Abstract
The nonlinear dynamic behaviors of viscoelastic axially functionally graded material (AFG) pipes conveying pulsating internal flow are very complex. And the dynamic behavior will induce the failure of the pipes, and research of vibration and stability of pipes becomes a major concern. Considering that the elastic modulus, density, and coefficient of viscoelastic damping of the pipe material vary along the axial direction, the transverse vibration equation of the viscoelastic AFG pipe conveying pulsating fluid is established based on the Euler-Bernoulli beam theory. The generalized integral transform technique (GITT) is used to transform the governing fourth-order partial differential equation into a nonlinear system of fourth-order ordinary differential equations in time. The time domain diagram, phase portraits, Poincaré map and power spectra diagram at different dimensionless pulsation frequencies, are discussed in detail, showing the characteristics of chaotic, periodic, and quasi-periodic motion. The results show that the distributions of the elastic modulus, density, and coefficient of viscoelastic damping have significant effects on the nonlinear dynamic behavior of the viscoelastic AFG pipes. With the increase of the material property coefficient k, the transition between chaotic, periodic, and quasi-periodic motion occurs, especially in the high-frequency region of the flow pulsation.
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References
An C, Su J (2017) Dynamic behavior of axially functionally graded pipes conveying fluid. Mathematical Problems in Engineering 2017: 6789634. https://doi.org/10.1155/2017/6789634
Babilio E (2014) Dynamics of functionally graded beams on viscoelastic foundation, International Journal of Structural Stability and Dynamics 14(08): 1440014. https://doi.org/10.1142/S0219455414400148
Cotta RM, Lisboa KM, Curi MF, Balabani S, Quaresma JN, Perez Guerrero JS, Mac’edo EN, Amorim NS (2019) A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier - Stokes equations formulation. Numerical Heat Transfer, Part B: Fundamentals 76(2): 60–87. https://doi.org/10.1080/10407790.2019.1642715
Dai J, Liu Y, Liu H, Miao C, Tong G (2019) A parametric study on thermo-mechanical vibration of axially functionally graded material pipe conveying fluid. International Journal of Mechanics and Materials in Design 15(4): 715–726. https://doi.org/10.1007/s10999-018-09439-5
Deng J, Liu Y, Zhang Z, Liu W (2017) Dynamic behaviors of multispan viscoelastic functionally graded material pipe conveying fluid. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231(17): 3181–3192. https://doi.org/10.1177/0954406216642483
Ebrahimi-Mamaghani A, Sotudeh-Gharebagh R, Zarghami R, Mostoufi N (2022) Thermo-mechanical stability of axially graded rayleigh pipes. Mechanics Based Design of Structures and Machines 50(2): 412–441. https://doi.org/10.1080/15397734.2020.1717967
Fu G, Li M, Yang J, Li S, Sun B, Estefen S F (2022a) A simplified equation for the collapse pressure of sandwich pipes with different core materials. Ocean Engineering 254: 111292. https://doi.org/10.1016/j.oceaneng.2022.111292
Fu G, Li M, Yang J, Sun B, Shi C, Estefen S F (2022b) The effect of eccentricity on the collapse behaviour of sandwich pipes. Applied Ocean Research 124(4): 103190. https://doi.org/10.1016/j.apor.2022.103190
Fu G, Peng Y, Sun B, An C, Su J (2019) An exact GITT solution for static bending of clamped parallelogram plate resting on an elastic foundation. Engineering Computations 36(6): 2034–2047. https://doi.org/10.1108/EC-12-2018-0582
Fu G, Tuo Y, Sun B, Shi C, Su J (2022c) Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution. Engineering Computations 39(7): 2689–2704. https://doi.org/10.1108/EC-11-2021-0692
Gupta A, Talha M (2015) Recent development in modeling and analysis of functionally graded materials and structures. Progress in Aerospace Sciences 79:1–14. https://doi.org/10.1016/j.paerosci.2015.07.001i
Heshmati M (2020) Influence of an eccentricity imperfection on the stability and vibration behavior of fluid-conveying functionally graded pipes. Ocean Engineering 203: 107192. https://doi.org/10.1016/j.oceaneng.2020.107192
Jiang M, Zhao J, Wang Q (2022) Linear energy stable numerical schemes for a general chemo-repulsive model. Journal of Computational and Applied Mathematics, 114436. https://doi.org/10.1016/j.cam.2022.114436
Jiang M, Zhao J (2023) Linear relaxation schemes for the Allen-Cahn-type and Cahn-Hilliard-type phase field models. Applied Mathematics Letter 137: 108477. https://doi.org/10.1016/j.aml.2022.108477
Jin JD (1997) Stability and chaotic motions of a restrained pipe conveying fluid. Journal of Sound and Vibration 208(3): 427–439. https://doi.org/10.1006/jsvi.1997.1195
Jin J, Song Z (2005) Parametric resonances of supported pipes conveying pulsating fluid. Journal of Fluids and Structures 20(6): 763–783. https://doi.org/10.1016/j.jfluidstmcts.2005.04.007
Khodabakhsh R, Saidi A R, Bahaadini R (2020) An analytical solution for nonlinear vibration and post-buckling of functionally graded pipes conveying fluid considering the rotary inertia and shear deformation effects. Applied Ocean Research 101: 102277. https://doi.org/10.1016/j.apor.2020.102277
Li F, An C, Duan M, Su J (2020) Combined damping model for dynamics and stability of a pipe conveying two-phase flow. Ocean Engineering 195: 106683. https://doi.org/10.1016/j.oceaneng.2019.106683
Loghman E, Kamali A, Bakhtiari-Nejad F, Abbaszadeh M (2021) Nonlinear free and forced vibrations of fractional modeled viscoelastic FGM micro-beam, Applied Mathematical Modelling 92: 297–314. https://doi.org/10.1016/j.apm.2020.11.011
Lu Z Q, Zhang K K, Ding H, Chen L Q (2020) Nonlinear vibration effects on the fatigue life of fluid-conveying pipes composed of axially functionally graded materials. Nonlinear Dynamics 100(2):1091–1104. https://doi.org/10.1007/s11071-020-05577-8
Ni Q, Zhang Z, Wang L, Qian Q, Tang M (2014) Nonlinear dynamics and synchronization of two coupled pipes conveying pulsating fluid. Acta Mechanica Solida Sinic 27(2): 162–171. https://doi.org/10.1016/S0894-9166(14)60026-4
Nikbakht S, Kamarian S, Shakeri M (2019) A review on optimization of composite structures part ii: Functionally graded materials. Composite Structures 214: 83–102. https://doi.org/10.1016/j.compstruct.2019.01.105
Oyelade AO, Oyediran A A (2020) The effect of various boundary conditions on the nonlinear dynamics of slightly curved pipes under thermal loading. Applied Mathematical Modelling 87: 332–350. https://doi.org/10.1016/j.apm.2020.06.019
Paidoussis M (1987) Flow-induced instabilities of cylindrical structures 40(2): 163–175. https://doi.org/10.1115/1.3149530
Paidoussis M, Cusumano J, Copeland G (1992) Low-dimensional chaos in a flexible tube conveying fluid. Journal of Applied Mechanics 59(1):196–205. https://doi.org/10.1115/1.2899428
Paidoussis M, Issid N (1974) Dynamic stability of pipes conveying fluid. Journal of Sound and Vibration 33(3): 267–294. https://doi.org/10.1016/S0022-460X(74)80002-7
Paidoussis M, Li G, Moon F (1989) Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. Journal of Sound and Vibration 135(1): 1–19. https://doi.org/10.1016/0022-460X(89)90750-5
Paidoussis M, Li G (1993) Pipes conveying fluid: a model dynamical problem, Journal of Fluids and Structures 7(2): 137–204. https://doi.org/10.1006/jfls.1993.1011
Paidoussis M, Moon F (1988) Nonlinear and chaotic fluid elastic vibrations of a flexible pipe conveying fluid, Journal of Fluids and Structures 2(6): 567–591. https://doi.org/10.1016/S0889-9746(88)80023-9
Paidoussis M, Semler C (1993) Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: a full nonlinear analysis. Nonlinear Dynamics 4(6): 655–670. https://doi.org/10.1007/BF00162236
Shafiei N, She G L (2018) On vibration of functionally graded nano-tubes in the thermal environment. International Journal of Engineering Science 133: 84–98. https://doi.org/10.1016/j.ijengsci.2018.08.004
Shariati A, Mohammad-Sedighi H, Zur K K, Habibi M, Safa M (2020) On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams. Materials 13(7): 1707. https://doi.org/10.3390/ma13071707
Shen J, Xu J, Yang J (2018) The scalar auxiliary variable (SAV) approach for gradient flows. Journal of Computational Physics 353:407–416. https://doi.org/10.1016/j.jcp.2017.10.021
Tang D, Dowell E (1988) Chaotic oscillations of a cantilevered pipe conveying fluid. Journal of Fluids and Structures 2(3): 263–283. https://doi.org/10.1016/S0889-9746(88)80011-2
Tang Y, Yang T (2018) Post-buckling behavior and nonlinear vibration analysis of a fluid conveying pipe composed of functionally graded material. Composite Structures 185: 393–400. https://doi.org/10.1016/j.compstruct.2017.11.032
Tuo Y, Fu G, Sun B, Lou M, Su J (2022) Stability of axially functionally graded pipe conveying fluid: Generalized integral transform solution. Applied Ocean Research 125:103218. https://doi.org/10.1016/j.apor.2022.103218
Wang L (2009) A further study on the non-linear dynamics of simply supported pipes conveying pulsating fluid. International Journal of Non-Linear Mechanics 44(1): 115–121. https://doi.org/10.1016/j.ijnonlinmec.2008.08.010
Wang L, Liu Z, Abdelkefi A, Wang Y, Dai H (2017) Nonlinear dynamics of cantilevered pipes conveying fluid: towards a further understanding of the effect of loose constraints, International Journal of Non-Linear Mecha 95: 19–29. https://doi.org/10.1016/j.ijnonlinmec.2017.05.012
Wang Y, Chen Y (2019) Dynamic analysis of the viscoelastic pipeline conveying fluid with an improved variable fractional order model based on shifted Legendre polynomials. Fractal and Fractional 3(4): 52. https://doi.org/10.3390/fractalfract3040052
Wang Z, Soares C G (2021) Upheaval thermal buckling of functionally graded subsea pipelines. Applied Ocean Research 116: 102881. https://doi.org/10.1016/j.apor.2021.102881
Wang Z, Chen B, Soares CG (2022) Analytical study on the upheaval thermal buckling of sandwich pipes. Marine Structures 85: 103245. https://doi.org/10.1016/j.marstruc.2022.103245
Zhao J, Wang Q, Yang X (2017) Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach. International Journal for Numerical Methods in Engineering 110: 279–300. https://doi.org/10.1002/nme.5372
Zhou X W, Dai H L, Wang L (2018) Dynamics of axially functionally graded cantilevered pipes conveying fluid. Composite Structures 190: 112–118. https://doi.org/10.1016/j.compstruct.2018.01.097
Funding
This work is supported by the National Natural Science Foundation of China (52171288, 51890914), the Key Research and Development Program of Shandong Province (Major Innovation Project) (2022CXGC020405), the National Ministry of Industry and Information Technology Innovation Special Project—Engineering Demonstration Application of Subsea Oil and Gas Production System-Subject 4 “Research on Subsea Christmas Tree and Wellhead Offshore Testing Technology” [MC-201901-S01-04], the Fundamental Research Funds for the Central Universities (20CX02410A), the Development Fund of Shandong Key Laboratory of Oil & Gas Storage and Transportation Safety, and CNPq, CAPES and FAPERJ of Brazil.
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Article Highlights
• The transverse vibration equation is established for the viscoelastic axially functionally graded material (AFG) pipe conveying pulsating fluid;
• The generalized integral transform technique is developed to analyze the nonlinear dynamics of AFG pipes;
• The effects of the elastic modulus, density, and coefficient of viscoelastic damping on nonlinear dynamics of AFG pipes are discussed.
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Fu, G., Tuo, Y., Zhang, H. et al. Effects of Material Characteristics on Nonlinear Dynamics of Viscoelastic Axially Functionally Graded Material Pipe Conveying Pulsating Fluid. J. Marine. Sci. Appl. 22, 247–259 (2023). https://doi.org/10.1007/s11804-023-00328-8
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DOI: https://doi.org/10.1007/s11804-023-00328-8