均发生显著变化。

Here,based on Winkler foundation beam theory considering finite depth soil body motion,the lateral dynamic equation of finite length beam on elastic foundation under moving load was derived.The analytical solution to dynamic response of finite length beam under moving load was obtained by using the modal superposition method,and then the first order approximate solution to free lateral vibration of finite length beam was obtained by using the separation variable method with beam’s response during moving load leaving taken as initial value.Through numerical calculation and parametric analysis,dynamic characteristics of simply-supported boundary beam on Winkler foundation with finite depth under moving load were revealed,effects of foundation depth,foundation viscous damping coefficient and load moving speed on dynamic response of forced vibration stage and free vibration stage of beam were analyzed,and the action effect of soil body motion with finite depth on critical speed was fully revealed.The results showed that foundation depth significantly reduces critical velocity;viscous damping of elastic foundation significantly prolongs free vibration attenuation time;load moving speed aggravates the interaction effect between finite depth elastic foundation and beam supported by foundation to cause system vibration amplitude and response period having significantchanges.