Research On The Influence Of Viscoelastic Materials On Vibration Control Of The Periodic Viaduct

In order to realize the vibration control of the periodic elevated railway,in this paper,the periodic viaduct beam and beam-beam-pier in the upper structure(BBP)of joint bearing with viscoelastic materials respectively,and based on the basic theory of viscoelasticity and the vibration equation of bridge piers and beams were established using viscoelastic materials of the periodic viaduct band calculation model and the dynamic response model,and analysis of viscoelastic beam respectively complex modulus and viscoelastic support complex stiffness to the influence of the band diagram,and the quality of the viscoelastic material factor’s influence on the seismic response of the periodic viaduct.The research contents of this paper mainly include:(1)Influence of viscoelasticity on natural vibration characteristics of the periodic elevated railway with the rigid support.In this part,the influence of viscoelasticity of beam and beam-beam-pier(BBP)joints in the superstructure on the natural vibration characteristics of the periodic elevated railway is considered.Using the transfer matrix method and the Bloch theorem,the energy band calculation model is established for the periodic viaduct with viscoelastic beam or viscoelastic support to generate in-plane and out-of-plane vibrations.By applying the transfer matrix between the beam and the pier,the connection conditions at the junction between the beam and the pier,and the Bloch theorem,the characteristic equations of the periodic elevated railway with complex modulus and complex stiffness for the beam and the support are obtained respectively.Based on the characteristic equation,the influence of the complex modulus of the beam and the complex stiffness of the support on the energy band of the structure is analyzed,and the wave propagation control in the structure is compared.The numerical results show that there are three kinds of characteristic waves in the periodic viaduct with in-plane and out-of-plane vibration,and the viscoelasticity of beam and support has little effect on the band of the first wave and the second wave.However,viscoelasticity has a significant influence on the number and width of forbidden band in the band diagram of the third wave,and the wave propagation is effectively controlled within a certain frequency forbidden band.(2)Influence of viscoelasticity on natural vibration characteristics of the periodic elevated railway supported by pile foundation.The flexibility of pile foundation is obtained by coupling boundary element model of pile-soil system.Application of the proceeds of the pile foundation flexibility,beam and pierto transfer matrix,BBP coupling conditions and joint Bloch theorem,respectively for viscoelastic beam and viscoelastic bearing the face of the inside and outside the surface vibration of the characteristic equation of a periodic elevated railway,based on the characteristic equation,respectively,analysis of viscoelastic beam complex modulus and viscoelastic support complex stiffness effect on the band.The numerical results show that the complex modulus and complex stiffness have little influence on the first wave and the second wave,but have significant influence on the number and width of the quasi-forbidden band in the imaginary part of the third wave number,whether it is in-plane vibration or out-plane vibration.(3)Influence of viscoelasticity on dynamic response of the periodic elevated railway with rigid support.The dynamic response model of viaduct under Rayleigh wave is established by using viscoelastic material at the junction of beam and BBP,according to the basic viscoelastic theory and the vibration equation of bridge pier and beam,and by using the transfer matrix method and the periodic condition of the periodic viaduct under harmonic Rayleigh wave.Based on the dynamic response model of the periodic viaduct,the influence of quality factors of viscoelastic materials on the dynamic response of the periodic viaduct under Rayleigh wave is analyzed,so as to verify the influence of viscoelastic material damping on the natural vibration characteristics of the periodic high-speed railway.The numerical results show that,compared with the undamped one,the damped one reduces the common amplitude of the wave at the pass-band edge or in the pass-band,or makes the resonance phenomenon at some pass-band edge disappear.Due to the damping of viscoelastic materials,the common amplitude value of the wave in the pass-band frequency decreases,or the number of resonance peaks decreases.