Research On Vibration Characteristics Of Tunnel Based On The Period Structure Theory

With the rapid development of the railway construction and the urban rail transit in China,the vibration problems of viaducts and tunnel structures on saturated soils are becoming more and more concerned.Based on the theory of periodic structure and Biot theory of the saturated soil,the vibration characteristics of periodic viaduct and circular tunnel structure are analyzed from the aspects of the periodic vibration energy band and the vibration and propagation of periodic structure caused by external excitation.The studies of the paper are as follows:The tunnel structure is regarded as a thin-walled cylindrical shell,the vibration characteristics of the cylindrical shell are analyzed.During the analysis,two kinds of cases,such as periodic cylindrical shell and cylindrical shell with variable cross section,are studied.For periodic cylindrical shell,using Love shell theory,the axi-symmetric vibration equations of circular tunnel is established,the fluctuating dynamic stiffness matrix of each cell in the periodic tunnel is obtained,and the transfer matrix between the adjacent cells can be derived based on the transfer matrix method.For cylindrical shell with variable cross section,the transfer matrix of the cylindrical shell was derived by Hamilton principle,and the characteristic value of the transfer matrix was calculated according to the precise integration method,the propagation characteristics of two kinds of variable cross section(exponential function and linear function)cylindrical shell were researched.The results show that the periodic cylindrical shell and the variation of cylindrical shell section size has a certain influence on the propagation of the vibration wave.Considering the interaction between the tunnel structure and the soil,combined with Biot theory,Helmholtz potential function theory,Fourier transformation,boundary conditions,displacement and stress continuity conditions,the vibration characteristics of periodic tunnel structures on elastic foundation and saturated soil are studied respectively.Acting the moving concentrated harmonic loads on the tunnel lining,the transfer matrix and the eigenvalue of the periodic circular tunnelare solved,the dynamic response of periodic tunnels in saturated soils under moving loads is studied.The research results show that,there exists a critical frequency for the homogeneous circular tunnel,the change of the length ratio and the elastic modulus ratio have effects on the band gap amplitude and bandwidth of the periodic circular tunnel;the elastic modulus of the saturated soil and the foundation stiffness of the elastic foundation have the inhibitory effect on the propagation of the bending wave in the specific frequency range,compared with the elastic foundation,the saturated soil has a significant effect on the propagation of the waves;under the action of moving load,there is a critical velocity for homogeneous circular tunnel;the change of the length ratio,the elastic modulus ratio,the elastic modulus of the saturated soil and the foundation stiffness of the elastic foundation have significant effects on the amplitude,width and number of the gap band in the periodic circular tunnel at different moving loads.