Fluid-conveying Pipe Research Articles

An Explanation for a Paradox in a Fluid-Discharging Cantilevered Pipe Attached With an End-Mass

Abstract For a fluid-discharging cantilevered pipe attached with an end-mass, there are two methods to account for the end-mass effect. The first is that the end-mass is considered in the boundary conditions. The second is that the end-mass is included in the equation of motion via a Dirac delta function. As the analytical solution of the linear free vibration model is not available due to the presence of Coriolis force, the eigenfunctions of a beam, which satisfy the same boundary conditions, are commonly employed in the Galerkin method. It has been found the first method is incorrect for natural frequency calculation when the internal flow velocity is nonzero. However, the intrinsic mechanism remains to be clarified. This study has demonstrated the eigenfunctions in the first method depend on the end-mass and the orthogonality relations are quite different from that of typical simple beams, based on which a new model is proposed and the prediction compares well with that in the second method. For further validation, the critical internal flow velocity, the onset flutter frequency, and the dynamic responses of suspended pipes under gravity are computed, which compare well with experimental observations. This study can provide a workbench for fluid-conveying pipes with various boundary conditions.

Free vibration analysis of Timoshenko pipes conveying fluid with gravity and different boundary conditions

Abstract In this paper, the free vibration of Timoshenko pipes conveying fluid with gravity and different boundary conditions is analyzed by using the weak form quadrature element method. The dimensionless frequency and critical flow velocity have been calculated considering various parameters such as the mass ratio of pipe to fluid, slenderness ratio and gravity. The numerical results with different numbers of discrete points are tested, and the results show that the method has a fast convergence speed. Some numerical results are compared with the existing literature, which proves that the weak form quadrature element method has high accuracy and computational efficiency. This paper shows that the weak form quadrature element method is a preferred method for analyzing fluid-conveying pipes with various boundary conditions.

Nonlinear planar and non-planar vibrations of viscoelastic fluid-conveying pipes with external and internal resonances

In this study, nonlinear vibrations of a viscoelastic fluid-conveying pipe under in-plane and out-of-plane transverse excitations are investigated, with emphasis on external and internal resonances. For this purpose, a three-dimensional pipe model that couples the in-plane and out-of-plane vibrations is developed based on the Euler–Bernoulli beam theory together with the Kelvin–Voigt viscoelasticity. The Galerkin method is performed on the nonlinear governing equations, and the resultant discretized equations are solved via the pseudo-arclength continuation method and a direct integration method. The dynamical responses of the pipe are examined in both sub- and super-critical regions and presented by plotting the frequency–amplitude curves, force–amplitude curves, basins of the attraction, time histories, and phase portraits. A comparison between the simplified two-dimensional model and the present three-dimensional model is presented to showcase the possibility of the in-plane and out-of-plane vibrations in regions of primary and principal parametric resonances, highlighting the modal interaction between the in-plane and out-of-plane transverse modes. In the presence of a two-to-one internal resonance, in addition to typical jumping and hysteresis, the two-peak resonance behavior is observed. The numerical results not only show complex nonlinear dynamics of the fluid–structure interaction system, but also provide hints for safe design and novel application of such structures.

Vibration characteristics analysis of fluid-conveying pipes concurrently subjected to base excitation and pulsation excitation

Previous studies mostly concentrated on the vibration characteristics of the fluid-conveying pipe (FCP) under a single excitation, which is insufficient to address the requirements of FCP vibration analysis under a complex load environment. Meanwhile, the aero-engine pipes may be affected by both base and pulsation excitations during operation, which could result in more complicated vibration behaviors. To solve the vibration response of FCPs concurrently subjected to base excitation and pulsation excitation, a modified transfer matrix model is proposed in this study. The proposed model overcomes the shortcoming that the traditional transfer matrix model (TMM) can only be utilized to analyze the frequency response of FCP under point excitation or pulsation excitation. By modifying the pipe’s governing equation, the base excitation is introduced into the whole pipe segment in the form of the external excitation vector. The proposed model is validated by comparing the collected vibration signals and simulation results of a straight FCP and L-shaped FCP under base excitation and pulsation excitation. Then, the study is further extended to the parallel fluid-conveying pipes (PFCPs), and the influences of base excitation amplitude, flow velocity, pressure, coupling stiffness, and dual clamp damping on the vibration characteristics of PFCPs are analyzed. This work can provide an efficient and general solution for vibration prediction of complex fluid-conveying pipes subjected to base and pulsation excitations in engineering.

Novel active-passive hybrid piezoelectric network for vibration suppression in fluid-conveying pipes

Given the failures like fatigue and fracture of the pipes conveying fluid induced by undesired dynamics and instability and the traditional passive damping cannot effectively attenuate the vibration in the low-frequency bands, this work introduces a novel active-passive control technique, namely, the hybrid piezoelectric network consisting of the piezoelectric layer, the circuit of the resistance and inductance, voltage source, controller, and sensor, which is attached on the cantilevered fluid-conveying pipes to suppress the vibration in wider frequency-bands. Built upon the location of the neutral axis in the segment of pipes is varied due to the integration of the pipeline and piezoelectric actuator, the governing equations of the fluid-conveying pipes attached with the hybrid piezoelectric network are established by virtue of Hamilton's principle in conjunction with the assumed mode method, and approximate analytical expressions of frequency responses are derived using the Laplace transform technique. The passive damping performance is carried out to achieve insightfully using the open-loop analysis based on the circuit of the resistance and inductance is set as the passive shunt characteristic, then the closed-loop features are also investigated according to the velocity feedback control. The numerical example illustrates the presented control method is effective and feasible to realize the vibration suppression on the pipes conveying fluid. Based on this, the optimal resistance and inductance are proposed through the theoretical analysis, which can further broaden the vibration attenuation.

Hopf Bifurcation of a Standing Cantilever Pipe Conveying Fluid with Time Delay

In this article, the dynamical behavior of a standing cantilever pipe conveying fluid is investigated with time − delay. By applying piezoelectric materials and considering the time delay of voltage, the motion equation is built with motion-limiting constraints and elastic support. The motion equation is discretized into ordinary differential equations by the Galerkin method. A stability analysis of the equilibrium point with three parameters is obtained. The system will lose stability at the equilibrium point and generate Hopf branches. The central manifold theorem and the canonical type theory are used to study the stability of Hopf branching directions and branching period solutions. Finally, numerical results validate the theoretical analysis.

Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection

Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection

Resonance response of fluid-conveying pipe with asymmetric elastic supports coupled to lever-type nonlinear energy sink

This paper studies the vibration absorber for a fluid-conveying pipe, where the lever-type nonlinear energy sink (LNES) and spring supports are coupled to the asymmetric ends of the system. The pseudo-arc-length method integrated with the harmonic balance method is used to investigate the steady-state responses analytically. Meanwhile, the numerical solution of the fluid-conveying pipe is calculated with the Runge-Kutta method. Moreover, a special response, called the collapsible closed detached response (CCDR), is first observed when the vibration response of mechanical structures is studied. Then, the relationship between the CCDR and the main structure primary response (PR) is obtained. In addition, the closed detached response (CDR) is also observed to research the resonance response of the fluid-conveying pipe. The appearance of either the CCDR or the CDR does affect the resonance attenuation. Furthermore, the mentioned two phenomena underline that the trend of vibration responses under external excitation goes continuous and gradual. Besides, the main advantage of the LNES is presented by contrasting the LNES with the nonlinear energy sink (NES) coupled to the same pipe system. It is found that the LNES can reduce the resonance response amplitude by 91.33%.

Periodic motion of microscale cantilevered fluid-conveying pipes with symmetric breaking on the cross-section

A new theoretical model is developed for the three-dimensional (3D) nonlinear vibration analysis of cantilevered fluid-conveying micropipes with asymmetric cross-section. Fluid-conveying microscale pipes with ring-shaped cross-sections of O(2) symmetry are widely used in engineering. However, their cross-sections usually have a small symmetric breaking owing to manufacturing errors, which can be described by a small parameter. Hence, the dynamic behaviors of such geometrically imperfect micropipes are extremely required to be explored. This study mainly investigates the effects of the symmetric breaking parameter, flow velocity and dimensionless material length scale parameter on the dynamic behaviors of microscale cantilevered fluid-conveying micropipes. Based on the modified couple stress theory (MCST) and Hamilton's principle, the governing equation is derived, where the effects of the asymmetry of cross-section on the equation are reflected. Using the center manifold theory and normal form method, the original governing equation is rigorously reduced to a two-degree-of-freedom (2DOF) dynamical system, and the averaging equation of the reduced system is obtained by combining the averaging method. The existence and stability of the equilibrium point of the averaging equation are studied to obtain the results of the existence and stability of periodic motions of the original system. The results demonstrate that the types of periodic motions and stability when the pipe loses stability from different places on the curve of the critical flow velocity versus mass ratio (critical flow velocity curve) may differ. Meanwhile, the effects of various parameters on these periodic motions are presented. The increase in the dimensionless material length scale parameter increases the section corresponding to stable plane periodic motion and reduces the section corresponding to stable spatial periodic motion on the critical flow velocity curve. When dimensionless material length scale parameter is given, the existence and stability of various periodic motions of the system depend on the ratio of the increment of flow velocity around the critical value to the symmetric breaking parameter. In addition, some new phenomena are found in this paper. Stable 0 planar periodic motion of the macropipe can occur when pipe loses its stability from the hysteresis part of the critical flow velocity curve. Stable 0 planar periodic motion of microscale pipes can occur when pipe loses its stability from the non-hysteresis part of the critical flow velocity curve, and then stable 0 planar periodic motion and stable π planar periodic motion can coexist. Furthermore, stable planar and stable spatial periodic motions of pipes with symmetric breaking can coexist, and stable torus motion has also been observed; this is different from the dynamics of pipes with O(2) symmetry.

Static and Dynamic Bifurcations Analysis of a Fluid-Conveying Pipe with Axially Moving Supports Surrounded by an External Fluid

In this study, nonlinear vibration and stability of a pipe conveying fluid, with axially moving supports, immersed in an external fluid is studied. The equation of motion is derived with the aid of the Newtonian method via employing the Euler–Bernoulli beam theory and plug flow assumption. Considering the stretching effect, the nonlinear equation of motion is obtained, and it is discretized via the Galerkin method. Afterward, the stability of the system is investigated using two different approaches, and their results are compared. Numerical simulations show the system has complex dynamic behavior. To unveil the dynamics of the system, various analysis techniques such as bifurcation diagram of Poincaré map, phase portrait, power spectrum, and time trajectories are used. Limit cycle, period-n, quasi-periodic, and chaotic regime are observed. It is found that pipe can flutter around the trivial solution or post-buckling equilibrium points. Moreover, the influences of some system parameters on the chaotic behavior of the pipe are discussed.

Post-buckling characteristics of functionally graded fluid-conveying pipe with geometric defects on Pasternak foundation

In this paper, the static buckling and post buckling dynamic characteristics of functionally graded pipeline with geometric imperfections on Pasternak foundation are studied. The functional gradient material is modeled based on the modified power law distribution, and the pores generated in the material during manufacturing are described based on the Voigt model. Based on the Euler-Bernoulli beam theory, considering Pasternak foundation and von-Kaman nonlinearity, the control equation is derived by using Hamilton principle. The closed solution of nonlinear stability is given. The effects of maximum defect amplitude, porosity, power law index and Pasternak foundation on the static buckling and vibration characteristics near the first-order buckling configuration are discussed. The numerical results show that the maximum defect amplitude and Pasternak foundation have significant effects on the critical buckling load, post-buckling structure and natural frequency of the pipeline.

Improved frequency-domain Spectral Element Method for vibration analysis of nonuniform pipe conveying fluid

The well-known Spectral Element Method (SEM) has a broad application in vibration analysis for various configurations, such as flat plates, beams and straight pipes. Considering the fluid–structure coupling effects in variable cross-section, it has one limitation in dealing with the nonuniform pipes conveying fluid. In the present work, an improved frequency-domain SEM (IFSEM) is proposed for the analysis of the nonuniform fluid-conveying pipes by introducing structural wave propagation. In the IFSEM, the wave propagation coefficient plays a critical role to construct the equivalent dynamic stiffness, improving the analysis accuracy and efficiency. And there is a rule that the propagation coefficients are mainly related to the pipe diameter, flow rate and hydrodynamic pressure. A Simplification is put forward to obtain these coefficients in advance, which can significantly facilitate the vibration analysis. Finally, the IFSEM is validated through several numerical examples and the results show that it can analyze the vibration of the liquid-conveying nonuniform pipes efficiently and accurately.

Three-dimensional vibration analysis in extensible pipes conveying fluid with different initial geometrical configurations

In this paper, three-dimensional vibration of fluid-conveying pipes with different initial configurations is investigated. With Green–Lagrange strain tensor, extensible theory, and Plug-flow, governing equations are built by applying Hamiltons principle. The governing partial differential equations are discretized into ordinary differential equations via the differential quadrature method (DQM) and solved numerically to obtain the dynamical character of the different initial configurations. Numerical results show static deflection under different initial geometrical configurations and variation of in-plane and out-of-plane frequencies with increasing fluid velocity. Natural frequency and mode shape are explored under the variation of flow velocity.

On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment

On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment

Investigation of a combined Monte Carlo simulation and Galerkin approach for probabilistic characteristics modelling the dynamic behaviour of the fluid-conveying pipe

ABSTRACT A probabilistic approach is used to compute the probabilistic responses of considered fluid-conveying pipes by combining the Galerkin method and Monte Carlo simulation. Analysing the fluid-conveying pipes is often performed based on the deterministic approaches, but the effect of uncertainty needs to be investigated. The natural frequencies can be represented using probabilistic methods by considering the inherent uncertainty in estimating values. The uncertainty was considered as a random variable. The effects of coefficient of variation (COV) associated with the fluid velocity on the probabilistic characteristics are evaluated. The probability distribution functions of natural frequencies are presented. The measured values were validated by comparing with results of the stochastic finite element method. The results imply that the peak points for the diagrams of the standard deviations of the velocity values gained by the Monte Carlo simulation versus the mean velocities of the related values are equal to the critical fluid velocity.

Pipes conveying fluid: A fertile dynamics problem

The early studies on the dynamics of pipes conveying fluid by Feodos’ev, Housner, Benjamin and Païdoussis in the 1950s and 1960s elucidated the basic dynamics of the system. Yet, further studies on variants of the basic system proliferated, so that, by 1993, Pipes Conveying Fluid was deemed to be a model problem in dynamics. The rate of publication of papers on the subject has increased exponentially, with over 1000 papers now published on the subject. This paper presents a very brief review of the fundamentals, and a more extensive review of some very recent work on the subject, which exemplifies the far-ranging variants of the system being studied.

Three-dimensional dynamics and synchronization of two coupled fluid-conveying pipes with intermediate springs

A system of two coupled oscillating structures may experience dynamical synchronization under coupling effects. Dynamical synchronization refers to the process in which two vibrating structures under coupling effects may display similar dynamics and vibrational behaviors even though their important parameters are not equivalent. In this study, the three-dimensional dynamics and synchronization behaviors of two coupled fluid-conveying pipes connected with linear springs are investigated. In the analytical model, the geometric nonlinearities due to axial elongation of the two pipes and the extension of linear springs are considered. The flow velocities of the internal fluid of the two pipes may be steady or pulsatile. In the case of the flow velocities of the two pipes being steady, the lowest several natural frequencies and the post-buckling behavior of the two-pipe system are obtained by changing the flow velocities in the two pipes. When one pipe conveys pulsatile fluid and the other conveys steady fluid, the dynamical bifurcation and synchronization behaviors of the two-pipe system are analyzed, with several typical synchronization patterns being explored by means of time traces, phase portraits, power spectral density (PSD) diagrams, Poincaré maps, etc. It is shown that making use of synchronization characteristics of the two-pipe system may provide a possible way to control the vibrations of the two-pipe system and to achieve some special engineering objectives.

Effect of two-parameter partial foundation and viscoelastic supports on free vibration of Terfenol-D layered functionally graded fluid conveying pipe using domain decomposition technique

The purpose of the current research work is to investigate the free vibration control characteristics of a Terfenol-D layered functionally graded fluid-conveying pipe when subjected to partial two-parameter foundation, viscoelastic supports, and multi-span length. The integration of differential quadrature method with domain decomposition and the δ point approach, as well as Terfenol-D layer actuation with viscoelastic supports, distinguishes the current study effort. The equivalent spring stiffness for the two-parameter partial foundation is determined methodically for various elastic soil materials. The effect of varied spans with viscoelastic supports on the stability of fluid conveying pipes is also explored.

Nonlinear Transient Dynamics of Graphene Nanoplatelets Reinforced Pipes Conveying Fluid under Blast Loads and Thermal Environment

This work aims at investigating the nonlinear transient response of fluid-conveying pipes made of graphene nanoplatelet (GPL)-reinforced composite (GPLRC) under blast loads and in a thermal environment. A modified Halpin–Tsai model is used to approximate the effective Young’s modulus of the GPLRC pipes conveying fluid; the mass density and Poisson’s ratio are determined by using the Voigt model. A slender Euler–Bernoulli beam is considered for modeling the pipes conveying fluid. The vibration control equation of the GPLRC pipes conveying fluid under blast loads is obtained by using Hamilton’s principle. A set of second-order ordinary differential equations are obtained by using the second-order Galerkin discrete method and are solved by using the adaptive Runge–Kutta method. Numerical experiments show that GPL distribution and temperature; GPL weight fraction; pipe length-to-thickness ratio; flow velocity; and blast load parameters have important effects on the nonlinear transient response of the GPLRC pipes conveying fluid. The numerical results also show that due to the fluid–structure interaction, the vibration amplitudes of the GPLRC pipes conveying fluid decay after the impact of blast loads.

STABILITY OF A MULTI-SPAN FLUID-CONVEYING PIPE ON ELASTIC SUPPORTS

A stability of a multi-span cantilevered fluid-conveying pipe supported by elastic supports is investigated. The equation of disturbed motion is solved with using the modal decomposition and Bubnov–Galerkin method. The natural frequencies and modes are found by the method of initial parameters. Depending on the stiffness of elastic supports, on the plane of the parameters characterizing the velocity and mass per unit length of the flowing fluid, the boundary of the stability is constructed.