Analysis on vertical vibration of coupled double-block ballastless track and subgrade system under high-speed train running

In combination with double-block ballastless track and subgrade structure characteristics, a vehicle-track-subgrade vertical coupled dynamic model was established in the frequency domain. In this model, the entire vehicle was represented by a rigid body model consisting of one car body, two bogies and four wheelsets connected to one another with springs and dampers; the double-block ballastless track and subgrade systems were considered as a multilayer beam model connected to each other with springs and dampers. The analytic expressions of vibration responses were derived, and the admittances of the coupled ballastless track and subgrade system were calculated. Combined with the virtual excitation method, the solution of random dynamic responses under excitation of random track irregularities was put forward. The random vibration responses and transfer characteristics of the double-block ballastless track and subgrade system under loading of running high-speed trains were analyzed. The results show as follows: Within the range of 10~5000 Hz, the magnitudes of the rail displacement admittances are much higher than those of the track slab and subgrade displacement admittances, and in the frequency bands above 30 Hz, the magnitudes of the displacement admittances of track slab are larger than those of the displacement admittances of subgrade; the frequency bands with rail vibration energy distributed are wider than those with track slab and subgrade vibration energy distributed, vibrations of track slab and subgrade are mainly concentrated in the frequency bands of about 163. 9 Hz; out of the vibration power of the coupled ballastless track and subgrade system, the rail lies the first, the track slab the second and the subgrade the minimum; in the middle and high frequency bands above 100 Hz, the vibration power of track slab and subgrade attenuates fast whereas in the low frequency bands below 100 Hz their vibration attenuation is not obvious; in the high frequency bands above 300 Hz, strong vibration attenuation between rail and subgrade is mainly due to the influence of fluctuations of vibration attenuation between rail and track slab.