Pith. sign in

REVIEW 3 minor 31 references

Reviewed by Pith at T0; open to challenge.

T0 means a machine referee read the full paper against a public rubric. The mark states how deep the mechanical check went, never who wrote it. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

For an inextensible spinning fluid-conveying pipe with pinned-roller supports, ninth-order Galerkin truncation is required to resolve the post-critical amplitude because cubic terms miss the geometric stiffening.

2026-06-29 00:39 UTC pith:GXDNRKN5

load-bearing objection The paper derives new nonlinear terms for pinned-roller inextensible spinning pipes and shows ninth-order Galerkin plus a matrix Hencky model are needed to capture post-critical amplitudes correctly, with solid cross-checks.

arxiv 2606.27552 v1 pith:GXDNRKN5 submitted 2026-06-25 nlin.CD

Large post-critical dynamics of an inextensible spinning fluid-conveying pipe with pinned-roller supports: high-order Galerkin and a modified Hencky bar-chain framework

Ali Fasihi , Grzegorz Kudra , Maryam GhandchiTehrani , Jan Awrejcewicz This is my paper
classification nlin.CD
keywords inextensible pipefluid-conveying pipespinning pipepost-critical dynamicsGalerkin truncationHencky bar-chainpinned-roller supportsnonlinear stability
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper studies the stability and large-amplitude post-critical behavior of a spinning pipe carrying fluid, supported by pinned-roller ends that allow sliding and remove axial stretching resistance. The inextensibility constraint introduces nonlinear terms from the bending curvatures that govern the large deflections after the stability limit is crossed. A Galerkin projection with bending curvatures expanded to ninth order is shown to be the minimal truncation that correctly captures the amplitude, while the common cubic approximation significantly overestimates the deflection. A modified Hencky bar-chain discretization with exact trigonometric kinematics provides an alternative discrete model that agrees closely with the continuous approach across linear and nonlinear regimes.

Core claim

The governing equations for this pinned-roller configuration feature nonlinear bending-curvature terms instead of axial stretching, leading to an elliptical stability boundary with semi-axes at flow velocity U = π and rotational speed Ω = π². The post-critical regime exhibits large deflections whose amplitude is only correctly predicted when the bending curvatures are Taylor-expanded to ninth order; lower orders, including the cubic truncation, miss the stiffening effect and overestimate deflections. The modified Hencky bar-chain model, formulated with a global angular description and n-independent matrices, reproduces the same linear stability, bifurcation diagrams, and time histories, conf

What carries the argument

Ninth-order Taylor expansion of the bending curvatures within the Galerkin discretization, which incorporates the geometric stiffening arising from the inextensibility constraint.

Load-bearing premise

That the post-critical amplitude cannot be resolved without carrying the Taylor expansion of the bending curvatures to ninth order, as lower truncations miss essential stiffening terms.

What would settle it

A high-fidelity numerical simulation or physical experiment measuring the steady post-critical deflection amplitude at a point above the critical flow speed and rotation rate that matches the ninth-order prediction but deviates from the cubic truncation result.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The linear stability boundary forms an ellipse-like region in the flow-velocity versus rotational-speed plane with semi-axes U=π and Ω=π².
  • Three distinct damping regimes appear, one of which is a high-rotation instability driven by rotating damping.
  • The modified Hencky bar-chain model with global angular description works as a closed matrix framework adaptable to both extensible and inextensible cases via boundary conditions.
  • Agreement between the high-order Galerkin and the discrete model holds for linear stability, bifurcation points, and time-history responses.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This approach may extend to other constrained beam or pipe systems where inextensibility produces similar geometric nonlinearities that demand high-order expansions.
  • The discrete Hencky framework could enable efficient parameter studies or control design for spinning fluid-conveying pipes in engineering applications.
  • Similar support changes might alter post-critical dynamics in related problems like rotating shafts or flexible risers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. The manuscript investigates the stability and large post-critical dynamics of an inextensible spinning fluid-conveying pipe with pinned-roller supports. Replacing pinned-pinned supports removes axial stretching, yielding new nonlinear terms from the inextensibility constraint and bending curvatures. The equations are discretized via a ninth-order Galerkin expansion of curvatures (claimed minimal for accurate post-critical amplitudes, as cubic overestimates due to missing geometric stiffening) and a modified Hencky bar-chain model with exact trigonometric kinematics and n-independent matrix form. Linearised dynamics produce an ellipse-like stability boundary (semi-axes U=π, Ω=π²) in the flow-velocity–rotational-speed plane; three damping regimes are identified, including high-rotation instability. Close agreement is reported between the two methods on linear stability, bifurcations, and time histories.

Significance. If the results hold, the work establishes the necessity of high-order curvature expansions for post-critical regimes in inextensible pipes and introduces an adaptable, matrix-based discrete framework usable for both extensible and inextensible cases. The explicit cross-validation between Galerkin and Hencky discretizations across multiple diagnostics is a methodological strength that supports the identified damping regimes and instability mechanisms.

minor comments (3)
  1. [Abstract and Galerkin section] Abstract and Galerkin section: the claim that ninth-order is the lowest truncation resolving post-critical amplitude (with cubic overestimating due to absent geometric stiffening) should be supported by a dedicated convergence plot or table quantifying amplitude error versus truncation order.
  2. [Linearised dynamics] Linearised dynamics: the ellipse-like stability boundary with semi-axes U=π and Ω=π² is presented as an outcome of the linearised equations; the characteristic equation or explicit reduction steps should be shown to allow direct verification.
  3. [Hencky model] Hencky model: the reduction yielding the n-independent matrix framework after imposing pinned-roller boundary conditions should include a brief algorithmic outline or pseudocode for reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were listed in the report, so we have no individual points requiring rebuttal or clarification at this stage. We will make any minor adjustments needed for the revised version.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives the governing PDEs from the inextensibility constraint and pinned-roller boundary conditions, obtains the elliptical stability boundary (semi-axes U=π, Ω=π²) directly from linearization, and demonstrates the necessity of ninth-order curvature truncation via explicit convergence comparisons and cross-validation against an independent modified Hencky bar-chain model using exact trigonometric kinematics. No load-bearing step reduces by construction to a fitted input, self-citation chain, or renamed ansatz; the two discretization frameworks are mutually independent and externally falsifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard beam-theory assumptions plus the modeling choice of inextensibility; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption The pipe is inextensible
    Explicitly stated as the property that removes axial-stretching restoring force and changes the nonlinear terms.
  • ad hoc to paper Bending curvatures require ninth-order Taylor expansion to resolve post-critical amplitude
    Claimed as the minimal order that captures geometric stiffening; lower orders are said to overestimate deflection.

pith-pipeline@v0.9.1-grok · 5865 in / 1303 out tokens · 36612 ms · 2026-06-29T00:39:37.484005+00:00 · methodology

0 comments
read the original abstract

This paper investigates the stability and large post-critical dynamics of an inextensible spinning fluid-conveying pipe with pinned-roller supports. Replacing the pinned-pinned support of the extensible counterpart with a sliding support removes the axial-stretching restoring mechanism and fundamentally changes the governing equations of motion. Derived here for this configuration, these equations contain a different set of nonlinear terms -- arising from the inextensibility constraint and the bending curvatures rather than the single axial-stretching term -- that drives a post-critical regime with large deflections. The regime is analysed with two complementary methods. The first is a Galerkin discretisation in which the bending curvatures are Taylor-expanded to ninth order, shown to be the lowest order resolving the post-critical amplitude; the standard cubic truncation overestimates the deflection significantly by missing the geometric stiffening from inextensibility. The second is a modified Hencky bar-chain model with a global angular description: a closed, $n$-independent matrix framework with exact trigonometric kinematics, directly implementable in any standard programming environment with matrix routines and adaptable to both extensible and inextensible configurations through a single boundary-condition reduction. The linearised dynamics give an ellipse-like stability boundary in the flow-velocity--rotational-speed plane with semi-axes $U=\pi$ and $\Omega=\pi^{2}$; three damping regimes are identified, including a high-rotation instability driven by rotating damping. Close agreement between the two methods across linear-stability, bifurcation, and time-history comparisons confirms the ninth-order Galerkin truncation and establishes the modified Hencky bar-chain as a reliable general-purpose discrete framework for spinning fluid-conveying pipes.

Figures

Figures reproduced from arXiv: 2606.27552 by Ali Fasihi, Grzegorz Kudra, Jan Awrejcewicz, Maryam GhandchiTehrani.

Figure 1
Figure 1. Figure 1: Spinning fluid-conveying pipe with pinned–roller supports. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Linear stability boundary in the (𝑈, Ω) plane and its parametric dependence, reproduced from [23]: (a) three damping regimes – 𝛼 = 0; 𝛼 > 0 at low Ω; 𝛼 > 0 at high Ω; (b) dependence on the mass ratio 𝛽; (c) dependence on the flow-profile modification factor 𝛾. A. Fasihi et al.: Preprint submitted to Elsevier Page 9 of 32 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Midpoint deflection |𝑟(0.5, 𝑡)| at 𝑈 = 4, Ω = 4 for the full model and for the four cases with one nonlinear group (NMT, NGT, NCT, NST) switched off. Parameters: 𝛼 = 0.023, √ 𝛽 = 0.536925 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Steady-state midpoint amplitude |𝑟(0.5)| for the full model and for each case with one group switched off, with the percentage shift relative to the full model annotated. The velocity-dependent groups NMT, NGT leave the equilibrium amplitude unchanged; NCT and NST shift it, with NST dominant. Parameters as in [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Convergence of the steady-state midpoint deflection with the truncation order of the bending curvatures [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Inertial-frame post-critical response at [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Rotating-frame counterpart of Fig [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Three-dimensional bifurcation surface: steady-state midspan deflection [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Steady-state midpoint deflection versus flow velocity for the extensible pinned–pinned pipe (left axis) and [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Modified Hencky bar-chain model of the spinning fluid-conveying pipe: (a) rigid-link chain with flexural [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Wall-clock computation time for a fixed simulation as a function of the number of links [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Stability boundary in the 𝑈–Ω plane from the frequency analysis of the modified Hencky model for 𝑛 = 3, 7, 11, 15, 30, compared with the continuum ellipse-like reference. Parameters as in [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Bifurcation diagram of |𝑟(0.5)| versus flow velocity 𝑈 at Ω = 0: (a) modified Hencky model at several values of 𝑛 vs the Galerkin reference; (b) magnified view of the onset, including 𝑛 = 30. Parameters as in [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Bifurcation diagram of |𝑟(0.5)| versus rotational speed Ω at 𝑈 = 0, modified Hencky model (𝑛 = 15) vs the Galerkin reference. Parameters as in [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Bifurcation diagram of |𝑟(0.5)| versus flow velocity 𝑈 at non-zero rotational speed: (a) Ω = 5; (b) Ω = 8. Modified Hencky model (𝑛 = 15) vs the Galerkin reference. Parameters as in [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Time history of the midpoint response under combined flow and rotation: (a) rotating-frame [PITH_FULL_IMAGE:figures/full_fig_p022_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Bifurcation diagram of |𝑟(0.5)| versus flow velocity 𝑈 at Ω = 0 for the pinned–roller pipe; modified Hencky model at 𝑛 = 5, 7, 11, 15. Parameters as in [PITH_FULL_IMAGE:figures/full_fig_p023_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Steady-state midpoint deflection |𝑟(0.5)| versus flow velocity at Ω = 8 for the pinned–roller pipe: modified Hencky model (𝑛 = 15) vs the Galerkin (𝜀 9 ) reference. Parameters as in [PITH_FULL_IMAGE:figures/full_fig_p024_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Time history of the midpoint response under combined flow and rotation for the pinned–roller pipe, modified [PITH_FULL_IMAGE:figures/full_fig_p025_19.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

31 extracted references · 30 canonical work pages

  1. [1]

    M. P. Paidoussis,Fluid-Structure Interactions: Second Edition, Elsevier Ltd, 2013. doi:10.1016/C2011-0-08057-2

    work page doi:10.1016/c2011-0-08057-2 2013

  2. [2]

    Vibrations of a Continuous Rotor,

    Y. Ishida and T. Yamamoto, “Vibrations of a Continuous Rotor,” inLinear and Nonlinear Rotordynamics: A Modern Treatment with Applications, John Wiley & Sons, Ltd, 2012, pp. 49–65. doi:10.1002/9783527651894.ch3

    work page doi:10.1002/9783527651894.ch3 2012

  3. [3]

    Areviewofdrillstringvibrationmodelingandsuppressionmethods,

    A.Ghasemloonia,D.G.Rideout,andS.D.Butt,“Areviewofdrillstringvibrationmodelingandsuppressionmethods,”Journal of Petroleum Science and Engineering, vol. 131, pp. 150–164, 2015. doi:10.1016/j.petrol.2015.04.030

    work page doi:10.1016/j.petrol.2015.04.030 2015

  4. [4]

    Buckling and dynamic analysis of drill string system in horizontal wells,

    Z. Wu, W. Zhang, R. Yuan, and J. Liu, “Buckling and dynamic analysis of drill string system in horizontal wells,”Nonlinear Dynamics, vol. 112, no. 6, pp. 4147–4168, 2024. doi:10.1007/s11071-023-09100-7

    work page doi:10.1007/s11071-023-09100-7 2024

  5. [5]

    DynamicBucklingCharacteristicsofDrillStringinHorizontalWells,

    J.Tian,H.Song,Y.Yang,L.Mao,andJ.Song,“DynamicBucklingCharacteristicsofDrillStringinHorizontalWells,”International Journal of Structural Stability and Dynamics, vol. 24, no. 11, pp. 2450121, 2024. doi:10.1142/S0219455424501219

    work page doi:10.1142/s0219455424501219 2024

  6. [6]

    Numericalinvestigationandfieldverificationofthetorqueandbendingmoment of drill string for different lateral motion states in the vertical well,

    H.Ni,B.Huang,W.Li,H.Zhang,Y.Jin,Y.Lu,andS.Liu,“Numericalinvestigationandfieldverificationofthetorqueandbendingmoment of drill string for different lateral motion states in the vertical well,”Mechanical Systems and Signal Processing, vol. 230, pp. 112637, 2025. doi:10.1016/j.ymssp.2025.112637

    work page doi:10.1016/j.ymssp.2025.112637 2025

  7. [7]

    Effectsofflow–pipeinteractionondrillpipebucklinganddynamics,

    Q.ZhangandS.Miska,“Effectsofflow–pipeinteractionondrillpipebucklinganddynamics,”Journal of Pressure Vessel Technology,vol.127, pp. 129–136, 2005. doi:10.1115/1.1858922

    work page doi:10.1115/1.1858922 2005

  8. [8]

    Dynamics of a long tubular cantilever conveying fluid downwards, which then flows upwards around the cantilever as a confined annular flow,

    M. P. Paidoussis, T. P. Luu, and S. Prabhakar, “Dynamics of a long tubular cantilever conveying fluid downwards, which then flows upwards around the cantilever as a confined annular flow,”Journal of Fluids and Structures, vol. 24, no. 1, pp. 111–128, 2008. doi:10.1016/j.jfluidstructs.2007.07.004

    work page doi:10.1016/j.jfluidstructs.2007.07.004 2008

  9. [9]

    On the Stability of Spinning Functionally Graded Cantilevered Pipes Subjected to Fluid-Thermomechanical Loading,

    M. Eftekhari and M. Hosseini, “On the Stability of Spinning Functionally Graded Cantilevered Pipes Subjected to Fluid-Thermomechanical Loading,”International Journal of Structural Stability and Dynamics, vol. 16, no. 9, 2016. doi:10.1142/S0219455415500625

    work page doi:10.1142/s0219455415500625 2016

  10. [10]

    Dynamicalmodelingandfreevibrationanalysisofspinningpipesconveyingfluidwithaxial deployment,

    F.Liang,X.D.Yang,W.Zhang,andY.J.Qian,“Dynamicalmodelingandfreevibrationanalysisofspinningpipesconveyingfluidwithaxial deployment,”Journal of Sound and Vibration, vol. 417, pp. 65–79, 2018. doi:10.1016/j.jsv.2017.12.005

    work page doi:10.1016/j.jsv.2017.12.005 2018

  11. [11]

    Transverse free vibration and stability analysis of spinning pipes conveying fluid,

    F. Liang, X. D. Yang, Y. J. Qian, and W. Zhang, “Transverse free vibration and stability analysis of spinning pipes conveying fluid,” International Journal of Mechanical Sciences, vol. 137, pp. 195–204, 2018. doi:10.1016/j.ijmecsci.2018.01.015

    work page doi:10.1016/j.ijmecsci.2018.01.015 2018

  12. [12]

    Vibrationsin3Dspaceofaspinningsupportedpipeexposedtointernalandexternalannular flows,

    F.Liang,X.D.Yang,W.Zhang,andY.J.Qian,“Vibrationsin3Dspaceofaspinningsupportedpipeexposedtointernalandexternalannular flows,”Journal of Fluids and Structures, vol. 87, pp. 247–262, 2019. doi:10.1016/j.jfluidstructs.2019.04.002

    work page doi:10.1016/j.jfluidstructs.2019.04.002 2019

  13. [13]

    Dynamical analysis of spinning functionally graded pipes conveying fluid with multiple spans,

    F. Liang, A. Gao, and X. D. Yang, “Dynamical analysis of spinning functionally graded pipes conveying fluid with multiple spans,”Applied Mathematical Modelling, vol. 83, pp. 454–469, 2020. doi:10.1016/j.apm.2020.03.011

    work page doi:10.1016/j.apm.2020.03.011 2020

  14. [14]

    Low-frequency band gap characteristics of a novel spinning metamaterial pipe with Timoshenko model,

    F. Liang, Y. Chen, D. Guan, and J. Li, “Low-frequency band gap characteristics of a novel spinning metamaterial pipe with Timoshenko model,”Journal of Sound and Vibration, vol. 541, pp. 117316, 2022. doi:10.1016/j.jsv.2022.117316

    work page doi:10.1016/j.jsv.2022.117316 2022

  15. [15]

    Vibration self-suppression of spinning fluid-conveying pipes composed of periodic composites,

    F. Liang, Y. Chen, J. Gong, and Y. Qian, “Vibration self-suppression of spinning fluid-conveying pipes composed of periodic composites,” International Journal of Mechanical Sciences, vol. 220, pp. 107150, 2022. doi:10.1016/j.ijmecsci.2022.107150

    work page doi:10.1016/j.ijmecsci.2022.107150 2022

  16. [16]

    StabilityoptimizationofspinningFGMpipesconveyingfluidviaintermediateelastic supports,

    J.Fan,X.Chang,B.Chen,Y.Yang,Q.Luo,andY.Li,“StabilityoptimizationofspinningFGMpipesconveyingfluidviaintermediateelastic supports,”Ocean Engineering, vol. 292, pp. 116368, 2024. doi:10.1016/j.oceaneng.2023.116368

    work page doi:10.1016/j.oceaneng.2023.116368 2024

  17. [17]

    Nonplanarvibrationandflutteranalysisofverticallyspinningcantileveredpiezoelectricpipesconveyingfluid,

    R.EbrahimiandS.Ziaei-Rad,“Nonplanarvibrationandflutteranalysisofverticallyspinningcantileveredpiezoelectricpipesconveyingfluid,” Ocean Engineering, vol. 261, pp. 112180, 2022. doi:10.1016/j.oceaneng.2022.112180

    work page doi:10.1016/j.oceaneng.2022.112180 2022

  18. [18]

    The Non-linear Equations of Motion of Pipes Conveying Fluid,

    C. Semler, G. X. Li, and M. P. Païdoussis, “The Non-linear Equations of Motion of Pipes Conveying Fluid,”Journal of Sound and Vibration, vol. 169, no. 5, pp. 577–599, 1994. doi:10.1006/jsvi.1994.1035

    work page doi:10.1006/jsvi.1994.1035 1994

  19. [19]

    Three-dimensionaldynamicsoffluid-conveyingpipesimultaneouslysubjectedtoexternalaxialflow,

    T.Jiang,H.Dai,andL.Wang,“Three-dimensionaldynamicsoffluid-conveyingpipesimultaneouslysubjectedtoexternalaxialflow,”Ocean Engineering, vol. 217, pp. 107970, 2020. doi:10.1016/j.oceaneng.2020.107970

    work page doi:10.1016/j.oceaneng.2020.107970 2020

  20. [20]

    Dynamic stability of pipes conveying fluid,

    M. P. Paidoussis and N. T. Issid, “Dynamic stability of pipes conveying fluid,”Journal of Sound and Vibration, vol. 33, no. 3, pp. 267–294,

  21. [21]

    doi:10.1016/S0022-460X(74)80002-7

    work page doi:10.1016/s0022-460x(74)80002-7

  22. [22]

    doi:10.1017/S0368393100076331

    F.M.Dimentberg,Flexural vibrations of rotating shafts,Butterworths(inassociationwithDept.ofScientificandIndustrialResearch),1961. doi:10.1017/S0368393100076331

    work page doi:10.1017/s0368393100076331 1961

  23. [23]

    Simulation of drill-string systems with fluid–structure and contact interactions in realistic geometries,

    S. Galasso, L. Santelli, R. Zambetti, and G. G. Giusteri, “Simulation of drill-string systems with fluid–structure and contact interactions in realistic geometries,”Computational Mechanics, vol. 75, no. 3, pp. 1165–1189, 2025. doi:10.1007/s00466-024-02555-4. A. Fasihi et al.:Preprint submitted to ElsevierPage 31 of 32 Large post-critical dynamics of an in...

    work page doi:10.1007/s00466-024-02555-4 2025

  24. [24]

    Nonlinear dynamics and stability boundaries of spinning fluid-conveying pipes: Galerkin and Hencky model approach,

    A. Fasihi, G. Kudra, M. GhandchiTehrani, and J. Awrejcewicz, “Nonlinear dynamics and stability boundaries of spinning fluid-conveying pipes: Galerkin and Hencky model approach,”Journal of Sound and Vibration, vol. 637, pp. 119820, 2026. doi:10.1016/j.jsv.2026.119820

    work page doi:10.1016/j.jsv.2026.119820 2026

  25. [25]

    Non-linear flexural-flexural-torsional-extensional dynamics of beams—I. Formulation,

    M. R. M. Crespo Da Silva, “Non-linear flexural-flexural-torsional-extensional dynamics of beams—I. Formulation,”International Journal of Solids and Structures, vol. 24, no. 12, pp. 1225–1234, 1988. doi:10.1016/0020-7683(88)90087-X

    work page doi:10.1016/0020-7683(88)90087-x 1988

  26. [26]

    Freevibrationsanalysisofarotatingshaftwithnonlinearitiesincurvatureandinertia,

    S.A.A.HosseiniandS.E.Khadem,“Freevibrationsanalysisofarotatingshaftwithnonlinearitiesincurvatureandinertia,”Mechanism and Machine Theory, vol. 44, no. 1, pp. 272–288, 2009. doi:10.1016/j.mechmachtheory.2008.01.007

    work page doi:10.1016/j.mechmachtheory.2008.01.007 2009

  27. [27]

    Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles,

    C. Q. Guo, C. H. Zhang, and M. P. Païdoussis, “Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles,”Journal of Fluids and Structures, vol. 26, no. 5, pp. 793–803, 2010. doi:10.1016/j.jfluidstructs.2010.04.005

    work page doi:10.1016/j.jfluidstructs.2010.04.005 2010

  28. [28]

    A study of swirling turbulent pipe and jet flows,

    L. Facciolo, N. Tillmark, A. Talamelli, and P. H. Alfredsson, “A study of swirling turbulent pipe and jet flows,”Physics of Fluids, vol. 19, no. 3, pp. 035105, 2007. doi:10.1063/1.2710287

    work page doi:10.1063/1.2710287 2007

  29. [29]

    C. M. Wang, H. Zhang, N. Challamel, and W. H. Pan,Hencky Bar-Chain/Net for Structural Analysis, World Scientific Publishing Co., 2020. doi:10.1142/q0237

    work page doi:10.1142/q0237 2020

  30. [30]

    Dynamics of a system of articulated pipes conveying fluid – I. Theory,

    T. B. Benjamin, “Dynamics of a system of articulated pipes conveying fluid – I. Theory,”Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 261, no. 1307, pp. 457–486, 1961. doi:10.1098/rspa.1961.0091

    work page doi:10.1098/rspa.1961.0091 1961

  31. [31]

    Articulated Models of Cantilevers Conveying Fluid: The Study of a Paradox,

    M. P. Paidoussis and E. Deksnis, “Articulated Models of Cantilevers Conveying Fluid: The Study of a Paradox,”Journal of Mechanical Engineering Science, vol. 12, pp. 288–300, 1970. doi:10.1243/JMES_JOUR_1970_012_050_02. A. Fasihi et al.:Preprint submitted to ElsevierPage 32 of 32

    work page doi:10.1243/jmes_jour_1970_012_050_02 1970