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假定任一时刻的位移可以根据其相邻时间步上的运动状态由Hermite插值函数确定,采用3节点高斯积分方法展开精细积分法中状态方程的Duhamel项,构造了一种改进的高斯精细积分算法用于求解结构非线性问题,在此基础上,提出了适用于车桥耦合振动研究的高效求解分析框架。车桥耦合系统由车辆、桥梁有限元子系统组成,其中车辆子系统引入部件刚体假定,而桥梁子系统借助于振型叠加法缩减自由度数目,两个子系统间的相互作用通过非线性的虚拟力表达。以一节4轴客车匀速通过32m简支梁为研究对象,分别采用所提出的分析框架、传统Newmark-β法进行动力分析。结果表明:相对于Newmark-β法,高斯精细积分方法既能避免求解线性方程组,又可显著提高计算收敛的积分步长,分析框架显示出良好的实用效果。
It is assumed that the displacement at any moment can be determined by the Hermite interpolation function according to the motion state of its adjacent time step. The Duhamel term of the state equation in the precise integral method is developed by using 3-node Gaussian integral method. An improved Gaussian precision integral algorithm Based on this, an efficient analytical framework suitable for the study of coupled vibration of vehicle-bridge is proposed. The vehicle-bridge coupling system consists of a vehicle and a bridge finite element subsystem, in which the vehicle subsystem introduces the component rigid body assumption, and the bridge subsystem reduces the number of degrees of freedom by means of the modal superposition method. The interaction between the two subsystems is simulated by a nonlinear virtual Force expression. Taking a 4-axle passenger car at a constant speed through 32 m simply supported girders as the research object, the proposed Newmark-β method was used to analyze the dynamic characteristics of the 4-axle passenger car. The results show that, compared with the Newmark-β method, the Gaussian precision integral method can not only solve the linear equations but also significantly improve the integral steps of the convergence. The analytical framework shows good practical results.