Research On Active And Passive Control Of Vibration Of Rectangular Thin Plates Under Moving Load

The dynamic response of plates under moving loads is involved in many engineering fields.For example,vehicle-bridge coupling vibration can be simplified to plate vibration under moving loads.In this paper,the vibration response of plate subjected to moving loads is studied,and the passive and active control vibration reduction models are established.Main technical work of the paper:Firstly,based on the fundamental equation of free vibration of thin plate,the natural vibration equation of plate with additional lumped mass is deduced and solved by MATLAB,which proves that lumped mass can effectively reduce the natural vibration frequency of plate.The differential equation of forced vibration of plate under concentrated mass and moving load is established.The time-varying mass,stiffness,damping and load matrices are obtained by using modal superposition method.The time-varying matrix is solved by Newmark-β step integration method.By changing the position,magnitude and speed of moving load of the concentrated mass,the analysis of transverse displacement,velocity and acceleration at the center of the plate can be obtained.Secondly,aiming at the vibration problem of the plate with lumped mass under moving load,the passive control of the plate with dynamic vibration absorber is studied.According to Newton’s second law,the dynamic equation of simply supported plate under moving load,additional concentrated mass and dynamic vibration absorber is established.The displacement,velocity and acceleration of transverse vibration at any point on thin plate are obtained by solving the equation by Newmark-β step integration method.The above three parameters at the center of the plate are selected as the objective function of vibration control,and the effects of the mass,stiffness,damping and quantity of the absorber on the objective function are analyzed.Thirdly,based on the active control principle of structural vibration,the active vibration absorption problem of thin plate under moving load is studied,and the coupled response equation of plate and electromagnetic vibration absorber is calculated.The driving current of the absorber is selected as the input of the velocity feedback loop,and the vibration speed at the contact point between the fixed plate and the thin plate of the absorber is taken as the output of the velocity negative feedback loop.The relationship between the driving current and the vibration speed of the absorber is established.The change of the driving current in the feedback loop can control the vibration speed so as to realize the active vibration absorption.Fourthly,based on transient dynamics analysis,ANSYS is used to model the dynamic model under two working conditions,and HHT time integration method is used to solve the model.The results are extracted by time history post-processor.The displacement,velocity and acceleration curves at the center of the plate are extracted according to the coordinates of nodes.The results are compared with the simulation results of MATLAB.