Nonlinear Vibrations Of Axially Moving Slender Structure Subjected To Axial Flow

Axially moving slender structures have wide-spread applications in engineering field.Common examples include power transmission chains,elevator cables,band saw blades,paper sheets through copiers,textile fibers,magnetic tapes,robotic arms,crane and mining hoists.It is known that the vibration of axially moving slender structure has important influence on the engineering equipment and production process.Therefore,investigations on the dynamic of this axially moving system are of great importance and values in practical applications.There is a long history of research on the dynamics of axially moving system.However,in the previous studies,the interaction between structure and fluid was usually ignored.Although few works have taken the effect of fluid on dynamics of this axially moving system,the fluid is basically assumed to be stationary.Namely,the fluid does not flow.It is noted that axially moving slender structures in axial flows is a common Fluid-Structure-Interaction(FSI)problem in ocean engineering,underwater equipment and other applications.Motivated by this,nonlinear vibrations of axially moving slender structure in axial flow are investigated in this paper.The main features of the present paper are organized as follows:1.The stability and nonlinear dynamics of a sliding cantilevered pipe conveying fluid are investigated.Linear and nonlinear equations of motion for a sliding cantilevered pipe conveying fluid are constructed based on the force balance method and energy method,respectively,which verifies the correctness of the modeling.An extended Hamilton's principle is proposed and utilized to derive the nonlinear governing equation of motion for this special system.Particular attention is paid on the stability of the system and the nonlinear dynamical behavior of the pipe in the post-critical region.The obtained results indicate that the system can lose stability by flutter as the inner flow velocity reaches to a critical value and the existence of sliding rate can greatly reduce the critical flow velocity by comparing with the traditional pipe conveying fluid system.This reflects that the cantilevered pipe conveying fluid system is easier to lose stability during its sliding motion.In addition,the increase of the mass ratio and gravity parameter of the system can enhance its stability.2.A theoretical model of two-ends supported axially moving beam subjected to external axial flow was constructed.The nonlinear coupled vibration between the beam and axial external flow is explored.During the theoretical modeling,the viscous force generated by the axial external flow on the axially moving beam is derived in detail.The stability and nonlinear responses of this axially moving system are studied through linear and nonlinear analysis,respectively.Effects of external axial flow velocity,axially moving speed and other system parameters on dynamic behavior of the pipe are elaborately addressed.Results show that the beam loses stability by buckling at a certain critical moving speed.In the post-critical region,buckling and flutter instability occur alternately.Moreover,the motion pattern of the beam in flutter state is mainly periodic or quasi-periodic motion.3.The mathematical model and nonlinear governing equation are constructed for investigating the nonlinear dynamics of a two-ends supported axially accelerating beam subjected to external axial flow.Based on Floquet theory and linear analysis,effects of system parameters on the stability and natural frequency of the beam are analyzed.Numerical results indicate there exist instability regions in the first subharmonic resonance,second subharmonic resonance and summation resonance.Based on nonlinear analysis,the nonlinear vibration response of the beam in the resonance frequency region is investigated.Moreover,the nonlinear dynamical behavior of the beam in the post-critical region is discussed.Results show that the beam performs period-1 vibration and quasi-periodic in the subharmonic resonance region and summation resonance region respectively.In the post-critical instability region,period-1,period-2,period-3,period-4,multi-period,quasi-periodic and chaotic motions are discovered.And the dynamical behavior of the beam undergoes a complex evolution between these motions with the increase of the pulsating frequency.From these contents mentioned above,theoretical and numerical studies are carried out on the nonlinear coupled vibration between axial flow and axially moving slender structure in this paper.The stability and nonlinear dynamics of the structure are represented.Effect of axial flow on the axially moving system is obtained and analyzed.Moreover,rich dynamical behaviors of this Fluid-Structure-Interaction(FSI)system are detected.These investigations not only enrich the dynamics of axially moving system,but also contribute to the production and usage of related equipment in engineering applications.