Nonlinear Dynamics Of Coupled Pipe System Conveying Fluid

The vibration stability and nonlinear dynamics of coupled pipe system are studied in the present paper. Three typical coupled pipe systems are considered in the current work: (1) fluid-conveying pipe-nonlinear elastic foundation system; (2) coupled two-pipe conveying fluid system; (3) coupled fluid-conveying pipe-beam system. The complex bifurcation path and chaotic motion of substructures of coupled pipe system are mainly investigated under different combination of system parameters. The semi-analytical methods employed to analyze the dynamical model of coupled pipe system, such as DTM, are also discussed. Based on numerical calculations, some interesting phenomena were observed, and some valuable results were put forward.(1) The vibration stability and nonlinear dynamical behavior of cantilevered fluid-conveying pipe-nonlinear elastic foundation system are studied. The equation of motion of a cantilevered pipe conveying fluid rested on nonlinear elastic foundation is obtained based on the nonlinear Pasternak foundation model. The internal resonance, mode exchange and nonlinear dynamics induced by internal flow are mainly investigated. Results show that the internal flow may induce 3:1 internal resonance,1:1 internal resonance; the shear stiffness has significant influence on the stability of the system; mode exchange may occur leading to the change of mode and type of instability with the variety of shear stiffness; the critical flow velocity corresponding to Hopf bifurcation increases and chaos may be controlled with the increasing of shear stiffness.(2) The forced vibration of cantilevered fluid-conveying pipe rested on nonlinear elastic foundation system under foundation excitation is further studied. The effect of excitation frequency and shear stiffness on the dynamical behavior of system is mainly investigated. The results demonstrate that the pipe system has complex response with the variation of foundation excitation, and period motions, quasi-periodic motions, chaos are observed; with the increase of foundation shear stiffness, the regions of quasi-periodic motions, chaos decrease. The system undergoes period motion with the variation of foundation excitation.(3) The dynamical behavior of simply supported pipe conveying pulsating fluid rested on nonlinear elastic foundation is studied. The influence of Galerkin mode truncation on the dynamics of the system is discussed. The results show that, the Galerkin mode truncation number may chose to be bigger when the forcing frequency is higher. Then, the Equation of motion of the pipe-foundation system is solved based on Galerkin method. Results show that, the shear stiffness has more significant influence on the dynamics of the system than linear stiffness and nonlinear stiffness. With the increasing of shear stiffness, the stability of the system can be reinforced and the chaotic motion may be controlled.(4) The nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The mean flow velocities of the two pipes are the same to each other. The pipe system is composed of two colligated pipes. The connection between two pipes taken into account is considered as a linear spring. Base on this consideration, the nonlinear equations of motion of the coupled two pipe system are derived, and solved numerically. The effect of connection stiffness and different combination of forcing frequencies on the dynamics of the system is explored. Results show that the connection stiffness has significant effect on the dynamic behavior of the coupled pipe system. The pipe system exhibits extremely rich dynamical behaviors when the connection stiffness is taken into account. The most interesting results obtained are that the motion types of the two pipes might be synchronous. The dynamical behavior may be very rich in different combination of the forcing frequencies, and in some cases, the stable response of the system is related to the initial conditions.(5) The nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid with different mean flow velocities is further studied. Two combinations of the mean flow velocities considered are:the mean flow velocity of one pipe is in sub-critical region, and of another is in super-critical region; the mean flow velocity of one pipe is in super-critical region, and of another is zero (considered as simply supported beam). Results show that, for two cases, the synchronous phenomenon can be observed; for different combinations, the coupled pipe system exhibits entire different dynamical behaviors; the dynamical response of the system is dominated by the pipe with the sub-critical mean flow velocity for case (1); the dynamical response of the system is dominated by both pipes for case (2).(6) The differential transformation method (DTM) is extended to analyze the vibration and stability of straight pipe conveying fluid. The vibration frequencies and critical velocities of different boundary conditions are obtained by using DTM and compared with that obtained by DQM and reported in Refs.[1,110]. Results show that, the DTM is an effective and precision method for solving the vibration problem of pipes conveying fluid. The calculation procedure of DTM does not get more complicated when the order of differential equation increases.From these contents listed above, the vibration stability and nonlinear dynamical behavior of coupled pipe system conveying are deeply investigated in the present paper. Especially, the bifurcations and chaotic mechanism of the coupled pipe system under different combination of system parameters are explored. The conclusions obtained in this study are significant for the design of pipes conveying fluid.