柔性梁与带摆动荷载小车的耦合动力学分析

摘要

起重机桥架结构的振动以及荷载的摆动会使桥架结构产生疲劳损伤并影响荷载的精确定位.基于荷载、起重小车组成的椭圆摆与移动质量通过桥梁模型,起重机柔性梁与带摆动荷载的移动小车多体刚柔耦合动力学系统,并采用拉格朗日方程推导了耦合系统的运动微分方程组.采用Newmark-β逐步积分方法进行数值求解,分析了起重小车的运动速度、荷载质量等参数对桥架结构振动以及荷载摆动的影响.研究结果表明:起重小车的运行速度会影响桥架结构的振型,桥架结构的最大振动幅度与荷载质量成正比;耦合系统桥架结构中点的挠度比采用ANSYS软件计算的静挠度增大4％;荷载的摆动导致起重小车的驱动力与驱动功率周期性地改变,起重小车驱动力以及驱动功率变化的幅度范围正相关于起重小车的加速度值.%The vibration of the crane beam and the residual swing of the payload cause fatigue damage of crane and affect the precise positioning of the payload.In this paper,a crane flexible beam with a moving trolley subjected to pendulum payload multibody coupled dynamic system was set up based on an elliptical pendulum constituted by payload with trolley and moving mass passing a bridge model.The differential equations of motions of the coupled system were deduced based on Lagrange equation.The numerical solution was derived by using the Newmark-β step-by-step integration method.The effects of the crane speed and the payload mass on the vibration of the beam and the load swing were analyzed.Numerical analysis results indicate that the crane speed affects the vibration mode of the beam overhead crane,and vibration amplitude is proportional to the mass of payload.The bend at the beam midpoint is 4％ larger than the results calculated by ANSYS.The swing of payload leads to periodic changes of the driving force and driving power of the overhead crane.The payload acceleration is positively related to the crane driving force and driving power range.