The vibration characteristics of transverse oscillation of an axially moving beam with high velocity is in- vestigated. The vibration equation and boundary conditions of the free-free axially moving beam are derived u...The vibration characteristics of transverse oscillation of an axially moving beam with high velocity is in- vestigated. The vibration equation and boundary conditions of the free-free axially moving beam are derived using Hamilton＇s principle. Furthermore, the linearized equations are set up based on Galerkinl s method for the ap- proximation solution. Finally, three influencing factors on the vibration frequency of the beam are considered： （1） The axially moving speed. The first order natural frequency decreases as the axial velocity increases, so there is a critical velocity of the axially moving beam. （2） The mass loss. The changing of the mass density of some part of the beam increases the beam natural frequencies. （3） The thermal effect.＇ The temperature increase will decrease the beam elastic modulus and induce the vibration frequencies descending.展开更多
The vehicle-track-bridge(VTB)element was used to investigate how a high-speed railway bridge reacted when it was subjected to near-fault directivity pulse-like ground motions.Based on the PEER NAG Strong Ground Motion...The vehicle-track-bridge(VTB)element was used to investigate how a high-speed railway bridge reacted when it was subjected to near-fault directivity pulse-like ground motions.Based on the PEER NAG Strong Ground Motion Database,the spatial analysis model of a vehicle-bridge system was developed,the VTB element was derived to simulate the interaction of train and bridge,and the elasto-plastic seismic responses of the bridge were calculated.The calculation results show that girder and pier top displacement,and bending moment of the pier base increase subjected to near-fault directivity pulse-like ground motion compared to far-field earthquakes,and the greater deformation responses in near-fault shaking are associated with fewer reversed cycles of loading.The hysteretic characteristics of the pier subjected to a near-fault directivity pulse-like earthquake should be explicitly expressed as the bending moment-rotation relationship of the pier base,which is characterized by the centrally strengthened hysteretic cycles at some point of the loading time-history curve.The results show that there is an amplification of the vertical deflection in the girder's mid-span owing to the high vertical ground motion.In light of these findings,the effect of the vertical ground motion should be used to adjust the unconservative amplification constant 2/3 of the vertical-to-horizontal peak ground motion ratio in the seismic design of bridge.展开更多
The dynamics of an axially accelerating beam subjected to axial flow is studied.Based on the Floquet theory and the Runge-Kutta algorithm,the stability and nonlinear vibration of the beam are analyzed by considering t...The dynamics of an axially accelerating beam subjected to axial flow is studied.Based on the Floquet theory and the Runge-Kutta algorithm,the stability and nonlinear vibration of the beam are analyzed by considering the effects of several system parameters such as the mean speed,flow velocity,axial added mass coefficient,mass ratio,slenderness ratio,tension and viscosity coefficient.Numerical results show that when the pulsation frequency of the axial speed is close to the sum of first-and second-mode frequencies or twice the lowest two natural frequencies,instability with combination or subharmonic resonance would occur.It is found that the beam can undergo the periodic-1 motion under subharmonic resonance and the quasi-periodic motion under combination resonance.With the change of system parameters,the stability boundary may be widened,narrowed or drifted.In addition,the vibration amplitude of the beam under resonance can also be affected by changing the values of system parameters.展开更多
In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilto...In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilton principle. The method of multiple scales is applied to analyze the nonlinear partial differential equation. The natural frequencies and modes are investigated by performing the complex mode approach. The effect of natural frequencies with the stiffness and the axial speeds are numerically demonstrated. The solvability conditions are established for the cases of without and with 3:1 internal resonances. The relationships between the nonlinear frequencies and the initial amplitudes at different axial speeds and the nonlinear coefficients are showed for the case of without internal resonances. The effects of the related coefficients are demonstrated for the case of 3:1 internal resonances.展开更多
基金Supported by the National Natural Science Foundation of China(10972104)~~
文摘The vibration characteristics of transverse oscillation of an axially moving beam with high velocity is in- vestigated. The vibration equation and boundary conditions of the free-free axially moving beam are derived using Hamilton＇s principle. Furthermore, the linearized equations are set up based on Galerkinl s method for the ap- proximation solution. Finally, three influencing factors on the vibration frequency of the beam are considered： （1） The axially moving speed. The first order natural frequency decreases as the axial velocity increases, so there is a critical velocity of the axially moving beam. （2） The mass loss. The changing of the mass density of some part of the beam increases the beam natural frequencies. （3） The thermal effect.＇ The temperature increase will decrease the beam elastic modulus and induce the vibration frequencies descending.
基金Project(2013CB036203)supported by the National Basic Research Program of ChinaProject(2013M530022)supported by China Postdoctoral Science Foundation+4 种基金Project(2013-K5-31)supported by Science and Technology Plan of Ministry of Housing and Urban-Rural Development of ChinaProject supported by High-level Scientific Research Foundation for the Introduction of Talent of Yangzhou University,ChinaProject supported by the Open Fund of the National Engineering Laboratory for High Speed Railway Construction,ChinaProject(IRT1296)supported by the Program for Changjiang Scholars and Innovative Research Team in University,ChinaProject(50908236)supported by the National Natural Science Foundation of China
文摘The vehicle-track-bridge(VTB)element was used to investigate how a high-speed railway bridge reacted when it was subjected to near-fault directivity pulse-like ground motions.Based on the PEER NAG Strong Ground Motion Database,the spatial analysis model of a vehicle-bridge system was developed,the VTB element was derived to simulate the interaction of train and bridge,and the elasto-plastic seismic responses of the bridge were calculated.The calculation results show that girder and pier top displacement,and bending moment of the pier base increase subjected to near-fault directivity pulse-like ground motion compared to far-field earthquakes,and the greater deformation responses in near-fault shaking are associated with fewer reversed cycles of loading.The hysteretic characteristics of the pier subjected to a near-fault directivity pulse-like earthquake should be explicitly expressed as the bending moment-rotation relationship of the pier base,which is characterized by the centrally strengthened hysteretic cycles at some point of the loading time-history curve.The results show that there is an amplification of the vertical deflection in the girder's mid-span owing to the high vertical ground motion.In light of these findings,the effect of the vertical ground motion should be used to adjust the unconservative amplification constant 2/3 of the vertical-to-horizontal peak ground motion ratio in the seismic design of bridge.
基金supported by the National Natural Science Foundation of China(Nos.11972167,12072119,12102139).
文摘The dynamics of an axially accelerating beam subjected to axial flow is studied.Based on the Floquet theory and the Runge-Kutta algorithm,the stability and nonlinear vibration of the beam are analyzed by considering the effects of several system parameters such as the mean speed,flow velocity,axial added mass coefficient,mass ratio,slenderness ratio,tension and viscosity coefficient.Numerical results show that when the pulsation frequency of the axial speed is close to the sum of first-and second-mode frequencies or twice the lowest two natural frequencies,instability with combination or subharmonic resonance would occur.It is found that the beam can undergo the periodic-1 motion under subharmonic resonance and the quasi-periodic motion under combination resonance.With the change of system parameters,the stability boundary may be widened,narrowed or drifted.In addition,the vibration amplitude of the beam under resonance can also be affected by changing the values of system parameters.
基金supported by the National Outstanding Young Scientists Foundation of China (Grant No. 10725209)the National Natural Science Foundation of China (Grant No. 90816001)+3 种基金Shanghai Subject Chief Scientist Project (Grant No. 09XD1401700)Innovation Foundation for Graduates of Shanghai University (Grant No. A.16-0401-08-005)Shanghai Leading Academic Discipline Project (Grant No. S30106)the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0844)
文摘In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilton principle. The method of multiple scales is applied to analyze the nonlinear partial differential equation. The natural frequencies and modes are investigated by performing the complex mode approach. The effect of natural frequencies with the stiffness and the axial speeds are numerically demonstrated. The solvability conditions are established for the cases of without and with 3:1 internal resonances. The relationships between the nonlinear frequencies and the initial amplitudes at different axial speeds and the nonlinear coefficients are showed for the case of without internal resonances. The effects of the related coefficients are demonstrated for the case of 3:1 internal resonances.
