zbMATH — the first resource for mathematics

Dynamic behavior of axially functionally graded pipes conveying fluid. (English) Zbl 1426.74179
Summary: Dynamic behavior of axially functionally graded (FG) pipes conveying fluid was investigated numerically by using the generalized integral transform technique (GITT). The transverse vibration equation was integral transformed into a coupled system of second-order differential equations in the temporal variable. The Mathematica’s built-in function, NDSolve, was employed to numerically solve the resulting transformed ODE system. Excellent convergence of the proposed eigenfunction expansions was demonstrated for calculating the transverse displacement at various points of axially FG pipes conveying fluid. The proposed approach was verified by comparing the obtained results with the available solutions reported in the literature. Moreover, parametric studies were performed to analyze the effects of Young’s modulus variation, material distribution, and flow velocity on the dynamic behavior of axially FG pipes conveying fluid.

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74H45 Vibrations in dynamical problems in solid mechanics
Mathematica; NDSolve
Full Text: DOI
[1] Sadeghi, M. H.; Karimi-Dona, M. H., Dynamic behavior of a fluid conveying pipe subjected to a moving sprung mass—an FEM-state space approach, International Journal of Pressure Vessels and Piping, 88, 4, 123-131, (2011)
[2] Païdoussis, M. P.; Li, G. X., Pipes conveying fluid: a model dynamical problem, Journal of Fluids and Structures, 7, 2, 137-204, (1993)
[3] Païdoussis, M. P., Fluid-Structure Interactions: Slender Structures and Axial Flow, (1998), San Diego, Calif, USA: Academic Press, San Diego, Calif, USA
[4] Païdoussis, M. P., The canonical problem of the fluid-conveying pipe and radiation of the knowledge gained to other dynamics problems across Applied Mechanics, Journal of Sound and Vibration, 310, 3, 462-492, (2008)
[5] Long, R. H., Experimental and theoretical study of transverse vibration of a tube containing flowing fluid, Journal of Applied Mechanics Transactions of the ASME, 22, 1, 65-68, (1955)
[6] Païdoussis, M. P.; Issid, N. T., Dynamic stability of pipes conveying fluid, Journal of Sound and Vibration, 33, 3, 267-294, (1974)
[7] Païdoussis, M. P., Flutter of conservative systems of pipes conveying in compressible fluid, Journal of Mechanical Engineering Science, 17, 1, 19-25, (1975)
[8] Xu, M.-R.; Xu, S.-P.; Guo, H.-Y., Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method, Computers & Mathematics with Applications, 60, 3, 520-527, (2010) · Zbl 1201.76199
[9] Liu, L.; Xuan, F., Flow-induced vibration analysis of supported pipes conveying pulsating fluid using precise integration method, Mathematical Problems in Engineering, 2010, (2010) · Zbl 1425.74159
[10] Ginsberg, J. H., The dynamic stability of a pipe conveying a pulsatile flow, International Journal of Engineering Science, 11, 9, 1013-1024, (1973) · Zbl 0263.76013
[11] Jin, J. D.; Song, Z. Y., Parametric resonances of supported pipes conveying pulsating fluid, Journal of Fluids and Structures, 20, 6, 763-783, (2005)
[12] Panda, L. N.; Kar, R. C., Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances, Journal of Sound and Vibration, 309, 3–5, 375-406, (2008)
[13] Zhao, F.-Q.; Wang, Z.-M.; Feng, Z.-Y.; Liu, H.-Z., Stability analysis of Maxwell viscoelastic pipes conveying fluid with both ends simply supported, Applied Mathematics and Mechanics, 22, 12, 1436-1445, (2001) · Zbl 1143.74333
[14] Zhang, Y. L.; Gorman, D. G.; Reese, J. M., A modal and damping analysis of viscoelastic Timoshenko tubes conveying fluid, International Journal for Numerical Methods in Engineering, 50, 2, 419-433, (2001) · Zbl 0982.74073
[15] Wang, Z.-M.; Zhang, Z.-W.; Zhao, F.-Q., Stability analysis of viscoelastic curved pipes conveying fluid, Applied Mathematics and Mechanics, 26, 6, 807-813, (2005) · Zbl 1144.74332
[16] Yang, X.; Yang, T.; Jin, J., Dynamic stability of a beam-model viscoelastic pipe for conveying pulsative fluid, Acta Mechanica Solida Sinica, 20, 4, 350-356, (2007)
[17] Gulyayev, V. I.; Tolbatov, E. Y., Forced and self-excited vibrations of pipes containing mobile boiling fluid clots, Journal of Sound and Vibration, 257, 3, 425-437, (2002)
[18] Seo, Y. S.; Jeong, W. B.; Jeong, S. H.; Oh, J. S.; Yoo, W. S., Finite element analysis of forced vibration for a pipe conveying harmonically pulsating fluid, JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing, 48, 4, 688-694, (2006)
[19] Liang, F.; Wen, B. C., Forced vibrations with internal resonance of a pipe conveying fluid under external periodic excitation, Acta Mechanica Solida Sinica, 24, 6, 477-483, (2011)
[20] Zhai, H.-B.; Wu, Z.-Y.; Liu, Y.-S.; Yue, Z.-F., Dynamic response of pipeline conveying fluid to random excitation, Nuclear Engineering and Design, 241, 8, 2744-2749, (2011)
[21] Zhai, H.-B.; Wu, Z.-Y.; Liu, Y.-S.; Yue, Z.-F., In-plane dynamic response analysis of curved pipe conveying fluid subjected to random excitation, Nuclear Engineering and Design, 256, 214-226, (2013)
[22] Kadoli, R.; Ganesan, N., Parametric resonance of a composite cylindrical shell containing pulsatile flow of hot fluid, Composite Structures, 65, 3-4, 391-404, (2004)
[23] Ganesan, N.; Kadoli, R., A study on the dynamic stability of a cylindrical shell conveying a pulsatile flow of hot fluid, Journal of Sound and Vibration, 274, 3–5, 953-984, (2004)
[24] Sheng, G. G.; Wang, X., Thermomechanical vibration analysis of a functionally graded shell with flowing fluid, European Journal of Mechanics—A/Solids, 27, 6, 1075-1087, (2008) · Zbl 1151.74364
[25] Qian, Q.; Wang, L.; Ni, Q., Instability of simply supported pipes conveying fluid under thermal loads, Mechanics Research Communications, 36, 3, 413-417, (2009) · Zbl 1258.74117
[26] Hosseini, M.; Fazelzadeh, S. A., Thermomechanical stability analysis of functionally graded thin-walled cantilever pipe with flowing fluid subjected to axial load, International Journal of Structural Stability and Dynamics, 11, 3, 513-534, (2011) · Zbl 1271.74217
[27] Shen, H.-S., Functionally Graded Materials : Nonlinear Analysis of Plates and Shells, (2009), Boca Raton, Fla, USA: CRC Press, Boca Raton, Fla, USA
[28] Zhong, Z.; Wu, L.; Chen, W., Mechanics of Functionally Graded Materials and Structures, (2012), New York, NY, USA: Nova Science, New York, NY, USA
[29] Huang, Y.; Li, X.-F., A new approach for free vibration of axially functionally graded beams with non-uniform cross-section, Journal of Sound and Vibration, 329, 11, 2291-2303, (2010)
[30] Huang, Y.; Yang, L.-E.; Luo, Q.-Z., Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section, Composites Part B: Engineering, 45, 1, 1493-1498, (2013)
[31] Shahba, A.; Attarnejad, R.; Marvi, M. T.; Hajilar, S., Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions, Composites Part B: Engineering, 42, 4, 801-808, (2011)
[32] Shahba, A.; Rajasekaran, S., Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials, Applied Mathematical Modelling, 36, 7, 3094-3111, (2012) · Zbl 1252.74021
[33] Şimşek, M.; Kocatürk, T.; Akbaş, Ş. D., Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load, Composite Structures, 94, 8, 2358-2364, (2012)
[34] Alshorbagy, A. E.; Eltaher, M. A.; Mahmoud, F. F., Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35, 1, 412-425, (2011) · Zbl 1202.74088
[35] An, C.; Su, J., Dynamic response of clamped axially moving beams: integral transform solution, Applied Mathematics and Computation, 218, 2, 249-259, (2011) · Zbl 1259.74018
[36] An, C.; Su, J., Dynamic analysis of axially moving orthotropic plates: integral transform solution, Applied Mathematics and Computation, 228, 489-507, (2014) · Zbl 1364.74043
[37] Gu, J.; An, C.; Duan, M.; Levi, C.; Su, J., Integral transform solutions of dynamic response of a clamped-clamped pipe conveying fluid, Nuclear Engineering and Design, 254, 237-245, (2015)
[38] An, C.; Su, J., Dynamic behavior of pipes conveying gas-liquid two-phase flow, Nuclear Engineering and Design, 292, 204-212, (2015)
[39] Matt, C. F. T., On the application of generalized integral transform technique to wind-induced vibrations on overhead conductors, International Journal for Numerical Methods in Engineering, 78, 8, 901-930, (2009) · Zbl 1183.74363
[40] Gu, J.-J.; An, C.; Levi, C.; Su, J., Prediction of vortex-induced vibration of long flexible cylinders modeled by a coupled nonlinear oscillator: integral transform solution, Journal of Hydrodynamics, 24, 6, 888-898, (2012)
[41] Matt, C. F., Simulation of the transverse vibrations of a cantilever beam with an eccentric tip mass in the axial direction using integral transforms, Applied Mathematical Modelling, 37, 22, 9338-9354, (2013) · Zbl 1427.74092
[42] Leissa, A. W.; Qatu, M. S., Vibrations of Continuous Systems, (2011), New York, NY, USA: McGrawHill, New York, NY, USA
[43] Wolfram, S., The Mathematica Book, (2003), Champaign, IIl, USA: Wolfram Media/Cambridge University Press, Champaign, IIl, USA
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.