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ORIGINAL ARTICLE

Two-phase flow-induced vibration of tilted curved bi-directional functionally graded nanopipe in supersonic airflow

, &
Received 07 Feb 2024, Accepted 08 May 2024, Published online: 22 May 2024

References

  • Y. Sun, C. Zheng, F. Zhang, X. Tan, K. Chen, X. Song, X. Zhang, and Y. Chen, Theoretical study of elastic effect of a cylindrical pipe wall on ultrasonic flow measurement, Measurement, vol. 219, pp. 113281, 2023. DOI: 10.1016/j.measurement.2023.113281.
  • H. Wang, Y. Bao, M. Liu, S. Zhu, X. Du, and Y. Hou, Experimental study on dynamic characteristics of cylindrical horizontal axially rotating heat pipe, Appl. Thermal Eng., vol. 209, pp. 118248, 2022a. DOI: 10.1016/j.applthermaleng.2022.118248.
  • N. D. Dat, N. V. Thanh, V. MinhAnh, and N. D. Duc, Vibration and nonlinear dynamic analysis of sandwich FG-CNTRC plate with porous core layer, Mech. Adv. Mater. Struct., vol. 29, no. 10, pp. 1431–1448, 2022. DOI: 10.1080/15376494.2020.1822476.
  • V. Gupta, M. S. Barak, and S. Das, Vibrational analysis of size-dependent thermo-piezo-photo-electric semiconductor medium under memory-dependent Moore–Gibson–Thompson photo-thermoelasticity theory, Mech. Adv. Mater. Struct., pp. 1–17, 2023. DOI: 10.1080/15376494.2023.2291804.
  • S. Han, Q. Ye, A. Hakamy, and A. M. Abd-Elnaiem, Numerical solution hybridized by machine-leaning-based algorithm to provide an efficient method for analyzing thermomechanical shock behavior of the circumferentially-graded graphene-plates reinforced composite sandwich panel, Mech. Adv. Mater. Struct., pp. 1–24, 2023. DOI: 10.1080/15376494.2023.2195417.
  • M. Janghorban, and M. R. Nami, Wave propagation in functionally graded nanocomposites reinforced with carbon nanotubes based on second-order shear deformation theory, Mech. Adv. Mater. Struct., vol. 24, no. 6, pp. 458–468, 2017. DOI: 10.1080/15376494.2016.1142028.
  • N. Liu, J. Yang, and W. Chen, Thin-film piezoelectric actuators of nonuniform thickness and nonhomogeneous material properties for modulating actuation stress, Mech. Adv. Mater. Struct., vol. 22, no. 10, pp. 803–812, 2015. DOI: 10.1080/15376494.2013.864431.
  • D. G. Ninh, N. M. Quan, and V. N. V. Hoang, Thermally vibrational analyses of functionally graded graphene nanoplatelets reinforced funnel shells with different complex shapes surrounded by elastic foundation, Mech. Adv. Mater. Struct., vol. 29, no. 26, pp. 4654–4676, 2022. DOI: 10.1080/15376494.2021.1934763.
  • M. Afzali, M. Farrokh, and E. Carrera, Nonlinear thermal post-buckling analysis of rectangular FG plates using CUF, Compos. Struct., vol. 321, pp. 117282, 2023. DOI: 10.1016/j.compstruct.2023.117282.
  • H. Ahmadi, and K. Foroutan, Nonlinear static and dynamic thermal buckling analysis of imperfect multilayer FG cylindrical shells with an FG porous core resting on nonlinear elastic foundation, J. Thermal Stress., vol. 43, no. 5, pp. 629–649, 2020. DOI: 10.1080/01495739.2020.1727802.
  • M. R. Barati, and A. Zenkour, Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments, Mech. Adv. Mater. Struct., vol. 25, no. 8, pp. 669–680, 2018. DOI: 10.1080/15376494.2017.1308603.
  • M. Jafari Niasar, A. A. Jafari, M. Irani Rahaghi, and S. Mohammadrezazadeh, Active control of free and forced vibration of a rotating FG cylindrical shell via FG piezoelectric patches, Mech. Based Des. Struct. Mach., pp. 1–25, 2023. DOI: 10.1080/15397734.2023.2212297.
  • N. Latroch, M. Dahmane, A. Soufiane Benosman, R. Bennai, H. A. Atmane, and Mourad Benadouda, Inclined crack identification in bidirectional FG beams on an elastic foundation using the h-version of the finite element method, Mech. Adv. Mater. Struct., pp. 1–7, 2023. DOI: 10.1080/15376494.2023.2290226.
  • M. Momeni, and M. B. Dehkordi, Frequency analysis of sandwich beam with FG carbon nanotubes face sheets and flexible core using high-order element, Mech. Adv. Mater. Struct., vol. 26, no. 9, pp. 805–815, 2019. DOI: 10.1080/15376494.2017.1410918.
  • L. Zhou, A novel similitude method for predicting natural frequency of FG porous plates under thermal environment, Mech. Adv. Mater. Struct., vol. 29, no. 27, pp. 6786–6802, 2022. DOI: 10.1080/15376494.2021.1985197.
  • M.Abedi, and A. Asnafi, On deriving exact probability density functions for functionally graded exponential profile orthotropic plates driven by laterally random excitation, Mech. Adv. Mater. Struct., vol. 24, no. 13, pp. 1124–1134, 2017. DOI: 10.1080/15376494.2016.1227497.
  • D. Bigoni, and O. Kirillov, 2019. Dynamic Stability and Bifurcation in Nonconservative Mechanics. Springer, Berlin.
  • R. C. Dash, D. K. Maiti, and B. N. Singh, Nonlinear dynamic analysis of galloping based piezoelectric energy harvester employing finite element method, Mech. Adv. Mater. Struct., vol. 29, no. 26, pp. 4964–4971, 2022. DOI: 10.1080/15376494.2021.1943082.
  • T. Dong, W. Zhang, and M. Dong, The dynamic regimes of the unsymmetric bistable laminate, Mech. Adv. Mater. Struct., pp. 1–19, 2022.
  • S. A. Ghasabi, M. Shahgholi, and M. Arbabtafti, Analysis and suppression of the nonlinear oscillations of a continuous rotating shaft using an active time-delayed control, Mech. Adv. Mater. Struct., vol. 28, no. 19, pp. 1978–1991, 2021. DOI: 10.1080/15376494.2020.1716411.
  • Z. Guo, J. Xu, D. Cao, T. Dong, and W. Ma, The static and dynamic regimes of the bistable asymmetric cross-ply composite laminated plates, Mech. Adv. Mater. Struct., pp. 1–15, 2023. DOI: 10.1080/15376494.2023.2264878.
  • J. P. Amezquita-Sanchez, A. Dominguez-Gonzalez, R. Sedaghati, R. de Jesus Romero-Troncoso, and R. A. Osornio-Rios, Vibration control on smart civil structures: a review, Mech. Adv. Mater. Struct., vol. 21, no. 1, pp. 23–38, 2014. DOI: 10.1080/15376494.2012.677103.
  • G. Kai, S.W. Yang, W. Zhang, X.J. Gu, and W.S. Ma, Transient and steady-state nonlinear vibrations of FGM truncated conical shell subjected to blast loads and transverse periodic load using post-difference method, Mech. Adv. Mater. Struct., vol. 30, no. 6, pp. 1188–1206, 2023. DOI: 10.1080/15376494.2022.2029638.
  • T. Y. Zhao, Y. Song Cui, Y. Q. Wang, and H. G. Pan, Vibration characteristics of graphene nanoplatelet reinforced disk-shaft rotor with eccentric mass, Mech. Adv. Mater. Struct., vol. 29, no. 24, pp. 3485–3498, 2022. DOI: 10.1080/15376494.2021.1904525.
  • M. Şimşek, Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions, Compos. Struct., vol. 133, pp. 968–978, 2015. DOI: 10.1016/j.compstruct.2015.08.021.
  • M. Şimşek, Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions, Compos. Struct., vol. 149, pp. 304–314, 2016. DOI: 10.1016/j.compstruct.2016.04.034.
  • P. S. Ghatage, V. R. Kar, and P. E. Sudhagar, On the numerical modelling and analysis of multi-directional functionally graded composite structures: a review, Compos. Struct., vol. 236, pp. 111837, 2020. DOI: 10.1016/j.compstruct.2019.111837.
  • B. Temel, and A. R. Noori, A unified solution for the vibration analysis of two-directional functionally graded axisymmetric Mindlin–Reissner plates with variable thickness, Int. J. Mech. Sci., vol. 174, pp. 105471, 2020. DOI: 10.1016/j.ijmecsci.2020.105471.
  • X. Han, Z. Wei, B. Zhang, Y. Li, T. Du, and H. Chen, Crop evapotranspiration prediction by considering dynamic change of crop coefficient and the precipitation effect in back-propagation neural network model, J. Hydrol., vol. 596, pp. 126104, 2021. DOI: 10.1016/j.jhydrol.2021.126104.
  • R. Chowdhury, S. Adhikari, C.Y. Wang, and F. Scarpa, A molecular mechanics approach for the vibration of single-walled carbon nanotubes, Comput. Mater. Sci., vol. 48, no. 4, pp. 730–735, 2010. DOI: 10.1016/j.commatsci.2010.03.020.
  • F.A.C.M. Yang, A.C.M. Chong, C. L. David Chuen, and T. Pin, Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., vol. 39, no. 10, pp. 2731–2743, 2002. DOI: 10.1016/S0020-7683(02)00152-X.
  • C.W. Lim, G. Zhang, and J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids., vol. 78, pp. 298–313, 2015. DOI: 10.1016/j.jmps.2015.02.001.
  • E. C. Aifantis, 1999. Strain gradient interpretation of size effects. In Fracture Scaling, 299–314 Springer, Berlin.
  • A. Eringen, and J. L W. Cemal, Nonlocal continuum field theories, Appl. Mech. Rev., vol. 56, no. 2, pp. B20–B22, 2003. DOI: 10.1115/1.1553434.
  • S. Behdad, and M. Arefi, A mixed two-phase stress/strain driven elasticity: in applications on static bending, vibration analysis and wave propagation, Eur. J. Mech. A/Solids., vol. 94, pp. 104558, 2022. DOI: 10.1016/j.euromechsol.2022.104558.
  • M. Fakher, S. Behdad, and S. Hosseini-Hashemi, Vibration analysis of stress-driven nonlocal integral model of viscoelastic axially FG nanobeams, Eur. Phys. J. Plus., vol. 135, no. 11, pp. 1–21, 2020. DOI: 10.1140/epjp/s13360-020-00923-6.
  • S. Behdad, M. Fakher, and S. Hosseini-Hashemi, Dynamic stability and vibration of two-phase local/nonlocal VFGP nanobeams incorporating surface effects and different boundary conditions, Mechanics of Materials., vol. 153, pp. 103633, 2021. DOI: 10.1016/j.mechmat.2020.103633.
  • Z. Zhang, X. Liu, and R. Mohammadi, Impacts of the hygro-thermo conditions on the vibration analysis of 2D-FG nanoplates based on a novel HSDT, Eng. Comput., vol. 38, no. S4, pp. 2995–3008, 2021. DOI: 10.1007/s00366-021-01443-2.
  • A. Rahmani, S. Faroughi, and M.I. Friswell, The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory, Mech.Syst. Signal Proces., vol. 144, pp. 106854, 2020. DOI: 10.1016/j.ymssp.2020.106854.
  • C. Dangi, R. Lal, and N. Sukavanam, Effect of surface stresses on the dynamic behavior of bi-directional functionally graded nonlocal strain gradient nanobeams via generalized differential quadrature rule, Eur. J. Mech. A/Solids., vol. 90, pp. 104376, 2021. DOI: 10.1016/j.euromechsol.2021.104376.
  • S. Wang, W. Kang, W. Yang, Z. Zhang, Q. Li, M. Liu, and X. Wang, Hygrothermal effects on buckling behaviors of porous bi-directional functionally graded micro-/nanobeams using two-phase local/nonlocal strain gradient theory, Eur. J. Mech. A/Solids., vol. 94, pp. 104554, 2022b. DOI: 10.1016/j.euromechsol.2022.104554.
  • M. Fakher, and S. Hosseini-Hashemi, On the vibration of nanobeams with consistent two-phase nonlocal strain gradient theory: exact solution and integral nonlocal finite-element model, Eng. Comput., vol. 38, no. 3, pp. 2361–2384, 2020. DOI: 10.1007/s00366-020-01206-5.
  • A. Ebrahimi-Mamaghani, R. Sotudeh-Gharebagh, R. Zarghami, and N. Mostoufi, Dynamics of two-phase flow in vertical pipes, J. Fluids Struct., vol. 87, pp. 150–173, 2019. DOI: 10.1016/j.jfluidstructs.2019.03.010.
  • A. S. Adegoke, and A. A. Oyediran, The analysis of nonlinear vibrations of top-tensioned cantilever pipes conveying pressurized steady two-phase flow under thermal loading, MCA., vol. 22, no. 4, pp. 44, 2017. DOI: 10.3390/mca22040044.
  • V. S. Chalgeri, and J. H. Jeong, Flow patterns of vertically upward and downward air-water two-phase flow in a narrow rectangular channel, Int. J. Heat Mass Transfer., vol. 128, pp. 934–953, 2019. DOI: 10.1016/j.ijheatmasstransfer.2018.09.047.
  • O. Pozos, J. Giesecke, W. Marx, E. A. Rodal, and A. Sanchez, Experimental investigation of air pockets in pumping pipeline systems, J. Hydraulic Res., vol. 48, no. 2, pp. 269–273, 2010. DOI: 10.1080/00221681003726262.
  • L. Wang, Y. Yang, Y. Li, and Y. Wang, Dynamic behaviours of horizontal gas-liquid pipes subjected to hydrodynamic slug flow: modelling and experiments, Int. J. Pressure Vessels Pip., vol. 161, pp. 50–57, 2018. DOI: 10.1016/j.ijpvp.2018.02.005.
  • F. C. T. Carvalho, M. de Melo Freire Figueiredo, and A. L. Serpa, Flow pattern classification in liquid-gas flows using flow-induced vibration, Exp. Thermal Fluid Sci., vol. 112, pp. 109950, 2020. DOI: 10.1016/j.expthermflusci.2019.109950.
  • C. Monette, and M.J. Pettigrew, Fluidelastic instability of flexible tubes subjected to two-phase internal flow, J. Fluids Struct., vol. 19, no. 7, pp. 943–956, 2004. DOI: 10.1016/j.jfluidstructs.2004.06.003.
  • Y. Shi, Q. Lan, X. Lan, J. Wu, T. Yang, and B. Wang, Robust optimization design of a flying wing using adjoint and uncertainty-based aerodynamic optimization approach, Struct. Multidisc. Optim., vol. 66, no. 5, pp. 110, 2023. DOI: 10.1007/s00158-023-03559-z.
  • Y. Shi, C. Song, Y. Chen, H. Rao, and T. Yang, Complex standard eigenvalue problem derivative computation for laminar–turbulent transition prediction, AIAA J., vol. 61, no. 8, pp. 3404–3418, 2023. DOI: 10.2514/1.J062212.
  • B. Li, T. Guan, X. Guan, K. Zhang, and K.-F. C. Yiu, Optimal fixed-time sliding mode control for spacecraft constrained reorientation, IEEE Trans. Automat. Contr., vol. 69, no. 4, pp. 2676–2683, 2024. DOI: 10.1109/TAC.2023.3341975.
  • J. Tan, K. Zhang, B. Li, and A.-G. Wu, Event-triggered sliding mode control for spacecraft reorientation with multiple attitude constraints, IEEE Trans. Aerosp. Electron. Syst., pp. 1–14, 2023. DOI: 10.1109/TAES.2023.3270391.
  • X. Song, Z. Fan, S. Lu, Y. Yan, and B. Yue, Predefined-time sliding mode attitude control for liquid-filled spacecraft with large amplitude sloshing, Eur. J. Control., vol. 77, pp. 100970, 2024. DOI: 10.1016/j.ejcon.2024.100970.
  • M. Yang, C. Cai, D. Wang, Q. Wu, Z. Liu, and Y. Wang, Symmetric differential demodulation-based heterodyne laser interferometry used for wide frequency-band vibration calibration, IEEE Trans. Ind. Electron., vol. 71, no. 7, pp. 8132–8140, 2024. DOI: 10.1109/TIE.2023.3299015.
  • Y. Fu, Y. Liu, J. Wang, Y. Wang, G. Xu, and J. Wen, Local resistance characteristics of elbows for supercritical pressure RP-3 flowing in serpentine micro-tubes, Propul. Power Res., 2024. DOI: 10.1016/j.jppr.2023.02.009.
  • L. Sun, G. Wang, and C. Zhang, Experimental investigation of a novel high performance multi-walled carbon nano-polyvinylpyrrolidone/silicon-based shear thickening fluid damper, J. Intell. Mater. Syst. Struct., vol. 35, no. 6, pp. 661–672, 2024. DOI: 10.1177/1045389X231222999.
  • W. Wang, Y. Jin, Y. Mu, M. Zhang, and J. Du, A novel tubular structure with negative Poisson’s ratio based on gyroid-type triply periodic minimal surfaces, Virtual Phys. Prototyp., vol. 18, no. 1, pp. e2203701, 2023. DOI: 10.1080/17452759.2023.2203701.
  • Y. Wang, J. Xu, L. Qiao, Y. Zhang, and J. Bai, Improved amplification factor transport transition model for transonic boundary layers, AIAA J., vol. 61, no. 9, pp. 3866–3882, 2023. DOI: 10.2514/1.J062341.
  • X. Bai, M. Xu, Q. Li, and L. Yu, Trajectory-battery integrated design and its application to orbital maneuvers with electric pump-fed engines, Adv. Space Res., vol. 70, no. 3, pp. 825–841, 2022. DOI: 10.1016/j.asr.2022.05.014.
  • B. Karami, M. Janghorban, and T. Rabczuk, Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory, Compos. Part B: Eng., vol. 182, pp. 107622, 2020. DOI: 10.1016/j.compositesb.2019.107622.
  • R. Barretta, F. Luciano, R. Luciano, F. Marotti de Sciarra, and R. Penna, Functionally graded Timoshenko nanobeams: a novel nonlocal gradient formulation, Compos. Part B: Eng., vol. 100, pp. 208–219, 2016. DOI: 10.1016/j.compositesb.2016.05.052.
  • S. K. Panda, and J. Srinivas, Electro-structural analysis and optimization studies of laminated composite beam energy harvester, Mech. Adv. Mater. Struct., vol. 29, no. 25, pp. 4193–4205, 2022. DOI: 10.1080/15376494.2021.1922787.
  • J. N. Reddy, 2006. Theory and Analysis of Elastic Plates and Shells. CRC Press, Boca Raton.
  • X. Liu, B. Karami, D. Shahsavari, and Ö. Civalek, Elastic wave characteristics in damped laminated composite nano-scaled shells with different panel shapes, Compos. Struct., vol. 267, pp. 113924, 2021. DOI: 10.1016/j.compstruct.2021.113924.
  • S.Z. Rouhani, and M.S. Sohal, Two-phase flow patterns: a review of research results, Progress in Nuclear Energy., vol. 11, no. 3, pp. 219–259, 1983. DOI: 10.1016/0149-1970(83)90012-4.
  • K.W. McQuillan, and P.B. Whalley, Flow patterns in vertical two-phase flow, Int. J. Multiphase Flow., vol. 11, no. 2, pp. 161–175, 1985. DOI: 10.1016/0301-9322(85)90043-6.
  • M. P. Paidoussis, 1998. Fluid-Structure Interactions: Slender Structures and Axial Flow. Vol. 1: Academic Press, London.
  • M. Mirramezani, and H. R. Mirdamadi, Effects of nonlocal elasticity and Knudsen number on fluid–structure interaction in carbon nanotube conveying fluid, Phys E: low-Dimen Syst. Nanostruct., vol. 44, no. 10, pp. 2005–2015, 2012. DOI: 10.1016/j.physe.2012.06.001.
  • V. Rashidi, H. R. Mirdamadi, and E. Shirani, A novel model for vibrations of nanotubes conveying nanoflow, Computat. Mater. Sci., vol. 51, no. 1, pp. 347–352, 2012. DOI: 10.1016/j.commatsci.2011.07.030.
  • R. Bahaadini, M. Hosseini, and B. Jamali, Flutter and divergence instability of supported piezoelectric nanotubes conveying fluid, Phys. B: Conden. Matter., vol. 529, pp. 57–65, 2018. DOI: 10.1016/j.physb.2017.09.130.
  • Ali Beskok, and G. E. Karniadakis, Report: a model for flows in channels, pipes, and ducts at micro and nano scales, Microscale Thermophysical Engineering., vol. 3, no. 1, pp. 43–77, 1999.
  • D. Chisholm, 1983. Two-Phase Flow in Pipelines and Heat Exchangers. London: Godwin in Association with Institution of Chemical Engineers.
  • P.A. Feenstra, D.S. Weaver, and R.L. Judd, Modelling two-phase flow-excited damping and fluidelastic instability in tube arrays, J. Fluids Struct., vol. 16, no. 6, pp. 811–840, 2002. DOI: 10.1006/jfls.2002.0442.
  • M. A. Woldesemayat, and A. J. Ghajar, Comparison of void fraction correlations for different flow patterns in horizontal and upward inclined pipes, Int. J. Multiphase Flow., vol. 33, no. 4, pp. 347–370, 2007. DOI: 10.1016/j.ijmultiphaseflow.2006.09.004.
  • A.Benahmed, M. S. A. Houari, S. Benyoucef, K. Belakhdar, and A. Tounsi, A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation, Geomech. Eng., vol. 12, no. 1, pp. 9–34, 2017. DOI: 10.12989/gae.2017.12.1.009.
  • M. Hosseini, and R. Bahaadini, Size dependent stability analysis of cantilever micro-pipes conveying fluid based on modified strain gradient theory, Int. J. Eng. Sci., vol. 101, pp. 1–13, 2016. DOI: 10.1016/j.ijengsci.2015.12.012.
  • X. Li, Y. Qin, Y.H. Li, and X. Zhao, The coupled vibration characteristics of a spinning and axially moving composite thin-walled beam, Mech. Adv. Mater. Struct., vol. 25, no. 9, pp. 722–731, 2018. DOI: 10.1080/15376494.2017.1308598.
  • M. Hossein Majidi, M. Azadi, and H. Fahham, Effect of CNT reinforcements on the flutter boundaries of cantilever trapezoidal plates under yawed supersonic fluid flow, Mech. Based Des. Struct. Mach., vol. 50, no. 2, pp. 630–650, 2020. DOI: 10.1080/15397734.2020.1723107.
  • P. F. Pai, X. Qian, and X. Du, Modeling and dynamic characteristics of spinning Rayleigh beams, Int. J. Mech. Sci., vol. 68, pp. 291–303, 2013. DOI: 10.1016/j.ijmecsci.2013.01.029.
  • J.N. Reddy, and C.D. Chin, Thermomechanical analysis of functionally graded cylinders and plates, J. Thermal Stress., vol. 21, no. 6, pp. 593–626, 1998. DOI: 10.1080/01495739808956165.
  • L. Lu, X. Guo, and J. Zhao, Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory, Int. J. Eng. Sci., vol. 116, pp. 12–24, 2017. DOI: 10.1016/j.ijengsci.2017.03.006.
  • J.N. Reddy, Microstructure-dependent couple stress theories of functionally graded beams, J. Mech. Phys. Solids., vol. 59, no. 11, pp. 2382–2399, 2011. DOI: 10.1016/j.jmps.2011.06.008.

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