| Floating slab track is widely used in urban rail transit because of its good vibration damping performance.In order to explore the propagation characteristics of elastic waves in such composite periodic orbital structures,the generalized plane wave expansion method and iterative method are used to obtain eight band gaps corresponding to the dispersion curves of real and imaginary parts of infinite periodic structures in the range of 300Hz: 0～11.3Hz、14.3～14.9Hz 、 24.83～43.6Hz 、 49.34～56.39 Hz 、 112.9～113.1Hz 、 160.2～160.8Hz 、118.1～195.1Hz、277.7～280.5Hz.The calculated vibration transfer curve of finite periodic structure shows that with the increase of the number of cycles(i.e.propagation distance),the vibration attenuation effect in the corresponding frequency band shows an increasingly obvious trend,and continues to approach the real frequency range of the band gap,and the attenuation amplitude matches the imaginary part of the band gap,which verifies the existence of the band gap.In addition,combined with the phononic crystal theory,the band gap analysis method of single periodic track and the elastic wave motion mode of floating plate track structure,it is concluded that the band gap formation mechanism of composite periodic floating plate track structure is different from that of single periodic track structure,that is,the local Bragg scattering or local resonance formed by single wave mode can not prevent the elastic wave propagation in other waveguide modes,Therefore,only when the elastic waves in the three waveguide modes cannot propagate,can the complete band gap characteristics appear.At the same time,the parametric analysis of steel spring,shear hinge and floating plate length shows that the width and position of band gap at each stage are affected by structural parameters.In addition,the increase of floating plate length will increase the richness of band gap,but reduce the total bandwidth rate.In order to analyze the vibration isolation effect and mechanism of floating slab under load,from the perspective of vibration and fluctuation,this paper pertinently considers the difference of vibration damping performance of track before and after floating slab setting:(1)By calculating and comparing the displacement admittance and insertion loss of floating slab track and monolithic track bed,it is obtained that the vibration damping effect of floating slab is worse than that of monolithic track bed in the range of 0 to 2 times of resonance frequency,only when crossing 2 times of resonance frequency,The damping effect is better than that of monolithic track bed.(2)By calculating the elastic wave propagation rate of floating slab track and monolithic track bed,it is found that the elastic wave propagation rate of floating slab track is lower than that of monolithic track bed structure in the frequency band of 0 ～15.0Hz,that is,it causes large environmental vibration,and the elastic wave propagation rate is higher than that of monolithic track bed structure in other frequency bands.(3)It is found that the peak value of reducing the insertion loss of the floating plate track will also appear at the frequency of the flat band generated in the dispersion curve,that is,there is a corresponding relationship between the natural mode dispersion curve flat band insertion loss peak,and the elastic wave propagation rate matches the band gap range of the corresponding track structure.In order to explore the excitation characteristics and propagation law of elastic wave under load,the dynamic acceleration response of infinite periodic structure is obtained through Floquet transformation,and the relationship between track dynamic acceleration response frequency dispersion curve load velocity line(i.e.DDL relationship)is explored.It is found that there is a one-to-one corresponding relationship between the peak acceleration response and the intersection of load velocity line and frequency dispersion curve,The excitation frequency of the moving wave source is located at the beginning of the band gap,the middle of the band gap,the end of the band gap and the passband band.The results show that:(1)The excitation of the moving wave source at the initial position of the bandgap is difficult to excite the main peak of high-frequency acceleration at the band gap side,resulting in the abnormal Doppler effect that the maximum main frequency receiving frequency of the acceleration response in front and behind the wave source is lower than the excitation frequency.(2)The moving wave source excitation in the middle of the band gap is difficult to excite the main peaks of low and high frequency acceleration in the band gap range on both sides,which shows the special Doppler effect of steep slope peak shape and obviously small order of magnitude of acceleration amplitude,and it is difficult to propagate in the structure.(3)The moving wave source excitation at the end of the band gap is difficult to excite the main peak of low-frequency acceleration at the band gap side,which shows the abnormal Doppler effect that the front and rear acceleration response of the wave source are the largest,and the receiving frequency of the main frequency is higher than the excitation frequency.(4)Under the excitation of the moving wave source at the passband position,the peak value of the structural acceleration response increases significantly,and the main frequency of the structural response before and after the wave source conforms to the forward Doppler shift.It can be concluded that the Doppler effect generated by the moving wave source can excite the main frequency peak of acceleration in the tunnel floating plate track structure,and the elastic wave band gap in the tunnel floating plate track structure can effectively suppress the excitation of the moving wave source,making it difficult for the structure to appear the elastic wave mode that can propagate in the band gap range.In conclusion,the elastic wave propagation law of floating slab track structure is clarified,which provides a new idea and theoretical support for the subsequent regulation of vibration and noise from the perspective of fluctuation. |
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