The traditional lumped parameter model of fluid pipe is introduced and itsdrawbacks are pointed out. Furthermore, two suggestions are put forward to remove these drawbacks.Firstly, the structure of equivalent circuit ...The traditional lumped parameter model of fluid pipe is introduced and itsdrawbacks are pointed out. Furthermore, two suggestions are put forward to remove these drawbacks.Firstly, the structure of equivalent circuit is modified, and then the evaluation of equivalentfluid resistance is change to take the frequency-dependent function into account. Both simulationand experiment prove that this model is precise to characterize the dynamic behaviors of fluid inpipe.展开更多
Multi-constrained pipes conveying fluid,such as aircraft hydraulic control pipes,are susceptible to resonance fatigue in harsh vibration environments,which may lead to system failure and even catastrophic accidents.In...Multi-constrained pipes conveying fluid,such as aircraft hydraulic control pipes,are susceptible to resonance fatigue in harsh vibration environments,which may lead to system failure and even catastrophic accidents.In this study,a machine learning(ML)-assisted weak vibration design method under harsh environmental excitations is proposed.The dynamic model of a typical pipe is developed using the absolute nodal coordinate formulation(ANCF)to determine its vibrational characteristics.With the harsh vibration environments as the preserved frequency band(PFB),the safety design is defined by comparing the natural frequency with the PFB.By analyzing the safety design of pipes with different constraint parameters,the dataset of the absolute safety length and the absolute resonance length of the pipe is obtained.This dataset is then utilized to develop genetic programming(GP)algorithm-based ML models capable of producing explicit mathematical expressions of the pipe's absolute safety length and absolute resonance length with the location,stiffness,and total number of retaining clips as design variables.The proposed ML models effectively bridge the dataset with the prediction results.Thus,the ML model is utilized to stagger the natural frequency,and the PFB is utilized to achieve the weak vibration design.The findings of the present study provide valuable insights into the practical application of weak vibration design.展开更多
The dynamic stability in transverse vibration of a viscoelastic pipe for conveying puisative fluid is investigated for the simply-supported case. The material property of the beammodel pipe is described by the Kelvin-...The dynamic stability in transverse vibration of a viscoelastic pipe for conveying puisative fluid is investigated for the simply-supported case. The material property of the beammodel pipe is described by the Kelvin-type viscoelastic constitutive relation. The axial fluid speed is characterized as simple harmonic variation about a constant mean speed. The method of multiple scales is applied directly to the governing partial differential equation without discretization when the viscoelastic damping and the periodical excitation are considered small. The stability conditions are presented in the case of subharmonic and combination resonance. Numerical results show the effect of viscosity and mass ratio on instability regions.展开更多
This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support.The nonlinear equation of motion is derived by forces equilibrium on microelement ...This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support.The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration.The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method.The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter, nonlinear spring stiffness.Based on this,the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness.The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.展开更多
This paper deals with the three-dimensional dynamics and postbuckling behavior of flexible supported pipes conveying fluid, considering flow velocities lower and higher than the critical value at which the buckling in...This paper deals with the three-dimensional dynamics and postbuckling behavior of flexible supported pipes conveying fluid, considering flow velocities lower and higher than the critical value at which the buckling instability occurs. In the case of low flow velocity, the pipe is stable with a straight equilibrium position and the dynamics of the system can be examined using linear theory. When the flow velocity is beyond the critical value, any motions of the pipe could be around the postbuckling configuration(non-zero equilibrium position) rather than the straight equilibrium position, so nonlinear theory is required. The nonlinear equations of perturbed motions around the postbuckling configuration are derived and solved with the aid of Galerkin discretization. It is found, for a given flow velocity,that the first-mode frequency for in-plane motions is quite different from that for out-of-plane motions. However, the second-or third-mode frequencies for in-plane motions are approximately equal to their counterparts for out-of-plane motions, keeping almost constant values with increasing flow velocity. Moreover, the orientation angle of the postbuckling configuration plane for a buckled pipe can be significantly affected by initial conditions, displaying new features which have not been observed in the same pipe system factitiously supposed to deform in a single plane.展开更多
It is a new attempt to extend the differential quadrature method(DQM) to stability analysis of the straight and curved centerlinepipes conveying fluid. Emphasis is placed on the study of theinfluences of several param...It is a new attempt to extend the differential quadrature method(DQM) to stability analysis of the straight and curved centerlinepipes conveying fluid. Emphasis is placed on the study of theinfluences of several parameters on the critical flow velocity.Compared to other methods, this method can more easily deal with thepipe with spring support at its boundaries and asks for much lesscomputing effort while giving ac- ceptable precision in the numericalresults.展开更多
In the past decades,it has been reported that divergence is the expected form of instability for fluid-conveying pipes with both ends supported.In this paper,the form of instability of supported pipes conveying fluid ...In the past decades,it has been reported that divergence is the expected form of instability for fluid-conveying pipes with both ends supported.In this paper,the form of instability of supported pipes conveying fluid subjected to distributed follower forces is investigated.Based on the Pflu¨ger column model,the equation of motion for supported pipes subjected concurrently to internal fluid flow and distributed follower forces is established.The analytical model,after Galerkin discretization to two degrees of freedom,is evaluated by analyzing the corresponding eigenvalue problem.The complex frequencies versus fluid velocity are obtained for various system parameters.The results show that either buckling or flutter instabilities could occur in supported fluid-conveying pipes under the action of distributed follower forces,depending on the parameter values of distributed follower forces.展开更多
Based on the differential constitutive relationship of linearviscoelastic material, a solid-liquid coupling vibration equation forviscoelastic pipe conveying fluid is derived by the D'Alembert'sprinciple. The ...Based on the differential constitutive relationship of linearviscoelastic material, a solid-liquid coupling vibration equation forviscoelastic pipe conveying fluid is derived by the D'Alembert'sprinciple. The critical flow velocities and natural frequencies ofthe cantilever pipe conveying fluid with the Kelvin model (flutterinstability) are calculated with the modified finite differencemethod in the form of the recurrence for- mula. The curves betweenthe complex frequencies of the first, second and third mode and flowvelocity of the pipe are plotted. On the basis of the numericalcalculation results, the dynamic behaviors and stability of the pipeare discussed. It should be pointed out that the delay time ofviscoelastic material with the Kelvin model has a remarkable effecton the dynamic characteristics and stability behaviors of thecantilevered pipe conveying fluid, which is a gyroscopicnon-conservative system.展开更多
In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration...In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.展开更多
Applying the multidimensional Lindstedt-Poincare （MDLP） method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under ex- ternal periodic excitation. The frequency-am...Applying the multidimensional Lindstedt-Poincare （MDLP） method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under ex- ternal periodic excitation. The frequency-amplitude response curves of the first-mode resonance with internal resonance are obtained and its characteristics are discussed; moreover, the motions of the first two modes are also analyzed in detail. The present results reveal rich and complex dynamic behaviors caused by internal resonance and that some of the internal resonances are de- cided by the excitation amplitude. The MDLP method is also proved to be a simple and efficient technique to deal with nonlinear dynamics.展开更多
The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping r...The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.展开更多
The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid. The order magnitudes of relevant physical parameters are analyzed q...The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid. The order magnitudes of relevant physical parameters are analyzed qualitatively to establish a foundation on the further study of the model. The method of multiple scales is used to obtain eigenfunctions of the linear free-vibration modes of the pipe. The boundary conditions yield the characteristic equations from which eigenvalues can be derived. It is found that flow velocity in the pipe may induced the 3：1, 2：1 and 1：1 internal resonances between the first and second modes such that the mechanism of flow-induced internal resonances in the pipe under consideration is explained theoretically. The 3：1 internal resonance first occurs in the system and is, thus, the most important since it corresponds to the minimum critical velocity.展开更多
A theoretical model is developed for the vibration and stability of a vertical pipe subjected concurrently to two dependent axial flows. The external fluid, after exiting the outer annular region between the pipe and ...A theoretical model is developed for the vibration and stability of a vertical pipe subjected concurrently to two dependent axial flows. The external fluid, after exiting the outer annular region between the pipe and a rigid cylindrical channel, is conveyed upwards inside the pipe. This configuration thus resembles of a pipe that aspirating fluid. The equation of planar mo- tion is solved by means of the differential quadrature method （DQM）. Calculations are conducted for a slender drill-string-like and a bench-top-size system, for different confinement conditions of the outer annular channel. It is shown that the vibrations of these two systems are closely related to the degree of confinement of the outer annular channel. For a drill-string-like system with narrow annuli, buckling instability may occur in the second and third modes. For a bench-top-size system, however, both buckling and flutter may occur in the lowest three modes. The form of instability depends on the annuli size.展开更多
The stability and chaotic vibrations of a pipe conveying fluid with both ends fixed, excited by the harmonic motion of its supporting base in a direction normal to the pipe span, were investigated with the aid of mode...The stability and chaotic vibrations of a pipe conveying fluid with both ends fixed, excited by the harmonic motion of its supporting base in a direction normal to the pipe span, were investigated with the aid of modern numerical techniques,involving the phase portrait,Lyapunov exponent and Poincare map tc. The nonlinear differential equations of motion of the system were derived by considering the additional axial force due to the lateral motion of the pipe. Attention was concentrated on the effect of forcing frequency and flow velocity on the dynamics of the system. It is shown that chaotic motions can occur in this system in a certain region of parameter space,and it is also found that three types of routes to chaos exist in the system:(i)period doubling bifurcations;(ii)quasi periodic motions;and (iii)intermittent chaos.展开更多
In this paper,the nonlinear parametric vibration of fluid-conveying pipes flexibly restrained at both ends and subjected to the pulsation flow excitation is investigated.The nonlinear equation of motion is derived usi...In this paper,the nonlinear parametric vibration of fluid-conveying pipes flexibly restrained at both ends and subjected to the pulsation flow excitation is investigated.The nonlinear equation of motion is derived using Hamilton^principle by considering the Kevin-Voigt viscoelastic damping,the geometric nonlinearity and the translational and rotational springs supported at the ends.The mode functions and eigen-frequencies are determined by the assumed mode method according to the elastic boundary conditions.The Galerkin method is implemented to obtain the natural frequencies and mode shapes of the pipe conveying fluid with different flow velocities.The effects of flexibly restrained conditions on stability of the pipe are analyzed.The nonlinear responses of the pipe under pulsating flow excitation are solved by the direct numerical method.The vibration behaviors are discussed in details,such as time history,frequency spectrum,phase-plane portrait,Poincare map and motion trajectory.The results show that the responses of sub-harmonic resonance and combination resonance can also be reflected in the rigidly supported pipes.The 1/5,1/8 and 1/13 sub-harmonic resonances can occur at certain excitation frequencies of the nonlinear parametric vibration system.The steady-state response amplitudes increase by a large margin and significantly affect the stability of the pipe.The effects of different spring stiffness coefficients on the parametric resonance responses are presented.For larger translational springs and rotational stiffness coefficients,the resonance frequencies shift to higher regions and the resonance amplitudes may reduce by a certain extent in accordance with the rigid-body motion.This study can provide helpful guidance on the analysis and design of piping systems subject to vibrations.展开更多
The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force b...The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system （H-S） and standing system （S-S） are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.展开更多
In this work,the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model,with particular focus on the mechanism of large-amplitude oscillations of...In this work,the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model,with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity.Four key parameters,including the flow velocity,the mass ratio,the gravity parameter,and the inclination angle between the pipe length and the gravity direction,are considered to affect the static and dynamic behaviors of the soft pipe.The stability analyses show that,provided that the inclination angle is not equal to π,the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value.As the inclination angle is equal to π,the pipe experiences,in turn,buckling instability,regaining stability,and flutter instability with the increase in the flow velocity.Interestingly,the stability of the pipe can be either enhanced or weakened by varying the gravity parameter,mainly dependent on the value of the inclination angle.In the nonlinear dynamic analysis,it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations.Besides,the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.展开更多
In this study,the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional(3 D)theoretical model.Th...In this study,the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional(3 D)theoretical model.The complete nonlinear governing equations are discretized via Galerkin’s method and then numerically solved by the use of a fourth-order Runge-Kutta integration algorithm.Different initial conditions are chosen for calculations to show the nonplanar buckling characteristics of the pipe in two perpendicular lateral directions.A detailed parametric analysis is performed in order to study the influence of several key system parameters such as the mass ratio,the flow velocity,and the gravity parameter on the post-buckling behavior of the pipe.Typical results are presented in the form of bifurcation diagrams when the flow velocity is selected as the variable parameter.It is found that the pipe will stay at its original straight equilibrium position until the critical flow velocity is reached.Just beyond the critical flow velocity,the pipe would lose stability by static divergence via a pitchfork bifurcation,and two possible nonzero equilibrium positions are generated.It is shown that the buckling and post-buckling behaviors of the pipe cannot be influenced by the mass ratio parameter.Unlike a pipe with two immovable ends,however,the pinned-pinned pipe with an axially sliding downstream end shows some different features regarding post-buckling behaviors.The most important feature is that the buckling amplitude of the pipe with an axially sliding downstream end would increase first and then decrease with the increase in the flow velocity.In addition,the buckled shapes of the pipe varying with the flow velocity are displayed in order to further show the new post-buckling features of the pipe with an axially sliding downstream end.展开更多
Fluid-structure interaction （FSI） is essentially a dynamic phenomenon and always exists in fluid-filled pipe system. The four-equation model, which has been proved to be effective to describe and predict the phenome...Fluid-structure interaction （FSI） is essentially a dynamic phenomenon and always exists in fluid-filled pipe system. The four-equation model, which has been proved to be effective to describe and predict the phenomenon of FSI due to friction coupling and Poisson coupling being taken into account, is utilized to describe the FSI of fluid-filled pipe system. Terse compatibility equations are educed by the method of characteristics （MOC） to describe the fluid-filled pipe system. To shorten computing time needed to get the solutions under the condition of keeping accuracy requirement, two steps are adopted, firstly the time step Δt and divided number of the straight pipe are optimized, sec-ondly the mesh spacing Δz close to boundary is subdivided in several submeshes automatically ac-cording to the speed gradient of fluid. The mathematical model and arithmetic are validated by com-parisons between simulation solutions of two straight pipe systems and experiment known from lit-erature.展开更多
The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourth- order Runge-Kutta integration algorithm is ...The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourth- order Runge-Kutta integration algorithm is used as a numerical tool to solve the discretized equations. The self-excited vibration is briefly discussed first, focusing on the effect of flow velocity on the stability and post-flutter dynamical behavior of the pipe system with parameters close to those in previous experiments. Then, the nonlinear forced vibrations are examined using several concrete examples by means of frequency response diagrams and phase-plane plots. It shows that, at low flow velocity, the resonant amplitude near the first-mode natural frequency is larger than its counterpart near the second-mode natural frequency. The second-mode frequency response curve clearly displays a softening-type behavior with hysteresis phenomenon, while the first-mode frequency response curve almost maintains its neutrality. At moderate flow velocity, interestingly, the first-mode resonance response diminishes and the hysteresis phenomenon of the second-mode response disappears. At high flow velocity beyond the flutter threshold, the frequency response curve would exhibit a quenching-like behavior. When the excitation frequency is increased through the quenching point, the response of the pipe may shift from quasiperiodic to periodic. The results obtained in the present work highlight the dramatic influence of internal fluid flow on the nonlinear forced vibrations of slender Pipes.展开更多
基金This project is supported by National Natural Science Foundation of China (No.59875076).
文摘The traditional lumped parameter model of fluid pipe is introduced and itsdrawbacks are pointed out. Furthermore, two suggestions are put forward to remove these drawbacks.Firstly, the structure of equivalent circuit is modified, and then the evaluation of equivalentfluid resistance is change to take the frequency-dependent function into account. Both simulationand experiment prove that this model is precise to characterize the dynamic behaviors of fluid inpipe.
基金Project supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(No.12421002)the National Science Funds for Distinguished Young Scholars of China(No.12025204)+1 种基金the National Natural Science Foundation of China(No.12372015)China Scholarship Council(No.202206890065)。
文摘Multi-constrained pipes conveying fluid,such as aircraft hydraulic control pipes,are susceptible to resonance fatigue in harsh vibration environments,which may lead to system failure and even catastrophic accidents.In this study,a machine learning(ML)-assisted weak vibration design method under harsh environmental excitations is proposed.The dynamic model of a typical pipe is developed using the absolute nodal coordinate formulation(ANCF)to determine its vibrational characteristics.With the harsh vibration environments as the preserved frequency band(PFB),the safety design is defined by comparing the natural frequency with the PFB.By analyzing the safety design of pipes with different constraint parameters,the dataset of the absolute safety length and the absolute resonance length of the pipe is obtained.This dataset is then utilized to develop genetic programming(GP)algorithm-based ML models capable of producing explicit mathematical expressions of the pipe's absolute safety length and absolute resonance length with the location,stiffness,and total number of retaining clips as design variables.The proposed ML models effectively bridge the dataset with the prediction results.Thus,the ML model is utilized to stagger the natural frequency,and the PFB is utilized to achieve the weak vibration design.The findings of the present study provide valuable insights into the practical application of weak vibration design.
基金Project supported by the National Natural Science Foundation of China (No.10372063).
文摘The dynamic stability in transverse vibration of a viscoelastic pipe for conveying puisative fluid is investigated for the simply-supported case. The material property of the beammodel pipe is described by the Kelvin-type viscoelastic constitutive relation. The axial fluid speed is characterized as simple harmonic variation about a constant mean speed. The method of multiple scales is applied directly to the governing partial differential equation without discretization when the viscoelastic damping and the periodical excitation are considered small. The stability conditions are presented in the case of subharmonic and combination resonance. Numerical results show the effect of viscosity and mass ratio on instability regions.
基金Project supported by the National Natural Science Foundation of China(No.10272051).
文摘This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support.The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration.The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method.The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter, nonlinear spring stiffness.Based on this,the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness.The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.
基金supported by the National Natural Science Foundation of China (Grants 11602090, 11622216, and 11672115)
文摘This paper deals with the three-dimensional dynamics and postbuckling behavior of flexible supported pipes conveying fluid, considering flow velocities lower and higher than the critical value at which the buckling instability occurs. In the case of low flow velocity, the pipe is stable with a straight equilibrium position and the dynamics of the system can be examined using linear theory. When the flow velocity is beyond the critical value, any motions of the pipe could be around the postbuckling configuration(non-zero equilibrium position) rather than the straight equilibrium position, so nonlinear theory is required. The nonlinear equations of perturbed motions around the postbuckling configuration are derived and solved with the aid of Galerkin discretization. It is found, for a given flow velocity,that the first-mode frequency for in-plane motions is quite different from that for out-of-plane motions. However, the second-or third-mode frequencies for in-plane motions are approximately equal to their counterparts for out-of-plane motions, keeping almost constant values with increasing flow velocity. Moreover, the orientation angle of the postbuckling configuration plane for a buckled pipe can be significantly affected by initial conditions, displaying new features which have not been observed in the same pipe system factitiously supposed to deform in a single plane.
基金National Key Project of China (No.PD9521907)the National Science Foundation of China (No.19872025).
文摘It is a new attempt to extend the differential quadrature method(DQM) to stability analysis of the straight and curved centerlinepipes conveying fluid. Emphasis is placed on the study of theinfluences of several parameters on the critical flow velocity.Compared to other methods, this method can more easily deal with thepipe with spring support at its boundaries and asks for much lesscomputing effort while giving ac- ceptable precision in the numericalresults.
基金supported by the National Natural Science Foundation of China (Nos. 10802031 and 11172107)the Program for New Century Excellent Talents in Universitythe Fundamental Research Funds for the CentralUniversities,HUST (grant number 2010MS021)
文摘In the past decades,it has been reported that divergence is the expected form of instability for fluid-conveying pipes with both ends supported.In this paper,the form of instability of supported pipes conveying fluid subjected to distributed follower forces is investigated.Based on the Pflu¨ger column model,the equation of motion for supported pipes subjected concurrently to internal fluid flow and distributed follower forces is established.The analytical model,after Galerkin discretization to two degrees of freedom,is evaluated by analyzing the corresponding eigenvalue problem.The complex frequencies versus fluid velocity are obtained for various system parameters.The results show that either buckling or flutter instabilities could occur in supported fluid-conveying pipes under the action of distributed follower forces,depending on the parameter values of distributed follower forces.
文摘Based on the differential constitutive relationship of linearviscoelastic material, a solid-liquid coupling vibration equation forviscoelastic pipe conveying fluid is derived by the D'Alembert'sprinciple. The critical flow velocities and natural frequencies ofthe cantilever pipe conveying fluid with the Kelvin model (flutterinstability) are calculated with the modified finite differencemethod in the form of the recurrence for- mula. The curves betweenthe complex frequencies of the first, second and third mode and flowvelocity of the pipe are plotted. On the basis of the numericalcalculation results, the dynamic behaviors and stability of the pipeare discussed. It should be pointed out that the delay time ofviscoelastic material with the Kelvin model has a remarkable effecton the dynamic characteristics and stability behaviors of thecantilevered pipe conveying fluid, which is a gyroscopicnon-conservative system.
基金Project supported by the National Natural Science Foundation of China(Nos.11172107 and 11172109)the Program for New Century Excellent Talents in University(No.NCET-11-0183)
文摘In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.
基金the National Natural Science Foundation of China (Nos. 10702045 and 10872135)the Aerospace Foundation of China (No. 2009ZA018)the Natural Science Foundation of Liaoning Province (No. 2009A572)
文摘Applying the multidimensional Lindstedt-Poincare （MDLP） method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under ex- ternal periodic excitation. The frequency-amplitude response curves of the first-mode resonance with internal resonance are obtained and its characteristics are discussed; moreover, the motions of the first two modes are also analyzed in detail. The present results reveal rich and complex dynamic behaviors caused by internal resonance and that some of the internal resonances are de- cided by the excitation amplitude. The MDLP method is also proved to be a simple and efficient technique to deal with nonlinear dynamics.
基金Project supported by the National Science and Technology Major Project(NMP)of China(No.2013ZX04011-011)
文摘The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.
基金Project supported by the National Natural Science Foundation of China (No.10472083) and the National Natural Science Key Foundation of China (No.10532050)
文摘The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid. The order magnitudes of relevant physical parameters are analyzed qualitatively to establish a foundation on the further study of the model. The method of multiple scales is used to obtain eigenfunctions of the linear free-vibration modes of the pipe. The boundary conditions yield the characteristic equations from which eigenvalues can be derived. It is found that flow velocity in the pipe may induced the 3：1, 2：1 and 1：1 internal resonances between the first and second modes such that the mechanism of flow-induced internal resonances in the pipe under consideration is explained theoretically. The 3：1 internal resonance first occurs in the system and is, thus, the most important since it corresponds to the minimum critical velocity.
基金supported by the National Natural Science Foundation of China (Nos. 10772071 and 10802031)theScientific Research Foundation of HUST (No. 2006Q003B).
文摘A theoretical model is developed for the vibration and stability of a vertical pipe subjected concurrently to two dependent axial flows. The external fluid, after exiting the outer annular region between the pipe and a rigid cylindrical channel, is conveyed upwards inside the pipe. This configuration thus resembles of a pipe that aspirating fluid. The equation of planar mo- tion is solved by means of the differential quadrature method （DQM）. Calculations are conducted for a slender drill-string-like and a bench-top-size system, for different confinement conditions of the outer annular channel. It is shown that the vibrations of these two systems are closely related to the degree of confinement of the outer annular channel. For a drill-string-like system with narrow annuli, buckling instability may occur in the second and third modes. For a bench-top-size system, however, both buckling and flutter may occur in the lowest three modes. The form of instability depends on the annuli size.
基金Supported by the Science Foundation of Liaoning Province Government!( 96 2 1 2 9)
文摘The stability and chaotic vibrations of a pipe conveying fluid with both ends fixed, excited by the harmonic motion of its supporting base in a direction normal to the pipe span, were investigated with the aid of modern numerical techniques,involving the phase portrait,Lyapunov exponent and Poincare map tc. The nonlinear differential equations of motion of the system were derived by considering the additional axial force due to the lateral motion of the pipe. Attention was concentrated on the effect of forcing frequency and flow velocity on the dynamics of the system. It is shown that chaotic motions can occur in this system in a certain region of parameter space,and it is also found that three types of routes to chaos exist in the system:(i)period doubling bifurcations;(ii)quasi periodic motions;and (iii)intermittent chaos.
基金the National Natural Science Foundation of China(Grant No.51305350,Grant No.11802235)National Key Basic Research Program of China(Grant No.613268)Aeronautics Power Foundation Program of China(Grant No.6141B090320).
文摘In this paper,the nonlinear parametric vibration of fluid-conveying pipes flexibly restrained at both ends and subjected to the pulsation flow excitation is investigated.The nonlinear equation of motion is derived using Hamilton^principle by considering the Kevin-Voigt viscoelastic damping,the geometric nonlinearity and the translational and rotational springs supported at the ends.The mode functions and eigen-frequencies are determined by the assumed mode method according to the elastic boundary conditions.The Galerkin method is implemented to obtain the natural frequencies and mode shapes of the pipe conveying fluid with different flow velocities.The effects of flexibly restrained conditions on stability of the pipe are analyzed.The nonlinear responses of the pipe under pulsating flow excitation are solved by the direct numerical method.The vibration behaviors are discussed in details,such as time history,frequency spectrum,phase-plane portrait,Poincare map and motion trajectory.The results show that the responses of sub-harmonic resonance and combination resonance can also be reflected in the rigidly supported pipes.The 1/5,1/8 and 1/13 sub-harmonic resonances can occur at certain excitation frequencies of the nonlinear parametric vibration system.The steady-state response amplitudes increase by a large margin and significantly affect the stability of the pipe.The effects of different spring stiffness coefficients on the parametric resonance responses are presented.For larger translational springs and rotational stiffness coefficients,the resonance frequencies shift to higher regions and the resonance amplitudes may reduce by a certain extent in accordance with the rigid-body motion.This study can provide helpful guidance on the analysis and design of piping systems subject to vibrations.
基金Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(No.51221004)the National Natural Science Foundation of China(Nos.11172260,11072213,and 51375434)the Higher School Specialized Research Fund for the Doctoral Program(No.20110101110016)
文摘The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system （H-S） and standing system （S-S） are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.
基金Project supported by the National Natural Science Foundation of China(Nos.11672115,11622216,and 11972167)。
文摘In this work,the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model,with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity.Four key parameters,including the flow velocity,the mass ratio,the gravity parameter,and the inclination angle between the pipe length and the gravity direction,are considered to affect the static and dynamic behaviors of the soft pipe.The stability analyses show that,provided that the inclination angle is not equal to π,the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value.As the inclination angle is equal to π,the pipe experiences,in turn,buckling instability,regaining stability,and flutter instability with the increase in the flow velocity.Interestingly,the stability of the pipe can be either enhanced or weakened by varying the gravity parameter,mainly dependent on the value of the inclination angle.In the nonlinear dynamic analysis,it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations.Besides,the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.
基金Project supported by the National Natural Science Foundation of China(Nos.11622216,11602090,and 11672115)the Natural Science Foundation of Hubei Province(No.2017CFB429)the fundamental Research Funds for the Central Universities of China(No.2017KFYXJJ135)
文摘In this study,the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional(3 D)theoretical model.The complete nonlinear governing equations are discretized via Galerkin’s method and then numerically solved by the use of a fourth-order Runge-Kutta integration algorithm.Different initial conditions are chosen for calculations to show the nonplanar buckling characteristics of the pipe in two perpendicular lateral directions.A detailed parametric analysis is performed in order to study the influence of several key system parameters such as the mass ratio,the flow velocity,and the gravity parameter on the post-buckling behavior of the pipe.Typical results are presented in the form of bifurcation diagrams when the flow velocity is selected as the variable parameter.It is found that the pipe will stay at its original straight equilibrium position until the critical flow velocity is reached.Just beyond the critical flow velocity,the pipe would lose stability by static divergence via a pitchfork bifurcation,and two possible nonzero equilibrium positions are generated.It is shown that the buckling and post-buckling behaviors of the pipe cannot be influenced by the mass ratio parameter.Unlike a pipe with two immovable ends,however,the pinned-pinned pipe with an axially sliding downstream end shows some different features regarding post-buckling behaviors.The most important feature is that the buckling amplitude of the pipe with an axially sliding downstream end would increase first and then decrease with the increase in the flow velocity.In addition,the buckled shapes of the pipe varying with the flow velocity are displayed in order to further show the new post-buckling features of the pipe with an axially sliding downstream end.
文摘Fluid-structure interaction （FSI） is essentially a dynamic phenomenon and always exists in fluid-filled pipe system. The four-equation model, which has been proved to be effective to describe and predict the phenomenon of FSI due to friction coupling and Poisson coupling being taken into account, is utilized to describe the FSI of fluid-filled pipe system. Terse compatibility equations are educed by the method of characteristics （MOC） to describe the fluid-filled pipe system. To shorten computing time needed to get the solutions under the condition of keeping accuracy requirement, two steps are adopted, firstly the time step Δt and divided number of the straight pipe are optimized, sec-ondly the mesh spacing Δz close to boundary is subdivided in several submeshes automatically ac-cording to the speed gradient of fluid. The mathematical model and arithmetic are validated by com-parisons between simulation solutions of two straight pipe systems and experiment known from lit-erature.
基金supported by the National Natural Science Foundation of China (Nos. 11622216 and 51409134)
文摘The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourth- order Runge-Kutta integration algorithm is used as a numerical tool to solve the discretized equations. The self-excited vibration is briefly discussed first, focusing on the effect of flow velocity on the stability and post-flutter dynamical behavior of the pipe system with parameters close to those in previous experiments. Then, the nonlinear forced vibrations are examined using several concrete examples by means of frequency response diagrams and phase-plane plots. It shows that, at low flow velocity, the resonant amplitude near the first-mode natural frequency is larger than its counterpart near the second-mode natural frequency. The second-mode frequency response curve clearly displays a softening-type behavior with hysteresis phenomenon, while the first-mode frequency response curve almost maintains its neutrality. At moderate flow velocity, interestingly, the first-mode resonance response diminishes and the hysteresis phenomenon of the second-mode response disappears. At high flow velocity beyond the flutter threshold, the frequency response curve would exhibit a quenching-like behavior. When the excitation frequency is increased through the quenching point, the response of the pipe may shift from quasiperiodic to periodic. The results obtained in the present work highlight the dramatic influence of internal fluid flow on the nonlinear forced vibrations of slender Pipes.
