Structural Engineering and Mechanics

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Assessment of Voigt and LRVE models for thermal shock analysis of thin FGM blade: A neutral surface approach

  • Ankit, Kumar (Department of Mechanical Engineering, National Institute of Technology Jamshedpur) ;
  • Shashank, Pandey (Department of Mechanical Engineering, National Institute of Technology Jamshedpur)
  • Received : 2022.04.02
  • Accepted : 2022.12.16
  • Published : 2023.01.10
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Abstract

The present work is an attempt to develop a simple and accurate finite element formulation for the assessment of thermal shock/thermally induced vibrations in pretwisted and tapered functionally graded material thin (FGM) blades obtained from Voigt and local representative volume elements (LRVE) homogenization models, based on neutral surface approach. The neutral surface of the FGM blade does not coincide with its mid-surface. A finite element model (FEM) is developed using first-order shear deformation theory (FSDT) and the FGM turbine blade is modelled according to the shallow shell theory. The top and the bottom layers of the FGM blade are made of pure ceramic and pure metal, respectively and temperature-dependent material properties are functionally graded in the thickness direction, the position of the neutral surface also depends on the temperature. The material properties are estimated according to two different homogenization models viz., Voigt or LRVE. The top layer of the FGM blade is subjected to high temperature and the bottom surface is either thermally insulated or kept at room temperature. The solution of the nonlinear profile of the temperature in the thickness direction is obtained from the Fourier law of heat conduction in the unsteady state. The results obtained from the present FEM are compared with the benchmark examples. Next, the effect of angle of twist, intensity of thermal shock, variable chord and span and volume fraction index on the transient response due to thermal shock obtained from the two homogenization models viz., Voigt and LRVE scheme is investigated. It is shown that there can be a significant difference in the transient response calculated by the two homogenization models for a particular set of material and geometric parameters.

Keywords

References

  1. Abbas, A.F. and Hamzah, A.A. (2022), "Studying the thermal influence on the vibration of rotating blades", Measur. Sci. Rev., 22, 65-72. https://doi.org/10.2478/msr-2022-0008.
  2. Akbarzadeh, A.H., Abedini, A. and Chen, Z.T. (2015), "Effect of micromechanical models on structural responses of functionally graded plates", Compos. Struct., 119, 598-609. https://doi.org/10.1016/j.compstruct.2014.09.031.
  3. Al-Basyouni, K.S. and Mahmoud, S.R. (2021), "Mathematical approach for the effect of the rotation, the magnetic field and the initial stress in the non-homogeneous an elastic hollow cylinder", Struct. Eng. Mech., 79(5), 593-599. https://doi.org/10.12989/sem.2021.79.5.593.
  4. Alipour, S.M., Kiani, Y. and Eslami, M.R. (2016), "Rapid heating of FGM rectangular plates", Acta Mech, 227, 421-436. https://doi.org/10.1007/s00707-015-1461-9.
  5. Ansari, E. and Setoodeh, A.R. (2020), "Applying isogeometric approach for free vibration, mechanical, and thermal buckling analyses of functionally graded variable-thickness blades", J. Vib. Control, 26, 1-17, https://doi.org/10.1177/1077546320915336.
  6. Ansari, E., Setoodeh, A.R. and Rabczuk, T. (2020), "Isogeometric-stepwise vibrational behavior of rotating functionally graded blades with variable thickness at an arbitrary stagger angle subjected to thermal environment", Compos. Struct., 244, 112281. https://doi.org/10.1016/j.compstruct.2020.112281.
  7. Burzynski, S., Chroscielewski, J., Daszkiewicz, K. and Witkowski W. (2016), "Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory", Compos. B. Eng., 107, 203-213. https://doi.org/10.1016/j.compositesb.2016.09.015.
  8. Cao, D., Yi, L.B., Hui, Y.M. and Wei, Z. (2017), "Free vibration analysis of a pre-twisted sandwich blade with thermal barrier coatings layers", Sci. Chin. Tech. Sci., 60, 1747-1761. https://doi.org /10.1007/s11431-016-9011-5.
  9. Chapra, S.C. and Canale, R.P. (2011), Numerical Methods for Engineers, Mcgraw-hill, New York, USA.
  10. Chen, Y., Jin, G., Ye, T. and Chen, M. (2021), "Quasi-3D dynamic model for free vibration analysis of rotating pre-twisted functionally graded blades", J. Sound Vib., 499, 115990. https://doi.org/10.1016/j.jsv.2021.115990.
  11. Gasik, M.M. (1998), "Micromechanical modelling of functionally graded materials", Comput. Mater. Sci., 13, 42-55. https://doi.org/10.1016/S0927-0256(98)00044-5.
  12. Goldenveizer, A.L. (1961), Theory of Elastic Thin Shells, Pergamon Press, Oxford.
  13. Hetnarski, R.B. and Eslami, M.R. (2009), Thermal Stresses-Advanced Theory and Applications, Springer, Amsterdam.
  14. Karami, B., Shahsavar, D., Janghorban, M. and Li, L. (2019), "Influence of homogenization schemes on vibration of functionally graded curved microbeams", Compos. Struct., 216, 67-79. https://doi.org/10.1016/j.compstruct.2019.02.089.
  15. Karmakar, A. and Sinha, P.K. (1997), "Finite element free vibration analysis of rotating laminated composite pretwisted cantilever plates", J. Reinf. Plast. Compos., 16, 1461-1491. https://doi.org/10.1177/073168449701601603.
  16. Lee, YH., Bae, SI. and Kim, J.H. (2016), "Thermal buckling behaviour of functionally graded plates based on neutral surface", Compos. Struct., 137, 208-214. https://doi.org/10.1016/j.compstruct.2015.11.023.
  17. Leissa, A.W. and Ewing, M.S. (1983), "Comparison of beam and shell theories for the vibrations of thin turbomachinery blades" J. Eng. Power, 105(2), 383-392. https://doi.org/10.1115/1.3227427.
  18. Librescu, L., Oh, S.Y., Song, O. and Kang, H.S. (2008), "Dynamics of advanced rotating blades made of functionally graded materials and operating in a high-temperature field", J. Eng. Math., 61, 1-16. https://doi.org/10.1007/s10665-007-9155-5.
  19. Liu, L.T., Hao, Y.X., Zhang, W. and Chen, J. (2018), "Free vibration analysis of rotating pretwisted functionally graded sandwich blades", Inte. J. Aerosp. Eng., 2018, Article ID 2727452. https://doi.org/10.1155/2018/2727452.
  20. Liu, Y., Su., S., Huang, H. and Liang Y. (2019), "Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane", Compos. Part B Eng., 168, 236-242. https://doi.org/10.1016/j.compositesb.2018.12.063.
  21. Mota, A.F., Loja, M.A.R., Barbosa, J.I. and Rodrigues J.A. (2020), "Porous functionally graded plates: An assessment of the influence of shear correction factor on static behaviour", Math. Comput. Appl., 25, 1-26. https://doi.org/10.3390/mca25020025.
  22. Na, S., Kim, K.W., Lee, B.H. and Marzocca, P. (2009), "Dynamic response analysis of rotating functionally graded thin-walled blades exposed to steady temperature and external excitation", J. Therm. Stress., 32, 209-225. https://doi.org/10.1080/01495730802507956.
  23. Nemati, A.R. and Mahmoodabadi, M.J. (2020), "Effect of micromechanical models on stability of functionally graded conical panels resting on Winkler-Pasternak foundation in various thermal environments", Arch. Appl. Mech., 90, 883-915. https://doi.org/10.1007/s00419-019-01646-6.
  24. Niu, Y., MingHui, Y. and Wei, Z. (2021), "Nonlinear transient responses of rotating twisted FGM cylindrical panels", Sci. Chin. Tech., 64, 317-330. https://doi.org/10.1007/s11431-019-1472-1.
  25. Oh, S.Y., Librescu, L. and Song, O. (2003), "Vibration of turbomachinery rotating blades made-up of functionally graded materials and operating in a high temperature field", Acta Mech., 166, 69-87. https://doi.org/10.1007/s00707-003-0049-y.
  26. Oh, Y. and Yoo, H.H. (2016), "Vibration analysis of rotating pretwisted tapered blades made of functionally graded materials", Int. J. Mech. Sci., 119, 68-79. https://doi.org/10.1016/j.ijmecsci.2016.10.002.
  27. Oh, Y. and Yoo, H.H. (2020), "Thermo-elastodynamic coupled model to obtain natural frequency and stretch characteristics of a rotating blade with a cooling passage", Int. J. Mech. Sci., 165, 105194. https://doi.org/10.1016/j.ijmecsci.2019.105194.
  28. Panchore, V. (2022), "Meshless local Petrov-Galerkin method for rotating Rayleigh beam", Struct. Eng. Mech., 81(5), 607-616. https://doi.org/10.12989/sem.2022.81.5.607.
  29. Pandey, S. and Pradyumna, S. (2015), "Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory", Eur. J. Mech. A Solid., 51, 55-66. https://doi.org/10.1016/j.euromechsol.2014.12.001.
  30. Pandey, S. and Pradyumna, S. (2018), "Analysis of functionally graded sandwich plates using a higher-order layerwise theory", Compos. B-Eng., 153, 325-336. https://doi.org/10.1016/j.compositesb.2018.08.121.
  31. Qatu, M.S. (2004), Vibration of Laminated Shells and Plates, Elsevier Academic Press.
  32. Rafiee, M., Nitzsche, F. and Labrosse, M. (2017), "Dynamics, vibration and control of rotating composite beams and blades: A critical review", Thin Wall. Struct., 119, 795-819. https://doi.org/10.1016/j.tws.2017.06.018.
  33. Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21, 593-626. https://doi.org/10.1080/01495739808956165.
  34. Setoodeh, A.R, Shojaee, M. and Malekzadeh, P. (2019), "Vibrational behaviour of doubly curved smart sandwich shells with FGCNTRC face sheets and FG porous core", Compos. Part B Eng., 165, 798-822. https://doi.org/10.1016/j.compositesb.2019.01.022.
  35. Shahsavari, D. and Karami, B. (2022), "Assessment of Reuss, Tamura, and LRVE models for vibration analysis of functionally graded nanoplates", Arch. Civil Mech. Eng., 22(2), 1-13. https://doi.org/10.1007/s43452-022-00409.
  36. Shojaee, M., Setoodeh, A.R. and Malekzadeh, P. (2017), "Vibration of functionally graded CNTs-reinforced skewed cylindrical panels using a transformed differential quadrature method", Acta Mech., 228, 2691-2711. https://doi.org/10.1007/s00707-017-1846-z.
  37. Singha, T.D., Bondyopadhay, T. and Karmakar, A. (2021b), "Thermoelastic free vibration of rotating pretwisted sandwich conical shell panels with functionally graded carbon nanotube-reinforced composite face sheets using higher-order shear deformation theory", Proc. Inst. Mech. Eng., Part L, J Mater: Des. Appl., 235(10), 2227-2253. https://doi.org/10.1177/1464420721999.
  38. Singha, T.D., Bondyopadhay, T. and Karmakar, A. (2022), "A numerical solution for thermal free vibration analysis of rotating pre-twisted FG-GRC cylindrical shell panel", Mech. Adv. Mater. Struct., 19, 1537-6494. https://doi.org/10.1080/15376494.2022.2067924.
  39. Singha, T.D., Rout, M., Bandyopadhyay, T. and Karmakar, A. (2021a), "Free vibration of rotating pretwisted FG-GRC sandwich conical shells in thermal environment using HSDT", Compos. Struct., 257, 113144. https://doi.org/10.1016/j.compstruct.2020.113144.
  40. Sungsoo N., Kim, K.W., Lee, B.H. and Marzocca P., (2009), "Dynamic response analysis of rotating functionally graded thin-walled blades exposed to steady temperature and external excitation", J. Therm. Stress., 32, 209-225. https://doi.org/10.1080/01495730802507956.
  41. Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials, IOM Communications, 1st Edition, London.
  42. Tauchert, T.R. (1989), "Thermal shock of orthotropic rectangular plates", J. Therm. Stress., 12, 241-258. https://doi.org/10.1080/01495738908961964.
  43. XiaoAn, H., Qiang, Z., Xiao-Guang, Y. and Duo-Qi, S. (2019), "Viscoplastic analysis method of an aeroengine turbine blade subjected to transient thermo-mechanical loading", Int. J. Mech. Sci., 152, 247-256. https://doi.org/10.1016/j.ijmecsci.2019.01.007.
  44. Zhao, T.Y., Jiang, L.P., Pan, H.G., Yang, J. and Kitipnchai, S. (2021), "Coupled free vibration of a functionally graded pretwisted blade-shaft system reinforced with grapheme nanoplatelets", Compos. Struct., 262, 113362. https://doi.org/10.1016/j.compstruct.2020.113362.
  45. Zhou, L. (2022), "Computerized responses of spinning NEMS via numerical and mathematical modelling", Struct. Eng. Mech., 82(5), 629-641. https://doi.org/10.12989/sem.2022.82.5.629.