The Dynamic Response Of Periodic Viaduct To Moving Spring-mass

Periodic viaduct is an important part of modern transportation system.Hence,the research on how to control the vibration of viaduct under the action of vehicles is very important.This article has established the dynamic response calculation model of rigid supported periodic viaduct and pile supported periodic viaduct under the action of spring-mass system based on the method of Fourier series,Fourier transform,sequential Fourier transform,finite element method and boundary element method.Then,the resonance and vibration elimination characteristics of viaduct are numerically simulated.The content of this paper can be divided into the following three parts.(1)Dynamic response of rigidly supported periodic viaduct(RPV)under the action of a spring-mass system(SMS).Firstly,the contact force of wheel-rail is expanded into a series of load components by Fourier series,and the wave number and frequency domain(FWD)dynamic response expression of RPV under unit load component is obtained by double Fourier transform.The dynamic response of RPV under unit harmonic load can be obtained by using the finite element equation of each span beam and pier of RPV,the connection condition of beam-beampier connection and the periodic condition of each span of RPV under harmonic load.The dynamic response of RPV caused by unit harmonic moving load can be obtained using the above basic solutions,the Fourier coefficients of contact force and spring restoring force can be calculated by using the dynamic equation of SMS.Finally,the total response of RPV and the SMS itself can be obtained by using the solution of Fourier coefficients and the unit harmonic moving load solution of RPV.(2)Dynamic response calculation model of rigidly supported periodic viaduct(RPV)under the action of series spring-mass system(SMS).Similarly,the contact forces acting on the viaducts by each SMS are decomposed into a series of harmonic moving load components by Fourier series expansion.The dynamic response of RPV under moving load component of each order can be obtained based on the fundamental solution of unit harmonic load.The dynamic equation of series SMS can be established according to the coupling condition,then,the Fourier coefficients of interaction force and spring restoring force of SMS series can be obtained according to the dynamic equation.Finally,the dynamic response of RPV under the action of series SMS and the dynamic response of series SMS itself can be obtained by using the Fourier coefficients and the solution caused by unit harmonic moving load.(3)Dynamic response of periodic viaduct supported by pile foundation(PPV)under the action of series spring-mass system.The flexibility of pile foundation is calculated by the boundary element model of pile-soil.The interaction force is also expanded into Fourier series by using Fourier transform and sequential Fourier transform.The dynamic response of PPV under the action of SMS series and the dynamic response of SMS series itself can be determined by using the method similar to RPV by adding the flexibility matrix of the pile foundation.The different dynamic response between PPV and RPV under the action of serial mobile SMS has compared through the above model.Finally,the difference resonance and vibration elimination characteristics between PPV and RPV are also explored.Numerical results show that the moving speed of spring-mass system will affect the number of peak responses in the frequency domain of the viaduct.When the frequency of contact force is close to the natural frequency of SMS system,the response of bridge will increase.The superposition of response caused by different spring-mass system will also cause the resonance of viaduct,vehicles with different speed have different resonance and damping distance.The shear dissipation speed of viaduct is much faster than that of resonance in the case of vibration elimination,which can be seen from the number of vibration in the time domain.When the bottom of the pier is supported by the pile foundation,the vibration energy of the beam will transfer to the pile because of the displacement of pier.Although the main vibration frequency of beam is unchanged when supported by pile foundation,the peak shear force and displacement in the middle of the span will decrease compared with RPV.Moreover,the vibration frequency of the bottom section of the pier is lower than beam section,so the shear attenuation at the bottom of the pile is very slow..