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

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.