周期性三维轨道结构弹性波耦合与转换

为了研究周期性三维轨道结构中弹性波传播规律,采用波有限元方法建立结构元胞动刚度矩阵,基于Bloch定理求解结构中弹性波波数和特征向量,得到其频散曲线,进一步结合弹性波叠加方法,计算无限长三维轨道结构响应。对比平面半轨道结构模型,三维轨道结构中频散曲线数量增加一倍,出现结构非对称波模态。此外,三维轨道结构中存在明显的弹性波耦合与转换,在同一条频散曲线中,可同时存在以弯曲波或扭转波为主的波模态,并在群速度最小位置发生波模态转换。由于三维轨道结构中存在对称与非对称弹性波模态,轨枕局域共振只与其中一类行波产生单一耦合,因此无法形成完全局域共振带隙。最后,采用振动传递系数验证弹性波在轨道结构中的传播规律,阐明不同荷载激励条件下轨道结构弹性波带隙的表现行为。

Coupling and Conversion of Elastic Waves in Periodic Three-dimensional Track Structure

To study the elastic wave propagation in periodic three-dimensional(3D)railway track structure,the wave finite element method was used to build the dynamic stiffness matrix of the unit cell.Combining the Bloch theorem,wavenumbers and eigenvectors of the structure were solved and the dispersion curves were obtained.Subsequently,the responses of infinite 3D track structure were calculated according to the wave superposition method.Compared with the plane half-track structure model,the number of dispersion curves in the 3D track structure was doubled with the appearance of the structural asymmetric wave modes.In addition,obvious coupling and conversion characteristics of the elastic waves in the 3D track structure can be observed.In the same dispersion curve,there can be wave modes mainly composed of bending waves or torsion waves,and the wave mode conversion occurred at the position where the group velocity was the minimum.Due to the existence of symmetric and asymmetric elastic wave modes in 3D track structure,the local resonance of the sleeper that only generated a single coupling with one type of the traveling waves,cannot form a complete local resonance band gap.Finally,the vibration transmission coefficient was used to verify the propagation of elastic waves in the track structure,and to clarify the band gap behaviors of the track structure under different load excitation conditions.