Research On Maximum Vibration Response And Control Of High Speed Railway Bridges Based On Frequency Domain

In order to ensure the safe and high-quality operation of high-speed railway,bridge has become the first choice of high-speed railway construction.With the increase of train speed,the time of train acting on the bridge becomes shorter and shorter,and the time of free vibration of bridge is much longer than that of forced vibration.And because of the small damping of the bridge,the amplitude of the free vibration response of the bridge decreases slowly.Therefore,the research on bridge free vibration appears to be very important.In this paper,the maximum response of free vibration of railway beam bridge under moving loads and the control of bridge vibration by tuned mass damper are analyzed in detail.The main content and research results of this article are as follows:1.To establish the relationship between the operating speed of train and the bridge’s maximum displacement response of bridge more effectively,a frequency domain analysis method was proposed for the maximum displacement response of bridge under a single moving load excitation.The Fourier transform was used to derive the moving load spectrum and the bridge vibration displacement response spectrum when a single moving load passes through the beam bridge at a constant speed.The moving load speed causing the extreme response of bridge free vibration displacement was obtained by analyzing the moving load amplitude spectrum,and a calculation formula for the moving load speed causing the maximum displacement response of bridge free vibration was proposed.Taking a simple supported beam as an example,the correctness of the numerical calculation procedure in this paper was verified by comparing with the results of related literature.Based on this procedure,the correctness of frequency domain analysis method and the accuracy of moving load speed formula were verified by the numerical analysis.Research result shows that the moving load amplitude spectrum obtained in the frequency domain is consistent with the amplitude response law of the free vibration of bridge obtained in the time domain,so the moving load amplitude spectrum can effectively reflect the free vibration of displacement response of bridge.The moving load speed corresponding to the maximum displacement response of bridge free vibration is equal to that corresponding to the maximum amplitude spectrum of moving load,and the moving load speeds corresponding to other extreme points of moving load amplitude spectrum are also consistent with those of the extreme points in the displacement response of bridge free vibration.In the free vibration phase,the speed of single moving load leading to the maximum bridge displacement response is only related to the natural frequency and span of bridge.When a single moving load passes through a bridge at the resonant speed,the responses of forced and free vibration displacements are not themaximum response.Therefore,for the train operation speed of high-speed railway bridges,in addition to the train resonance speed,more attention should be paid to the speed causing the maximum displacement response of bridge.When the bridge vibration cancellation phenomena occur under multiple moving loads,the cancellation speed of moving loads is not only related to the fundamental frequency of the bridge and the distance between moving loads,but also to the span of the bridge and the number of moving loads.2.In order to ensure that the bridge dynamic response caused by the train under high-speed operation is within the safe range,it is particularly important to establish the relationship between the train operation speed and the bridge displacement response amplitude.In this paper,the relationship between the maximum displacement response of the bridge free vibration and the load speed is obtained by the frequency domain analysis method.The method uses the Fourier transform on the equation of motion of the bridge to obtain the displacement response spectrum and the moving load spectrum of the bridge when multiple moving loads are applied to the bridge.And Based on the moving load spectrum,the dimensionless speed? and the span ratio? are derived,and then the relationship between the moving load speed and the maximum displacement response of the bridge is established.And by analyzing the moving load spectrum,the relationship between the moving load speed and the bridge vibration-damping effect is also established.Finally,railway simply supported beam is taken as examples to verify the correctness of the theoretical analysis and the validity of the speed formula.The moving load amplitude spectrum obtained by the frequency-domain analysis method can effectively reflect the bridge free vibration,and the moving load amplitude spectrum is consistent with the bridge free vibration amplitude response law obtained from the time-domain angle;The maximum resonance speed of the bridge under multiple moving loads is related not only to the fundamental frequency and span of the bridge but also to the distance between moving loads.3.This paper proposes a frequency-domain analysis method of bridge vibration that can consider the influence of TMD.In this method,the time-domain motion equation of bridge-TMD under moving concentrated loads excitation is first established;Then,the equation of motion is Fourier transformed to obtain the displacement response spectrum of bridge based on TMD device;Then,the 2-norm of the displacement response spectrum of the bridge is optimized by the augmented Lagrangian optimization method to obtain the optimal TMD parameters;Finally,numerical simulations verify the superiority of this method over the traditional optimization method(Den Hartog)in terms of maximum displacement control,And the effects of bridge damping ratio,number of loads,and load axle-span ratio on the optimal parameters and effectiveness of TMD to control the maximum displacement response of the bridge were studied.The results show that: Using the augmented Lagrangian optimization method to optimize the 2-norm of the displacement response spectrum of the bridge can not only effectively analyze the influence of each bridge and loads parameters on the selection of TMD optimal parameters,but also it can also reasonably configure TMD parameters for all kinds of simply supported beam Bridges,which can provide references forpractical engineering applications.