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通过倾斜界面耦合的弹性层散射能量计算模型的混合求解方法

THE SCATTERED ENERGY SOLUTION OF TWO ELASTIC LAYERS COUPLED THROUGH AN INCLINED INTERFACE REALIZING BY A HYBRID METHOD

  • 摘要: 过渡段动力稳定性问题已成为制约400 km/h及以上高铁运营关键难题, 亟需从波动和能量的角度探究由基础非均匀引发的线路系统动力响应放大机理. 本文将高铁过渡段车致弹性波传播问题提炼为非均匀介质刚性基弹性层中波的散射问题, 采用模态叠加法+有限差分法的混合求解方法构建倾斜界面耦合刚性基弹性层散射计算模型, 该模型优势体现在设置有限差分区域有效模拟弹性层材料非均匀变化的同时, 保留了两侧连续介质区, 这样可在实现网格数量控制的同时, 获取各导波模式散射系数并由此分析反射及透射场各导波模式对能量的分配及运载情况, 模型两类区域间建立的数学关系也可成功反映模型计算精度与参与计算导波模式数量间正向关系. 结果表明: 当弹性层耦合界面由垂直转为倾斜后, 使原本占据主体能量的透射场基阶模式导波能量发生转移, 界面偏转越多, 散射场能量的分配越分散, 这直接体现在透射场基阶模式能量占比下降上; 入射波入射锐角界面时, 反射场及透射场的高阶模式导波容易获得更多的能量; 在高阶模式导波波函数值沿弹性层厚度起伏分布特征作用下, 高阶模式导波分配到更多能量的原因可与导波复杂传播方向与其位移活跃区间产生更多匹配有关.

     

    Abstract: The dynamic stability of subgrade in transition zones has become a key problem restricting the operation of high-speed railway with a speed of 400 km/h and above. It urgent to explore the amplification mechanism of system dynamic response caused by non-uniform subgrade from the perspective of wave and energy. In this paper, the problem of vehicle induced elastic wave propagation in the transition zones in high-speed railway is refined into the problem of wave scattering in the inhomogeneous elastic layer. A hybrid solution method of modal superposition and finite difference is proposed to determine the scattered energy solution of two elastic layers coupled through an inclined interface. The advantage of this method lies in the effective simulation of non-uniform changes in the elastic layer material by setting a finite difference region, while retaining the continuous regions on both sides. In this way, while controlling the number of grids, the scattered coefficients of guided wave modes are obtained to analyze the energy distribution of each guided wave mode in the reflected and transmitted fields. In addition, the mathematical relationship established between the two types of regions successfully reflects the positive relationship between the calculation accuracy and the number of guided wave modes involved in the calculation. The results show that when the interface of the elastic layer changes from vertical to inclined, the guided wave energy of the fundamental mode of the transmitted field, which originally occupied the main energy, is transferred. The more interface deflection occurs, the more dispersed the distribution of scattered field energy. When the incident wave enters the acute angle interface, the higher guided wave modes of the reflected and transmitted fields are more likely to obtain more energy. Considering the fluctuation distribution characteristics of displacement values along the thickness of the elastic layer of higher guided wave modes, the reason why higher modes allocate more energy may be related to the more matching between the complex propagation direction of guided waves and their displacement active range.

     

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