Local resonance metamaterial-based integrated design for suppressing longitudinal and transverse waves in fluid-conveying pipes

To solve the problem of low broadband multi-directional vibration control of fluid-conveying pipes,a novel metamaterial periodic structure with multi-directional wide bandgaps is proposed.First,an integrated design method is proposed for the longitudinal and transverse wave control of fluid-conveying pipes,and a novel periodic structure unit model is constructed for vibration reduction.Based on the bandgap vibration reduction mechanism of the acoustic metamaterial periodic structure,the material parameters,structural parameters,and the arrangement interval of the periodic structure unit are optimized.The finite element method(FEM)is used to predict the vibration transmission characteristics of the fluid-conveying pipe installed with the vibration reduction periodic structure.Then,the wave/spectrum element method(WSEM)and experimental test are used to verify the calculated results above.Lastly,the vibration attenuation characteristics of the structure under different conditions,such as rubber material parameters,mass ring material,and fluid-structure coupling effect,are analyzed.The results show that the structure can produce a complete bandgap of 46 Hz-75 Hz in the low-frequency band below 100 Hz,which can effectively suppress the low broadband vibration of the fluidconveying pipe.In addition,a high damping rubber material is used in the design of the periodic structure unit,which realizes the effective suppression of each formant peak of the pipe,and improves the vibration reduction effect of the fluid-conveying pipe.Meanwhile,the structure has the effect of suppressing both bending vibration and longitudinal vibration,and effectively inhibits the transmission of transverse waves and longitudinal waves in the pipe.The research results provide a reference for the application of acoustic metamaterials in the multi-directional vibration control of fluid-conveying pipes.

Vibration of fluid-conveying pipe with nonlinear supports at both ends

The axial fluid-induced vibration of pipes is very widespread in engineering applications.The nonlinear forced vibration of a viscoelastic fluid-conveying pipe with nonlinear supports at both ends is investigated.The multi-scale method combined with the modal revision method is formulated for the fluid-conveying pipe system with nonlinear boundary conditions.The governing equations and the nonlinear boundary conditions are rescaled simultaneously as linear inhomogeneous equations and linear inhomogeneous boundary conditions on different time-scales.The modal revision method is used to transform the linear inhomogeneous boundary problem into a linear homogeneous boundary problem.The differential quadrature element method(DQEM)is used to verify the approximate analytical results.The results show good agreement between these two methods.A detailed analysis of the boundary nonlinearity is also presented.The obtained results demonstrate that the boundary nonlinearities have a significant effect on the dynamic characteristics of the fluid-conveying pipe,and can lead to significant differences in the dynamic responses of the pipe system.

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%.

A novel way for vibration control of FGM fluid-conveying pipes via NiTiNOL-steel wire rope

In this study,a coupling model of fluid-conveying pipes made of functionally graded materials(FGMs)with NiTiNOL-steel(NiTi-ST)for vibration absorption is investigated.The vibration responses of the FGM fluid-conveying pipe with NiTi-ST are studied by the Galerkin truncation method(GTM)and harmonic balance method(HBM).The harmonic balance solutions and the numerical results are consistent.Also,the linearized stability of the structure is determined.The effects of the structure parameters on the absorption performance are also studied.The results show that the NiTi-ST is an effective means of vibration absorption.Furthermore,in studying the effect of the NiTi-ST,a closed detached response(CDR)is first observed.It is noteworthy that the CDR may dramatically change the vibration amplitude and that the parameters of the NiTi-ST may determine the emergence or disappearance of the CDR.This vibration absorption device can be extended to offer more general vibration control in engineering applications.

NONLINEAR RESPONSES OF A FLUID-CONVEYING PIPE EMBEDDED IN NONLINEAR ELASTIC FOUNDATIONS

The nonlinear responses of planar motions of a fluid-conveying pipe embedded in nonlinear elastic foundations are investigated via the differential quadrature method discretization （DQMD） of the governing partial differential equation. For the analytical model, the effect of the nonlinear elastic foundation is modeled by a nonlinear restraining force. By using an iterative algorithm, a set of ordinary differential dynamical equations derived from the equation of motion of the system are solved numerically and then the bifurcations are analyzed. The numerical results, in which the existence of chaos is demonstrated, are presented in the form of phase portraits of the oscillations. The intermittency transition to chaos has been found to arise.

VIBRATION AND STABILITY OF VERTICAL UPWARD-FLUID-CONVEYING PIPE IMMERSED IN RIGID CYLINDRICAL CHANNEL

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.

Vibration control of fluid-conveying pipes: a state-of-the-art review

Fluid-conveying pipes are widely used to transfer bulk fluids from one point to another in many engineering applications.They are subject to various excitations from the conveying fluids,the supporting structures,and the working environment,and thus are prone to vibrations such as flow-induced vibrations and acoustic-induced vibrations.Vibrations can generate variable dynamic stress and large deformation on fluid-conveying pipes,leading to vibration-induced fatigue and damage on the pipes,or even leading to failure of the entire piping system and catastrophic accidents.Therefore,the vibration control of fluid-conveying pipes is essential to ensure the integrity and safety of pipeline systems,and has attracted considerable attention from both researchers and engineers.The present paper aims to provide an extensive review of the state-of-the-art research on the vibration control of fluid-conveying pipes.The vibration analysis of fluid-conveying pipes is briefly discussed to show some key issues involved in the vibration analysis.Then,the research progress on the vibration control of fluid-conveying pipes is reviewed from four aspects in terms of passive control,active vibration control,semi-active vibration control,and structural optimization design for vibration reduction.Furthermore,the main results of existing research on the vibration control of fluid-conveying pipes are summarized,and future promising research directions are recommended to address the current research gaps.This paper contributes to the understanding of vibration control of fluid-conveying pipes,and will help the research work on the vibration control of fluidconveying pipes attract more attention.

Impact vibration properties of locally resonant fluid-conveying pipes

Fluid-conveying pipe systems are widely used in various equipments to transport matter and energy.Due to the fluid–structure interaction effect,the fluid acting on the pipe wall is easy to produce strong vibration and noise,which have a serious influence on the safety and concealment of the equipment.Based on the theory of phononic crystals,this paper studies the vibration transfer properties of a locally resonant(LR)pipe under the condition of fluid–structure interaction.The band structure and the vibration transfer properties of a finite periodic pipe are obtained by the transfer matrix method.Further,the different impact excitation and fluid–structure interaction effect on the frequency range of vibration attenuation properties of the LR pipe are mainly considered and calculated by the finite element model.The results show that the existence of a low-frequency vibration bandgap in the LR pipe can effectively suppress the vibration propagation under external impact and fluid impact excitation,and the vibration reduction frequency range is near the bandgap under the fluid–structure interaction effect.Finally,the pipe impact experiment was performed to verify the effective attenuation of the LR structure to the impact excitation,and to validate the finite element model.The research results provide a technical reference for the vibration control of the fluid-conveying pipe systems that need to consider blast load and fluid impact.

Enhanced vibration suppression and energy harvesting in fluid-conveying pipes

A novel vibration absorber is designed to suppress vibrations in fluidconveying pipes subject to varying fluid speeds.The proposed absorber combines the fundamental principles of nonlinear energy sinks(NESs)and nonlinear energy harvesters(NEHs).The governing equation is derived,and a second-order discrete system is used to assess the performance of the developed device.The results demonstrate that the proposed absorber achieves significantly enhanced energy dissipation efficiency,reaching up to 95%,over a wider frequency range.Additionally,it successfully harvests additional electric energy.This research establishes a promising avenue for the development of new nonlinear devices aimed at suppressing fluid-conveying pipe vibrations across a broad frequency spectrum.

Dynamic modeling of fluid-conveying pipes restrained by a retaining clip

Although most pipes are restrained by retaining clips in aircraft,the influence of the clip parameters on the vibration of the fluid-conveying pipe has not been revealed.By considering the clip width,a new dynamic model of a fluid-conveying pipe restrained by an intermediate clip is established in this paper.To demonstrate the necessity of the proposed model,a half pipe model is established by modeling the clip as one end.By comparing the two models,it is found that the half pipe model overestimates the critical velocity and may estimate the dynamical behavior of the pipe incorrectly.In addition,with the increase in the clip stiffness,the conversion processes of the first two modes of the pipe are shown.Furthermore,by ignoring the width of the clip,the effect of the flow velocity on the accuracy of a concentrated restraint clip model is presented.When the flow velocity is close to the critical velocity,the accuracy of the concentrated restraint clip model significantly reduces,especially when the width of the clip is large.In general,the contribution of this paper is to establish a dynamic model of the fluid-conveying pipe which can describe the influence of the clip parameters,and to demonstrate the necessity of this model.

Fractional Dynamics of Fluid-Conveying Pipes Made of Polymer-Like Materials

The fluid-conveying pipes made of polymer-like materials are widely applied in engineering fields. However, the fractional dynamics of fluid-solid interaction remain unknown. In this work, the fractional dynamics of the pipes subjected to the excitation of supporting foun- dation are studied. A new nonlinear, fractional-order dynamic model is presented. The method of multiple scales is adopted directly to solve the model for the case of primary resonances. Numerical results are presented to show the effects of fractional order, foundation vibration, and other physical parameters on the steady-state response and stability.

In-plane dynamics of a fluid-conveying corrugated pipe supported at both ends

The dynamics and stability of fluid-conveying corrugated pipes are investigated. The flow velocity is assumed to harmonically vary along the pipe rather than with time. The dimensionless equation is discretized with the differential quadrature method (DQM). Subsequently, the effects of the mean flow velocity and two key parameters of the corrugated pipe, i.e., the amplitude of the corrugations and the total number of the corrugations, are studied. The results show that the corrugated pipe will lose stability by flutter even if it has been supported at both ends. When the total number of the corrugations is sufficient, this flutter instability occurs at a micro flow velocity. These phenomena are verified via the Runge-Kutta method. The critical flow velocity of divergence is analyzed in detail. Compared with uniform pipes, the critical velocity will be reduced due to the corrugations, thus accelerating the divergence instability. Specifically, the critical flow velocity decreases if the amplitude of the corrugations increases. However, the critical flow velocity cannot be monotonously reduced with the increase in the total number of the corrugations. An extreme point appears, which can be used to realize the parameter optimization of corrugated pipes in practical applications.

Nonlinear Parametric Vibration of a Fluid-Conveying Pipe Flexibly Restrained at the Ends

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.

New insight into the stability and dynamics of fluid-conveying supported pipes with small geometric imperfections

In several previous studies,it was reported that a supported pipe with small geometric imperfections would lose stability when the internal flow velocity became sufficiently high.Recently,however,it has become clear that this conclusion may be at best incomplete.A reevaluation of the problem is undertaken here by essentially considering the flow-induced static deformation of a pipe.With the aid of the absolute nodal coordinate formulation(ANCF)and the extended Lagrange equations for dynamical systems containing non-material volumes,the nonlinear governing equations of a pipe with three different geometric imperfections are introduced and formulated.Based on extensive numerical calculations,the static equilibrium configuration,the stability,and the nonlinear dynamics of the considered pipe system are determined and analyzed.The results show that for a supported pipe with the geometric imperfection of a half sinusoidal wave,the dynamical system could not lose stability even if the flow velocity reaches an extremely high value of 40.However,for a supported pipe with the geometric imperfection of one or one and a half sinusoidal waves,the first-mode buckling instability would take place at high flow velocity.Moreover,based on a further parametric analysis,the effects of the amplitude of the geometric imperfection and the aspect ratio of the pipe on the static deformation,the critical flow velocity for buckling instability,and the nonlinear responses of the supported pipes with geometric imperfections are analyzed.

Nonlinear Fractional-Order Dynamic Stability of Fluid-Conveying Pipes Constituted by the Viscoelastic Materials with Time-Dependent Velocity

Considering that the fluid-conveying pipes made of fractional-order viscoelastic material such as polymeric materials with pulsatile flow are widely applied in engineering,we focus on the stability and bifurcation behaviors in parametric resonance of a viscoelastic pipe resting on an elastic foundation.The Riemann–Liouville fractional-order constitutive equation is used to accurately describe the viscoelastic property.Based on this,the nonlinear governing equations are established according to the Euler–Bernoulli beam theory and von Karman’s nonlinearity,with using the generalized Hamilton’s principle.The stability boundaries and steady-state responses undergoing parametric excitations are determined with the aid of the direct multiple-scale method.Some numerical examples are carried out to show the effects of fractional order and viscoelastic coefficient on the stability region and nonlinear bifurcation behaviors.It is noticeable that the fractional-order viscoelastic property can effectively reconstruct the dynamic behaviors,indicating that the stability of the pipes can be conspicuously enhanced by designing and tuning the fractional order of viscoelastic materials.

Experimental,Numerical,and Analytical Studies on the Bending of Mechanically Lined Pipe

Mechanically lined pipe(MLP)is often used for offshore oil and gas transport because of its low cost and corrosion resistance.During installation and operation,the pipe may undergo severe bending deformation,which causes the liner to separate from the outer pipe and buckles,affecting the stability of the whole line.In this paper,the buckling response of MLP subjected to bending is investigated to clarify its bending characteristics by employing both experiments,numerical simulation,as theoretical methods.Two types of MLPs were manufactured with GB 45 carbon steel(SLP)and Al 6061(ALP)used as the outer pipe material,respectively.The hydraulic expansion and bending experiments of small-scale MLPs are conducted.In addition to the ovalized shape of the cross-section for the SLP specimens,the copper liner was found to wrinkle on the compressive side.In contrast,the liner of ALP remains intact without developing any wrinkling and collapse mode.In addition,a dedicated numerical framework and theoretical models were also established.It was found both the manufacturing and bending responses of the MLP can be well reproduced,and the predicted maximum moment and critical curvatures are in good agreement with the experimental results.

A Comparative Study on the Post-Buckling Behavior of Reinforced Thermoplastic Pipes(RTPs)Under External Pressure Considering Progressive Failure

The collapse pressure is a key parameter when RTPs are applied in harsh deep-water environments.To investigate the collapse of RTPs,numerical simulations and hydrostatic pressure tests are conducted.For the numerical simulations,the eigenvalue analysis and Riks analysis are combined,in which the Hashin failure criterion and fracture energy stiffness degradation model are used to simulate the progressive failure of composites,and the“infinite”boundary conditions are applied to eliminate the boundary effects.As for the hydrostatic pressure tests,RTP specimens were placed in a hydrostatic chamber after filled with water.It has been observed that the cross-section of the middle part collapses when it reaches the maximum pressure.The collapse pressure obtained from the numerical simulations agrees well with that in the experiment.Meanwhile,the applicability of NASA SP-8007 formula on the collapse pressure prediction was also discussed.It has a relatively greater difference because of the ignorance of the progressive failure of composites.For the parametric study,it is found that RTPs have much higher first-ply-failure pressure when the winding angles are between 50°and 70°.Besides,the effect of debonding and initial ovality,and the contribution of the liner and coating are also discussed.

Seismic performance evaluation of water supply pipes installed in a full-scale RC frame structure based on a shaking table test

As an important part of nonstructural components,the seismic response of indoor water supply pipes deserves much attention.This paper presents shaking table test research on water supply pipes installed in a full-scale reinforced concrete(RC)frame structure.Different material pipes and different methods for penetrating the reinforced concrete floors are combined to evaluate the difference in seismic performance.Floor response spectra and pipe acceleration amplification factors based on test data are discussed and compared with code provisions.A seismic fragility study of displacement demand is conducted based on numerical simulation.The acceleration response and displacement response of different combinations are compared.The results show that the combination of different pipe materials and different passing-through methods can cause obvious differences in the seismic response of indoor riser pipes.

Flow Patterns and Heat Transfer Characteristics of a Polymer Pulsating Heat Pipe Filled with Hydrofluoroether

Visualization experiments were conducted to clarify the operational characteristics of a polymer pulsating heat pipe(PHP).Hydrofluoroether(HFE)-7100 was used as a working fluid,and its filling ratio was 50%of the entire PHP channel.A semi-transparent PHP was fabricated using a transparent polycarbonate sheet and a plastic 3D printer,and the movements of liquid slugs and vapor plugs of the working fluid were captured with a high-speed camera.The video images were then analyzed to obtain the flow patterns in the PHP.The heat transfer characteristics of the PHPwere discussed based on the flowpatterns and temperature distributions obtainedwith thermocouples.Before starting heating,because of high wettability,large liquid slugs positioned at the evaporator section of the PHP.After starting heating,since the occurrence of boiling divided the large liquid slugs,oscillatory flowof smaller liquid slugs and vapor plugs was found in the PHP.Clear circulation flow of liquid slugs and vapor plugs was observed when the power input to the PHP was larger than 12.0 W.The flow patterns and temperature distributions confirmed that the circulation flow enhanced the heat transfer from the evaporator section to the condenser section of the PHP.In the circulation flow mode,large growth and contraction of vapor plugs were found one after another in all even-numbered PHP channels.However,the analysis of flow patterns clarified that the phase-change heat transfer rate by large growth and contraction of vapor plugs was 19%of the total heat transfer rate of the PHP.Although the generation of large vapor plugs was found in the PHP,most of the heat was transferred by the sensible heat of the working fluid.

A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.