Investigation Of Low Frequency Vibration Control On High Speed Train Body Structures

High-speed train body structure is usually a long,thin-walled space structure,coupled with the bogie containing non-linear wheel-track relationship,constituting a rigid-flexible coupling system under the complex excitation of multi-dimensional,time-varying,non-linear,fluid-solid coupling,resulting in "shaking","flutter".The result is that abnormal vibrations such as "shake" and " flutter" occur frequently.However,the current virtual prototype design methods,such as finite element analysis and modal testing,have problems such as low computational efficiency,closed environment and poor flexibility.In addition the uncertainties in vehicle parameters and the complexity of the excitation endured further lead to the inability of traditional analysis methods to quickly,accurately and flexibly achieve the design and control of vehicle vibration performance.Therefore,it is of far-reaching significance for the design of high-speed trains to consider the elastic vibration of the vehicle body,establish a multi-dimensional coupled dynamics model,analyse the mechanism of the elastic vibration of the vehicle body and propose a reasonable control method.Therefore,this paper focuses on the design of the vibration performance of the vehicle body in the conceptual design stage of high-speed trains,starting from the vibration theory of elastic beams and medium-thickness plates and shells,establishing a vertical vibration analysis model for the variable-section vehicle body and a three-dimensional vibration analysis model for the combination of multiple plates respectively,and deriving the corresponding analytical rigid-flexible coupling dynamics modeling method.On this basis,the mechanisms and transmission characteristics of abnormal vibration phenomena of high-speed trains are investigated.Finally,a systematic study of whole vehicle vibration and local vibration is carried out from the perspectives of uncertainty design and passive control respectively.Specific studies include.Firstly,the vibration of the vehicle body of high-speed trains is divided into two-dimensional elastic vibration,which is dominated by vertical vibration,and three-dimensional elastic vibration,which is multi-directional vibration,according to the vibration characteristics.For the vertical elastic vibration,instead of treating the car body as a homogeneous elastic beam,the equivalent model of vertical vibration is established based on the variable-section Timoshenko or Euler beam theory using the transfer matrix method.Based on the two-dimensional variable-section beam body vibration equations,a vehicle vertically dynamic model is established including the variable-section body.The effect of different vehicle body modelling methods and calculation methods on the vehicle dynamic response is analysed using actual vehicle parameters as an example,and compared with commercial dynamics software for verification.The results show that the dynamics model based on variable-section Timoshenko beams is closer to the results of commercial dynamics calculations in terms of both vibration response and dynamics indexes,and is also flexible in terms of modelling and fast in terms of calculation speed.Secondly,for the three-dimensional elastic body,the Hamilton equations for a multi-plate coupled body are established based on Mindlin’s theory of elastic vibration in thick plates.The analytical solution of the vibration equation is given by using the energy generalisation principle and the improved Fourier series method.The computational efficiency and accuracy of the proposed method are also verified by comparison with the finite element method.Finally,based on the analytical model,the energy method is used to model the three-dimensional dynamics of the whole vehicle including the three-dimensional elastic body and bogie.The method is also used to compare with the results of commercial dynamics software calculations,and the errors can meet engineering needs and enable vibration transfer analysis and custom calculations.At the same time,in order to compensate for the errors between the analytical model and the actual test model,a vehicle dynamics model correction method based on the Kriging approximation model is proposed.By constructing a multi-objective function containing frequency response functions of multiple measurement points to consider the whole vehicle vibration.Secondly,the Kriging numerical approximation model is used instead of the analytical model to avoid the complex calculation of the analytical model in the correction process.The model is then combined with the particle swarm method and the mode search method to obtain the amount of parameters to be corrected for the analytical model.The method is combined with the measured vehicle data to modify the analytical dynamics model,and the rationality and applicability of the method is verified.Then,on the basis of the established analytical dynamics model containing the three-dimensional elastic vehicle body,the study of abnormal vibration of the vehicle body is carried out.The analysis of the coupled vibration modes and excitation transmission paths is carried out through the analysis of the measured data and the replication of the analytical model,and the main forms and processes of the abnormal vibration of the shaking vehicle are identified.The modal covariance characteristics of the whole vehicle are then investigated to reveal the relationship between the effect of speed change on vehicle stability and frequency steering.Finally,the "modal localisation" theory is introduced to explain the shaking phenomenon caused by bogie snaking,laying the foundation for subsequent abnormal vibration control.Finally,in order to control the elastic vibration of the car body,it is divided into whole car vibration and local vibration according to the characteristics of the car body vibration.For the whole-vehicle vibration dominated by vertical bending,a random response synthesis method considering multi-point vibration is proposed based on statistical methods,and parameter uncertainty and interval analysis methods are used to define the whole-vehicle modal frequencies and responses and give the upper and lower limits of vibration performance.The optimum parameter configuration is also given by means of an optimisation design approach.The optimal configuration of the kinetic parameters is based on modal tracking,and the transmission path is cut off to ensure that the vehicle does not shake at high tread taper.The optimisation results show that the proposed method is effective in suppressing shuddering vibrations and has no significant effect on other dynamic parameters.For the local vibration of the floor and other structures,two methods are used to control the vibration from the perspective of passive control,namely non-homogeneous multiple power absorbers and net power flow,from the wide-frequency and multi-modal perspectives respectively.A conjugate gradient descent method based on partial derivatives is proposed for the optimization of the absorber parameters.Finally,the proposed control method is applied to high-speed train floor vibration control,and the results show that the proposed method has significant control effects in both time and frequency domains.