简谐荷载作用下弹性土体中圆形隧道和轨道结构的动力响应

Dynamic response of circular tunnels and track structures in elastic soil under harmonic load

采用解析的方法研究了弹性土体中圆形隧道和轨道结构的动力响应。将隧道视为无限长的薄壁圆管,轨道被简化成铺设在隧道仰拱上无限长的欧拉梁,周围土体为无限空间弹性介质。通过在环向采用模态叠加法,在轴向采用傅里叶变换求解隧道与轨道之间的耦合问题,获得了在简谐荷载作用下弹性土体中圆形隧道和轨道结构的动力响应。研究结果表明:低支承刚度的结构体系会产生连续的干涉现象,这种情况在高频的情况下尤为明显;虽然轨道的弯曲刚度越大,结构的位移越小,但是整体规律保持不变;支承刚度的增加会导致轨道固有频率向高频偏移;无轨道结构中土体位移会随着荷载频率的升高而降低,在加入轨道后荷载会与轨道固有频率产生共振效应,形成特定的极大值。

The dynamic response of circular tunnels and track structures in elastic soil is studied.The tunnel is regarded as an infinitely long thin-walled circular tube and the track is simplified as an infinitely long Euler beam laid on the inverted arch of the tunnel.The surrounding soil is an elastic medium in an infinite space.By using the modal superposition method in the circumferential direction and Fourier transform in the axial direction to solve the coupling problem between tunnel and track,the dynamic response of the circular tunnel and the track structure in elastic soil under moving harmonic load is obtained.The results show that the structural system with low supporting stiffness could produce continuous interference,which is particularly obvious at high frequencies.Although the larger the bending stiffness of the track is,the smaller the displacement of the structure is,the overall law remains unchanged.An increase in support stiffness leads to a shifting of the natural frequency of the track to higher frequency.The soil displacement of the trackless structure decreases with the increase of load frequency and the load has a resonance effect with the natural frequency of the track after adding the track,forming a specific maximum value.