基于谱几何法的轨道结构全频域数值分析OA

To study the full frequency domain vibration of track structures,a frequency domain vibration model of ballastless track structures is established based on spectral geometry method.Firstly,the track structure is dis-cretized into several spectral geometric element,which are coupled to each other by setting virtual springs.Sec-ondly,the characteristic matrix,element coupling stiffness matrix,and load vector of the spectral geometric ele-ment of the ballastless track structure is derived by the Rayleigh-Ritz method.Adopting the principle of element matching,the spectral geometric element characteristic matrix and element coupling stiffness matrix of the track structure are combined into the overall characteristic matrix of the track structure.By solving the spectral geo-metric dynamic equation of the track structure,the full frequency vibration response of the track structure is ob-tained.Finally,a program is developed using Matlab to verify the feasibility of the spectral geometry method.By comparing with the finite element method,the feasibility and high efficiency of the spectral geometry method is verified.The influence of track structure parameters on the vibration characteristics of track structures in the full frequency domain has been studied.The calculation results show that the computational speed of the spectral ge-ometry method is 8 times faster than that of the finite element method within the frequency range of 1～2 000 Hz;fastener stiffness mainly affects the third-order natural frequency of rail;the CA mortar stiffness mainly affects the second-order natural frequency of the track structure;the subgrade stiffness mainly affects the first-order nat-ural frequency of the track structure;the fasteners damping mainly attenuates the peak values at the second-order natural frequencies of track structures and the third-order natural frequencies of rails;the damping of CA mortar mainly attenuates the peak value at the second-order natural frequency of the track structure.The subgrade damp-ing mainly attenuates the peak value at the first-order natural frequency of the track structure;the Pinned-Pinned frequency of rails is not affected by the stiffness of fasteners,CA mortar stiffness,and subgrade stiffness,and is mainly related to the spacing between the rail fasteners.The research results can provide efficient computational methods and technical support for vibration and noise reduction within the wide-frequency range of track structures.