Abstract
The conveyance of fluid through pipes is a common occurrence in practical applications, and the dynamic stability of such systems has been a subject of interest for many decades. In this paper, we investigate the dynamic stability of a cantilevered pipe conveying fluid, considering the lateral distributed load as a critical factor. To achieve this, we employ the differential quadrature method to solve the eigenvalue equations for various load patterns. Remarkably, we observe excellent agreement with exact solutions and the Argand diagram. By analyzing the relationship between circular frequency and dimensionless velocity, we demonstrate that the descending distributed load pattern exhibits the highest stability. For certain conditions, it is possible to enhance stability. The results obtained in this study provide valuable insights for improving the stability of cantilevered pipe conveying fluid through a different approach.
Similar content being viewed by others
References
Paidoussis, M.P.: Fluid Structure Interactions: Slender Structures and Axial Flow, vol. 2. Academic Press, London (2016)
Ibrahim, R.A.: Overview of mechanics of pipes conveying fluids-part I: fundamental studies. J. Press. Vessel Technol. 132(3), 034001 (2010)
Zeng, L., Lv, T., Chen, H., Ma, T., Fang, Z., Shi, J.: Flow accelerated corrosion of X65 steel gradual contraction pipe in high CO2 partial pressure environments. Arab. J. Chem. 16(8), 104935 (2023)
Xia, Y., Shi, M., Zhang, C., Wang, C., Sang, X., Liu, R., Zhao, P., An, G., Fang, H.: Analysis of flexural failure mechanism of ultraviolet cured-in-place-pipe materials for buried pipelines rehabilitation based on curing temperature monitoring. Eng. Fail. Anal. 142, 106763 (2022)
Wang, Y., Lou, M., Wang, Y., Wu, W., Yang, F.: Stochastic failure analysis of reinforced thermoplastic pipes under axial loading and internal pressure. China Ocean Eng. 36, 614–628 (2022)
Wang, Y., Lou, M., Wang, Y., Fan, C., Tian, C., Qi, X.: Experimental investigation of the effect of rotation rate and current speed on the dynamic response of riserless rotating drill string. Ocean Eng. 280, 114542 (2023)
Sazesh, S., Shams, S.: Vibration analysis of cantilever pipe conveying fluid under distributed random excitation. J. Fluids Struct. 87, 84–101 (2019)
Paidoussis, M.P., Li, G.X.: Pipes conveying fluid: a model dynamical problem. J. Fluids Struct. 7(2), 137–204 (1993)
Zhou, K., Dai, H.L., Wang, L., Ni, Q., Hagedorm, P.: Modeling and nonlinear dynamics of cantilevered pipe with tapered free end concurrently subjected to axial internal and external flows. Mech. Syst. Signal Process. 169, 108794 (2022)
Tang, Y., Zhen, Y., Fang, B.: Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid. Appl. Math. Model. 56, 123–136 (2018)
El-Sayed, T.A., El-Mongy, H.H.: Free vibration and stability analysis of a multi-span pipe conveying fluid using exact and variational iteration methods combined with transfer matrix method. Appl. Math. Model. 71, 173–193 (2019)
Oyelade, A.O., Oyediran, A.A.: The effect of various boundary conditions on the nonlinear dynamics of slightly curved pipes under thermal loading. Appl. Math. Model. 87, 332–350 (2020)
Ni, Q., Zhang, Z.L., Wang, L.: Application of the differential transformation method to vibration analysis of pipes conveying fluid. Appl. Math. Comput. 217, 7028–7038 (2011)
Wang, L., Jiang, T.L., Dai, H.L., Ni, Q.: Three-dimensional vortex-induced vibrations of supported pipes conveying fluid based on wake oscillator models. J. Sound Vib. 422, 590–612 (2018)
Ding, H., Ji, J., Chen, L.: Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics. Mech. Syst. Signal Process. 121, 675–688 (2019)
Yoon, H., Son, I.S.: Dynamic response of rotating flexible cantilever pipe conveying fluid with tip mass. Int. J. Mech. Sci. 49, 878–887 (2007)
Zhou, K., Xiong, F.R., Jiang, N.B., et al.: Nonlinear vibration control of a cantilevered fluid-conveying pipe using the idea of nonlinear energy sink. Nonlinear Dyn. 95, 1435–1456 (2019)
Ghayesh, M.H., Paidoussis, M.P., Modarres-Sadeghi, Y.: Three-dimensional dynamics of a fluid-conveying cantilevered pipe fitted with an additional spring-support and an end-mass. J. Sound Vib. 330, 2869–2899 (2011)
Paidoussis, M.P., Li, G.X., Moon, F.C.: Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. J. Sound Vib. 135(1), 1–19 (1989)
Paidoussis, M.P., Semler, C.: Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: a full nonlinear analysis. Nonlinear Dyn. 4, 655–670 (1993)
Ni, Q., Wang, Y., Tang, M., et al.: Nonlinear impacting oscillations of a fluid-conveying pipe subjected to distributed motion constraints. Nonlinear Dyn. 81, 893–906 (2015)
Liu, Z.Y., Wang, L., Dai, H.L., et al.: Nonplanar vortex-induced vibrations of cantilevered pipes conveying fluid subjected to loose constraints. Ocean Eng. 178, 1–19 (2019)
Wang, Y., Tang, M., Yang, M., et al.: Three-dimensional dynamics of a cantilevered pipe conveying pulsating fluid. Appl. Math. Model. 114, 502–524 (2023)
Zhou, J., Chang, X., Xiong, Z., Li, Y.: Stability and nonlinear vibration analysis of fluid-conveying composite pipes with elastic boundary conditions. Thin-Walled Struct. 179, 109597 (2022)
Dai, H.L., Wang, L., Ni, Q.: Dynamics of a fluid-conveying pipe composed of two different materials. Int. J. Eng. Sci. 73, 67–75 (2013)
Bahaadini, R., Dashtbayazi, M.R., Hosseini, M., Parizi, Z.K.: Stability analysis of composite thin-walled pipes conveying fluid. Ocean Eng. 160, 311–323 (2018)
ElNajjar, J., Daneshmand, F.: Stability of horizontal and vertical pipes conveying fluid under the effects of additional point masses and springs. Ocean Eng. 206, 106943 (2020)
Jiang, T., Dai, H., Wang, L.: Three-dimensional dynamics of fluid-conveying pipe simultaneously subjected to external axial flow. Ocean Eng. 217, 107970 (2020)
Abdelbaki, A.R., Paidoussis, M.P., Misra, A.K.: A nonlinear model for a hanging tubular cantilever simultaneously subjected to internal and confined external axial flows. J. Sound Vib. 449, 349–367 (2019)
Bonanos, A.M., Georgiou, M.C., Stokos, K.G., Papanicolas, C.N.: Engineering aspects and thermal performance of molten salt transfer lines in solar power applications. Appl. Therm. Eng. 154, 294–301 (2019)
Zhang, M., Xie, Y., Wang, Z.: An air heat tracing system of firefighting pipeline in cold region highway tunnel. Sustainability 14, 16056 (2022)
Wang, X., Wang, Y.: Free vibration analysis of multiple-stepped beams by the differential quadrature element method. Appl. Math. Comput. 219, 5802–5810 (2013)
Charles, W.B., Moinuddin, M.: Differential quadrature method in computational mechanics: a review. Appl. Mech. Rev. 49(1), 1–28 (1996)
Xu, J., Wang, L.: Dynamics and Control of Fluid-Conveying Pipe Systems. Science Press, Beijing (2015)
Liu, Y., Chen, L., Chen, W.: Mechanics of Vibrations, 3rd edn. Higher Education Press, Beijing (2019)
Thomson, W.T.: Theory of Vibration with Applications. Unwin Hyman Ltd., London (1988)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhang, Y., Li, P. Dynamical stability of pipe conveying fluid with various lateral distributed loads. Arch Appl Mech 93, 4093–4106 (2023). https://doi.org/10.1007/s00419-023-02481-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-023-02481-6