离散支承梁分段动力学建模方法

A Piecewise Dynamic Modeling Method for Discretely Supported Beams

为了更准确分析轨道交通振动与噪声的成因及传播机理,需要构建车辆-轨道耦合模型,模拟在移动载荷作用下全系统的动力学响应,其中,轨道结构振动方程作为模型中的重要组成环节,其求解方法对于模型数值分析的计算精度有直接影响。常用求解方法—Rayleigh-Ritz法是将简支梁的各阶振型作为基函数,通过模态叠加法求得轨道在外部激励作用下的动力学响应。然而,当轨道计算长度不足、周期支承特性缺失时,基于有限长简支梁得到的振型函数不能充分表征轨枕的离散支承特性,因此,针对一般离散支承梁,提出一种分段建模方法,通过边界条件把轨枕的约束作为弹性恢复力纳入轨道模型中,而不是作为外力项,从而求解出更符合实际的修正振型函数以及固有频率。进一步,对比动力学建模与有限元仿真结果,验证了所提方法在其适用范围内的精确性和有效性。

In order to well understand the cause and transmission mechanism of rail transit noise and vibration,it is necessary to establish a vehicle-rail coupled model to simulate the dynamic response of whole system under moving loads.As an important part of the model,rail vibration equation’s solution method directly affects the calculation accuracy of numerical analysis.Rayleigh-Ritz method,a common solution method,takes modals of a simply supported beam as the Basis functions,and calculates the dynamic response of rail under external excitation by modal superposition method.However,when the calculation length is insufficient or the periodic support characteristic is missing,the mode shape obtained by regarding the rail as a finite simply supported beam cannot adequately reveals the discrete support characteristics of sleepers.Therefore,a piecewise modeling method is proposed for general discretely supported beams in this paper,which incorporates the restraint of sleepers into the rail model as elastic elements through boundary conditions,rather than as an external force.So,more realistic modified mode shapes and natural frequencies can be obtained by the proposed method.Furthermore,the accuracy and validity of this method in its applicable range are verified by means of the comparison between the solutions of this method and finite element analysis.