车桥耦合振动分析的两种常用插值方法比较

利用模态综合法分析车辆与桥梁之间的相互作用时,合理地构造桥梁的插值振型函数可以大幅提高计算精度.其中,分段三次Hermite插值函数和三次样条插值函数较为常用.为研究二者的异同,以简支梁桥为例分别采用这两种插值函数构造结构梁单元模型的一维插值振型函数和板单元模型的二维插值振型函数.基于以上两类插值振型函数,分析单自由度簧上质量匀速过桥时,桥梁的跨中位移、跨中梁底正应力和轮-桥接触力时程响应.结果表明:无论是一维问题还是二维问题,由三次样条插值法构造的插值振型函数与结构的实际振型较为吻合,计算结果具有较高的收敛性和精度.而要达到相同的精度,分段三次Hermite插值法则须加密单元网格,但其误差仅存在于独立网格内,不会累积放大.

Comparison of Interpolation Methods Used in Vehicle-Bridge Interaction Analysis

When vehicle-bridge interaction problem is to be analyzed with modal coupled method,the properly constructed interpolation modal functions are vital for the accuracy.The piecewise cubic Hermite interpolation and cubic spline interpolation were introduced into the analysis of a free beam traversed by a single degree of freedom spring-mass system.Both beam model and shell model were built for the same bridge.And modal analysis were carried out on both models.With the discrete vibration modes of these models,one dimensional modal interpolation function was constructed for beam model and two dimensional interpolation modal function for shell model respectively.The dynamic responses of the vehicle-bridge system were obtained based on these functions.The analytical results show that the interpolation modal function constructed with cubic spline interpolation method is more close to the target function with higher precision.And in order to reach the same precision,piecewise cubic Hermite interpolation method demands more elements.But its error will not accumulate.