Parametric Vibration Of Nonlinear Multi-parameter Flow Pipeline System

As an important engineering structure,the pipeline is widely used in many engineering fields,such as hydrodynamic engineering,mining engineering,oil and gas transportation,nuclear power equipment and so on.In the actual engineering,the safety and durability of the pipeline are becoming more and more prominent.The research on the coupling dynamics of the pipeline can not only provide important reference for the normal operation design of the pipeline,but also have very important academic value in the field of fluid-solid coupling mechanics.In this paper,the nonlinear dynamic behavior of nonlinear multi-parameter pipeline system is studied.The complex bifurcation path and chaotic motion of coupled pipelines under multi-parameter combination are investigated.By numerical calculation,the bifurcation diagram,phase plan and Poincare section diagram are used to analyze the nonlinear dynamic response of the system.The following results are obtained:(1)The nonlinear dynamic behavior of pipelines conveying fluid on two-parameter nonlinear elastic foundation under distributed follower force is studied.The effects of mean flow velocity,distribution follower force and shear stiffness of foundation on periodic and chaotic motions of the system are discussed.The results show that with the continuous change of the follower forces,the vibration state of the system transitions from period to chaos,and the amplitude of vibration increases gradually.It can be seen that the follower force is not conducive to system stability;the shear stiffness of the foundation has periodic motion and chaotic motion of the system.when the shear stiffness reaches a certain value,the system is in a steady state.Considering the follower force,the system needs greater shear stiffness to reach a stable state.(2)The nonlinear dynamic behavior of a coupled system of two parallel pipelines under distributed follower forces is studied.The influence of the distribution follower force and linear connection stiffness between the two simple supported pipelines on the dynamic characteristics of the system is discussed.The results show that when the connection stiffness between the coupled pipelines is small,the dynamic response of the two pipelines is different,the synchronization phenomenon will not be obvious.When the connection stiffness between the coupled pipelines is large enough,the dynamic behavior with the connection stiffness as the control parameter can be observed.The system exhibits abundant dynamic behavior,including periodic motion,almost periodic motion and chaotic motion.When the connection stiffness is large enough,the system will always be in periodic motion.It can be seen that the chaotic motion and almost periodic motion of the system can be suppressed when the connection stiffness between the coupled pipelines is large enough.(3)The nonlinear dynamic behavior of a cantilever pipeline under combinedexcitation of foundation excitation and pulsating flow is studied.The variation of system motion state with excitation frequency and phase difference is discussed.The results show that under the basic excitation,the system has a very rich dynamic response,including periodic,almost periodic and chaotic motion.Under the action of pulsating excitation,the system enters and leaves chaos through the jump of the motion pattern,and finally the periodic motion.Under the joint action of the basic excitation and the pulsation excitation,when the basic excitation frequency is equal to the pulsation frequency,the system is chaotic motion when the excitation frequency is low.As the excitation frequency increases,the system response will eventually transition to the cycle through intermittent bursts of chaos Movement;when the system base excitation and pulsation excitation are close but not equal,the system will behave as chaotic and other complex motions;when the pulsation excitation and the basic excitation frequency differ greatly,the system response is basically the same as when only the basic excitation is considered.When the excitation frequency of the basic excitation and the pulsating internal current is the same and the phase difference is small,the motion pattern of the system changes drastically.There are two forms of transition from chaos to chaos:period doubling bifurcation and jumping transition of the vibration pattern.