Wave Prorogation Analysis Of Guided Waves Of Tracks Based On The Semi-analytical Finite Element Model

The guided wave method is one of the best non-destructive detection methods used for track structure nondestructive detection. The guided waves selected should have the characteristics of low decay rate. Usually there are many types of wave guide mode exist in the waveguide structure, it is important to accurately predict the wave characteristics of guided waves, such as frequency, the wavelength, the group velocity, decaying rate, and so on, of the various types of wave guide. For the waveguide structures with simple structure (such as pipes, panels, beams, etc.), we usually use the analytical method or the finite element method to calculate the wave characteristics, because of few guided wave modes existing. However, for complex cross-sectional shape of the track, it is impossible to establish a theoretical equation for the complex guided waves. Meanwhile, the finite element method is only suitable for the lower frequency range and shorter structure. Also, it is difficult to distinguish different modes from each others between the wave guides from the finite element solutions. In this case, the conventional finite element method and analytical methods on the track guide wave characteristics have application defects insurmountable. With the above in mind, in this study, we use the Semi-analytical Finite Element Method (SAFEM) which combines the wave theory and finite element method to calculate the wave characteristics of infinitely long structures with complex sections.Firstly, the basic theory of the SAFEM is described, and the modeling method of SAFEM using the example of a beam is introduced. And then some research is done on the effects of cross-section mesh. To verify the accuracy of the semi-analytical finite element method, the theory of Euler-Bernoulli beam, Timoshenko Beam, and the FE method are used. And then experiments on wave numbers based on a6.1m-long beam are carried out. The results show the accuracy of the semi-analytical finite element method.Then the model of UIC60rail and rail pad is set up. The validity and efficiency of the rail model are verified by using the finite element method. These then follow the research on the influence of the rail pad. And the wave characteristics of Chinese rail, such as dispersion, phase velocity and group velocity, are calculated based on the semi-analytical model.At last, the damping loss factor of the1meter rail and6meters track are tested in the condition of the laboratory. And the decay rate in the0-100kHz frequency range of the track is calculated by using the group velocity calculated and the damping loss factor measured. From the decay curve we find that there are19types of guided wave in the UIC60track which can propagate more than1kilometer. Especially there is a type of guided wave near44kHz which can propagate more than1.3kilometers.The results of the research on the influence of the rail pad show that the influence of the pads is mainly in the low frequency range below20kHz. With the increasing of stiffness of the rubber pad, the wave numbers increase for the same type of guided waves. From the damping loss factor of the rail and track, it shows that the influence of the rail pad on damping loss factor is mainly in the low frequency range. The experimental results also shows that rail pad mainly influence the low frequency region of the guide waves from the side.The method of semi-analytical finite element method used in this paper is not only applicable to the track, but also suitable for pipelines, cables, beams and other waveguide structure. Because the limitation of experimental conditions, the single mode of rail guided wave cannot be excited, so the accuracy of the track high frequency numerical model cannot be verified by experiment.