Dynamics of axially functionally graded pipes conveying fluid using a higher order shear deformation theory

Year 2021, Volume: 5 Issue: 2, 209 - 217, 15.08.2021

Reza Aghazadeh

https://doi.org/10.35860/iarej.878194

Cited By: 2

Abstract

This study presents a novel approach for addressing dynamical characteristics of fluid conveying axially functionally graded pipes. The variation of material properties of the pipe along axial direction is taken into account according to a power-law function. Owing to a unified expression for displacement field, the developed model can be recast into classical Euler – Bernoulli and Timoshenko tube models as well as a newly developed higher order shear deformable tube model; the latter satisfies zero-shear conditions on free surfaces, and hence yields more realistic results. The system of partial differential equations governing dynamics of fluid conveying axially functionally graded pipes is derived through utilization of Hamilton’s principle. Differential quadrature scheme is used to discretize the system of differential equations and generate numerical results. Detailed numerical investigations of the current fluid-solid interaction problem elucidate the effects of material gradation pattern, transverse shear deformation distribution profile along radial direction and fluid velocity on the natural frequencies of fluid conveying functionally graded pipes. The critical fluid velocity, which is a significant design parameter, can also be determined by means of developed procedures in this study.

Keywords

Axially functionally graded material, Critical flow velocity, Differential quadrature method, Fluid conveying pipes, Refined pipe model

References

• 1. Paidoussis, M.P., Fluid-Structure Interactions: Slender Structures and Axial Flow. 1998, London: Academic Press.
• 2. Lee, U. and J. Park, Spectral element modelling and analysis of a pipeline conveying internal unsteady fluid. Journal of Fluids and Structures, 2006. 22(2): p. 273-292.
• 3. Xu, M.R., S.P. Xu, and H.Y. Guo, Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method. Computers & Mathematics with Applications, 2010. 60(3): p. 520-527.
• 4. Zhang, T., et al., Nonlinear dynamics of straight fluid-conveying pipes with general boundary conditions and additional springs and masses. Applied Mathematical Modelling, 2016. 40(17): p. 7880-7900.
• 5. Tang, Y., Y. Zhen, and B. Fang, Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid. Applied Mathematical Modelling, 2018. 56: p. 123-136.
• 6. ElNajjar, J. and F. Daneshmand, Stability of horizontal and vertical pipes conveying fluid under the effects of additional point masses and springs. Ocean Engineering, 2020. 206: p. 106943.
• 7. Dagli, B.Y. and A. Ergut, Dynamics of fluid conveying pipes using Rayleigh theory under non-classical boundary conditions. European Journal of Mechanics - B/Fluids, 2019. 77: p. 125-134.
• 8. Abdollahi, R., R. Dehghani Firouz-abadi, and M. Rahmanian, On the stability of rotating pipes conveying fluid in annular liquid medium. Journal of Sound and Vibration, 2021. 494: p. 115891.
• 9. Szmidt, T., D. Pisarski, and R. Konowrocki, Semi-active stabilisation of a pipe conveying fluid using eddy-current dampers: state-feedback control design, experimental validation. Meccanica, 2019. 54(6): p. 761-777.
• 10. Mahamood, R.M. and E.T. Akinlabi, Types of Functionally Graded Materials and Their Areas of Application, in Functionally Graded Materials, R.M. Mahamood and E.T. Akinlabi, Editors. 2017, Springer International Publishing: Cham. p. 9-21.
• 11. Petit, C., L. Montanaro, and P. Palmero, Functionally graded ceramics for biomedical application: Concept, manufacturing, and properties. International Journal of Applied Ceramic Technology, 2018. 15(4): p. 820-840.
• 12. Safaei, B., The effect of embedding a porous core on the free vibration behavior of laminated composite plates. Steel and Composite Structures, 2020. 35(5): p. 659-670.
• 13. Moradi-Dastjerdi, R., et al., Buckling behavior of porous CNT-reinforced plates integrated between active piezoelectric layers. Engineering Structures, 2020. 222: p. 111141.
• 14. Fan, F., S. Sahmani, and B. Safaei, Isogeometric nonlinear oscillations of nonlocal strain gradient PFGM micro/nano-plates via NURBS-based formulation. Composite Structures, 2021. 255: p. 112969.
• 15. Aghazadeh, R., S. Dag, and E. Cigeroglu, Modelling of graded rectangular micro-plates with variable length scale parameters. Structural engineering and mechanics: An international journal, 2018. 65(5): p. 573-585.
• 16. Tang, Y. and T. Yang, Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material. Composite Structures, 2018. 185: p. 393-400.
• 17. Liu, H., Z. Lv, and H. Tang, Nonlinear vibration and instability of functionally graded nanopipes with initial imperfection conveying fluid. Applied Mathematical Modelling, 2019. 76: p. 133-150.
• 18. Zhu, B., et al., Static and dynamic characteristics of the post-buckling of fluid-conveying porous functionally graded pipes with geometric imperfections. International Journal of Mechanical Sciences, 2021. 189: p. 105947.
• 19. Dehrouyeh-Semnani, A.M., et al., Nonlinear thermo-resonant behavior of fluid-conveying FG pipes. International Journal of Engineering Science, 2019. 144: p. 103141.
• 20. Khodabakhsh, R., A.R. Saidi, and R. Bahaadini, 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, 2020. 101: p. 102277.
• 21. Deng, J., et al., Stability analysis of multi-span viscoelastic functionally graded material pipes conveying fluid using a hybrid method. European Journal of Mechanics - A/Solids, 2017. 65: p. 257-270.
• 22. Reddy, R.S., S. Panda, and G. Natarajan, Nonlinear dynamics of functionally graded pipes conveying hot fluid. Nonlinear Dynamics, 2020. 99(3): p. 1989-2010.
• 23. Zhu, B., et al., Nonlinear free and forced vibrations of porous functionally graded pipes conveying fluid and resting on nonlinear elastic foundation. Composite Structures, 2020. 252: p. 112672.
• 24. An, C. and J. Su, Dynamic Behavior of Axially Functionally Graded Pipes Conveying Fluid. Mathematical Problems in Engineering, 2017. 2017: p. 6789634.
• 25. Zhou, X.-w., H.-L. Dai, and L. Wang, Dynamics of axially functionally graded cantilevered pipes conveying fluid. Composite Structures, 2018. 190: p. 112-118.
• 26. Ebrahimi-Mamaghani, A., et al., Thermo-mechanical stability of axially graded Rayleigh pipes. Mechanics Based Design of Structures and Machines, 2020: p. 1-30.
• 27. Lu, Z.-Q., et al., Nonlinear vibration effects on the fatigue life of fluid-conveying pipes composed of axially functionally graded materials. Nonlinear Dynamics, 2020. 100(2): p. 1091-1104.
• 28. Mirtalebi, S.H., A. Ebrahimi-Mamaghani, and M.T. Ahmadian, Vibration Control and Manufacturing of Intelligibly Designed Axially Functionally Graded Cantilevered Macro/Micro-tubes. IFAC-PapersOnLine, 2019. 52(10): p. 382-387.
• 29. Şimşek, M. and J.N. Reddy, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory. International Journal of Engineering Science, 2013. 64: p. 37-53.
• 30. Aghazadeh, R., E. Cigeroglu, and S. Dag, Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories. European Journal of Mechanics - A/Solids, 2014. 46: p. 1-11.
• 31. Zhang, P. and Y. Fu, A higher-order beam model for tubes. European Journal of Mechanics - A/Solids, 2013. 38: p. 12-19.
• 32. Babaei, H. and M. Reza Eslami, Size-dependent vibrations of thermally pre/post-buckled FG porous micro-tubes based on modified couple stress theory. International Journal of Mechanical Sciences, 2020. 180: p. 105694.
• 33. She, G.-L., et al., Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory. Composite Structures, 2018. 203: p. 614-623.
• 34. She, G.-L., et al., On buckling and postbuckling behavior of nanotubes. International Journal of Engineering Science, 2017. 121: p. 130-142.
• 35. Zhong, J., et al., Nonlinear bending and vibration of functionally graded tubes resting on elastic foundations in thermal environment based on a refined beam model. Applied Mathematical Modelling, 2016. 40(17): p. 7601-7614.
• 36. Hutchinson, J.R., Shear Coefficients for Timoshenko Beam Theory. Journal of Applied Mechanics, 2000. 68(1): p. 87-92.
• 37. Sahmani, S. and B. Safaei, Large-amplitude oscillations of composite conical nanoshells with in-plane heterogeneity including surface stress effect. Applied Mathematical Modelling, 2021. 89: p. 1792-1813.
• 38. Wang, L., Size-dependent vibration characteristics of fluid-conveying microtubes. Journal of Fluids and Structures, 2010. 26(4): p. 675-684.