Structural Engineering and Mechanics

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Thermoelastic eigenfrequency of pre-twisted FG-sandwich straight/curved blades with rotational effect

  • Souvik S. Rathore (Department of Mechanical Engineering, National Institute of Technology Jamshedpur) ;
  • Vishesh R. Kar (Department of Mechanical Engineering, National Institute of Technology Jamshedpur) ;
  • Sanjay (Department of Mechanical Engineering, National Institute of Technology Jamshedpur)
  • Received : 2022.06.21
  • Accepted : 2023.04.13
  • Published : 2023.05.25
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Abstract

This work focuses on the dynamic analysis of thermal barrier coated straight and curved turbine blades modelled as functionally graded sandwich panel under thermal environment. The pre- twisted straight/curved blade model is considered to be fixed to the hub and, the complete assembly of the hub and blade are assumed to be rotating. The functionally graded sandwich composite blade is comprised of functionally graded face-sheet material and metal alloy core. The constituents' material properties are assumed to be temperature-dependent, however, the overall properties are evaluated using Voigt's micromechanical scheme in conjunction with the modified power-law functions. The blade model kinematics is based on the equivalent single-layer shear deformation theory. The equations of motion are derived using the extended Hamilton's principle by including the effect of centrifugal forces, and further solved via 2D- isoparametric finite element approximations. The mesh refinement and validation tests are performed to illustrate the stability and accurateness of the present model. In addition, frequency characteristics of the pre-twisted rotating sandwich blades are computed under thermal environment at various sets of parametric conditions such as twist angles, thickness ratios, aspect ratios, layer thickness ratios, volume fractions, rotational velocity and blade curvatures which can be further useful for designing the blade type structures under turbine operating conditions.

Keywords

References

  1. Al-Osta, M.A., Saidi, H., Tounsi, A., Al-Dulaijan, S.U., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2021), "Influence of porosity on the hygro-thermo-mechanical bending response of an AFG ceramic-metal plates using an integral plate model", Smart Struct. Syst., 28(4), 499-513. https://doi.org/10.12989/sss.2021.28.4.499.
  2. 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.
  3. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088.
  4. Bot, I.K., Bousahla, A.A., Zemri, A., Sekkal, M., Kaci, A., Bourada, F., Tounsi, A., Ghazwani, M.H. and Mahmoud, S.R. (2022), "Effects of Pasternak foundation on the bending behavior of FG porous plates in hygrothermal environment", Steel Compos. Struct., 43(6), 821-837. https://doi.org/10.12989/scs.2022.43.6.821.
  5. Cao, D., Liu, B., Yao, M. and Zhang, W. (2017), "Free vibration analysis of a pre-twisted sandwich blade with thermal barrier coatings layers", Sci. Chin. Technol. Sci., 60(11), 1747-1761. https://doi.org/10.1007/s11431-016-9011-5.
  6. Chandra Mouli, B, Ramji, K., Kar, V.R., Panda, S.K. and Pandey, H.K. (2018), "Numerical study of temperature dependent eigenfrequency responses of tilted functionally graded shallow shell structures", Struct. Eng. Mech., 68(5), 527-536. https://doi.org/10.12989/sem.2018.68.5.527.
  7. Cook, R.D., Malkus, D.S. and Plesha, M. (1989), Concepts and Applications of Finite Element Analysis, John Wiley Sons, Singapore.
  8. Devarajan, B. and Kapania, R.K. (2020), "Thermal buckling of curvilinearly stiffened laminated composite plates with cutouts using isogeometric analysis", Compos. Struct., 238, 111881. https://doi.org/10.1016/j.compstruct.2020.111881.
  9. Devarajan, B. and Kapania, R.K. (2022), "Analyzing thermal buckling in curvilinearly stiffened composite plates with arbitrary shaped cutouts using isogeometric level set method", Aerosp. Sci. Technol., 121, 107350. https://doi.org/10.1016/j.ast.2022.107350.
  10. Djilali, N., Bousahla, A.A., Kaci, A., Selim, M.M., Bourada, F., Tounsi, A., ... and Mahmoud, S.R. (2022), "Large cylindrical deflection analysis of FG carbon nanotube-reinforced plates in thermal environment using a simple integral HSDT", Steel Compos. Struct., 42(6), 779-789. https://doi.org/10.12989/scs.2022.42.6.779.
  11. Dokainish, M.A. and Rawtani, S. (1971), "Vibration analysis of rotating cantilever plates", Int. J. Numer. Meth. Eng., 3(2), 233-248. https://doi.org/10.1002/nme.1620030208.
  12. Du, C.F., Zhang, D.G. and Liu, G.R. (2019), "A cell-based smoothed finite element method for free vibration analysis of a rotating plate", Int. J. Comput. Meth., 16(05), 1840003. https://doi.org/10.1142/S0219876218400030.
  13. Fang, J.S. and Zhou, D. (2017), "Free vibration analysis of rotating mindlin plates with variable thickness", Int. J. Struct. Stab. Dyn., 17(04), 1750046. https://doi.org/10.1142/S0219455417500468.
  14. Gibson, L.J., Ashby, M.F., Karam, G.N., Wegst, U. and Shercliff, H.R. (1995), "The mechanical properties of natural materials. II. Microstructures for mechanical efficiency", Proc. Roy. Soc. London. Ser. A: Math. Phys. Sci., 450(1938), 141-162. https://doi.org/10.1098/rspa.1995.0076.
  15. Gu, X.J., Hao, Y.X., Zhang, W., Liu, L.T. and Chen, J. (2019), "Free vibration of rotating cantilever pre-twisted panel with initial exponential function type geometric imperfection", Appl. Math. Model., 68, 327-352. https://doi.org/10.1016/j.apm.2018.11.037.
  16. Hashemi, S.H., Farhadi, S. and Carra, S. (2009), "Free vibration analysis of rotating thick plates", J. Sound Vib., 323(1-2), 366-384. https://doi.org/10.1016/j.jsv.2008.12.007.
  17. Hirane, H., Belarbi, M.O., Houari, M.S.A. and Tounsi, A. (2021), "On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates", Eng. Comput., 38, 3871-3899. https://doi.org/10.1007/s00366-020-01250-1.
  18. Hu, X.X. and Tsuiji, T. (1999a), "Free vibration analysis of curved and twisted cylindrical thin panels", J. Sound Vib., 219(1), 63-88. https://doi.org/10.1006/jsvi.1998.1825.
  19. Hu, X.X. and Tsuiji, T. (1999b), "Free vibration analysis of rotating twisted cylindrical thin panels", J. Sound Vib., 222(2), 209-224. https://doi.org/10.1006/jsvi.1998.2118.
  20. Kar, V.R. and Panda, S.K. (2015 a), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693.
  21. Kar, V.R. and Panda, S.K. (2015 b), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Lat. Am. J. Solid. Struct., 12, 2006-2024. https://doi.org/10.1590/1679-78251691.
  22. Karmakar, A. and Sinha, P.K. (2001), "failure analysis of laminated composite pretwisted rotating plates", J. Reinf. Plast. Compos., 20(14-15), 1326-1357. https://doi.org/10.1106/OBEG-9CXC-0F26-Q368.
  23. Kee, Y.J. and Kim, J.H. (2004), "Vibration characteristics of initially twisted rotating shell type composite blades", Compos. Struct., 64(2), 151-159. https://doi.org/10.1016/j.compstruct.2003.07.001.
  24. Kim, W.Y. (2005), "Temperature dependent vibration analysis of functionally graded rectangular plates", J. Sound Vib., 284(3-5), 531-549. https://doi.org/10.1016/j.jsv.2004.06.043.
  25. Leissa, A.W., Lee, J.K. and Wang, A.J. (1984), "Vibrations of twisted rotating blades", J. Vib. Acoust. Stress Reliab. Des., 106(2), 251. https://doi.org/10.1115/1.3269178.
  26. Li, C. and Cheng, H. (2021), "Free vibration analysis of a rotating varying-thickness-twisted blade with arbitrary boundary conditions", J. Sound Vib., 492, 115791. https://doi.org/10.1016/j.jsv.2020.115791.
  27. Li, L. and Zhang, D.G. (2016), "Free vibration analysis of rotating functionally graded rectangular plates", Compos. Struct., 136, 493-504. https://doi.org/10.1016/j.compstruct.2015.10.013.
  28. Liu, L.T., Hao, Y.X., Zhang, W. and Chen, J. (2018), "Free vibration analysis of rotating pretwisted functionally graded sandwich blades", Int. J. Aerosp. Eng., 2018, Article ID 2727452. https://doi.org/10.1155/2018/2727452.
  29. Lu, X., Lin, X., Chiumenti, M., Cervera, M., Hu, Y., Ji, X., Ma, L., Yang, H. and Huang, W. (2019), "Residual stress and distortion of rectangular and S-shaped Ti-6Al-4V parts by directed energy deposition: Modelling and experimental calibration", Add. Manuf., 26, 166-179. https://doi.org/10.1016/j.addma.2019.02.001.
  30. Macbain, J.C. (1975), "Vibratory behavior of twisted cantilevered plates", J. Aircraft, 12(4), 343-349. https://doi.org/10.2514/3.44453.
  31. Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, K. and Al-Zahrani, M.M. (2021), "Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39(5), 631-643. https://doi.org/10.12989/scs.2021.39.5.631.
  32. Miglani, J., Devarajan, B. and Kapania, R.K. (2018), "Thermal buckling analysis of periodically supported composite beams using isogeometric analysis", 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.
  33. Mudhaffar, I.M., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Zahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermomechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Struct., 33, 2177-2189. https://doi.org/10.1016/j.istruc.2021.05.090.
  34. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B: Eng., 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  35. Niino, M., Hirai, T. and Watanabe, R. (1987), "Functionally gradient materials. In pursuit of super heat resisting materials for spacecraft", J. JPN. Soc. Compos. Mater., 13, 257-264. https://doi.org/10.6089/jscm.13.257
  36. Niu, Y., Zhang, W. and Guo, X.Y. (2019), "Free vibration of rotating pretwisted functionally graded composite cylindrical panel reinforced with graphene platelets", Eur. J. Mech.-A/Solid., 77, 103798. https://doi.org/10.1016/j.euromechsol.2019.103798.
  37. Parida, S. and Mohanty, S.C. (2019), "Vibration analysis of FG rotating plate using nonlinear-FEM", Multidisc. Model. Mater. Struct., 15(1), 26-49. https://doi.org/10.1108/MMMS-11-2017-0141.
  38. Ramamurti, V. and Kielb, R. (1984), "Natural frequencies of twisted rotating plates", J. Sound Vib., 97(3), 429-449. https://doi.org/10.1016/0022-460X(84)90271-2.
  39. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, New York, USA.
  40. Rostami, H., Bakhtiari-Nejad, F. and Ranji, A.R. (2019), "Vibration of the rotating rectangular orthotropic Mindlin plates with an arbitrary stagger angle", J. Vib. Control, 25(6), 1194-1209. https://doi.org/10.1177/1077546318814012.
  41. Rostami, H., Ranji, A.R., Bakhtiari-Nejad, F. (2018), "Vibration characteristics of rotating orthotropic cantilever plates using analytical approaches: A comprehensive parametric study", Arch. Appl. Mech., 88, 481-502. https://doi.org/10.1007/s00419-017-1320-3.
  42. Rout, M. and Karmakar, A. (2019), "Free vibration of rotating pretwisted CNTs-reinforced shallow shells in thermal environment", Mech. Adv. Mater. Struct., 26(21), 1-13. https://doi.org/10.1080/15376494.2018.1452317.
  43. Sinha, S.K. and Turner, K.E. (2011), "Natural frequencies of a pre-twisted blade in a centrifugal force field", J. Sound Vib., 330(11), 2655-2681. https://doi.org/10.1016/j.jsv.2010.12.017.
  44. Sreenivasamurthy, S. and Ramamurti, V. (1981), "A parametric study of vibration of rotating pre-twisted and tapered low aspect ratio cantilever plates", J. Sound Vib., 76(3), 311-328. https://doi.org/10.1016/0022-460X(81)90515-0.
  45. Tahir, S.I., Chikh, A., Tounsi, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021), "Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment", Compos. Struct., 269, 114030. https://doi.org/10.1016/j.compstruct.2021.114030.
  46. Van Vinh, P., Van Chinh, N. and Tounsi, A. (2022), "Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM", Eur. J. Mech.-A/Solid., 96, 104743. https://doi.org/10.1016/j.euromechsol.2022.104743.
  47. Xiao, S. and Chen, B. (2006), "Dynamic behavior of thin rectangular plate attached to moving rigid", Appl. Math. Mech., 27(4), 555-566. https://doi.org/10.1007/s10483-006-0416-1.
  48. Yang, J. and Shen, H.S. (2002), "Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments", J. Sound Vib., 255(3), 579-602. https://doi.org/10.1006/jsvi.2001.4161.
  49. Yoo, H. and Chung, J. (2001), "Dynamics of rectangular plates undergoing prescribed overall motion", J. Sound Vib., 239(1), 123-137. https://doi.org/10.1006/jsvi.2000.3111.
  50. Yoo, H.H. and Kim, S.K. (2002), "Free vibration analysis of rotating cantilever plates", AIAA J., 40(11), 2188-2196. https://doi.org/10.2514/2.1572.
  51. Yoo, H.H. and Pierre, C. (2003), "Modal characteristic of a rotating rectangular cantilever plate", J. Sound Vib., 259(1), 81-96. https://doi.org/10.1006/jsvi.2002.5182.
  52. Zaitoun, M.W., Chikh, A., Tounsi, A., Al-Osta, M.A., Sharif, A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2022), "Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic-metal plate in a hygrothermal environment", Thin Wall. Struct., 170, 108549. https://doi.org/10.1016/j.tws.2021.108549.
  53. Zaitoun, M.W., Chikh, A., Tounsi, A., Sharif, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021), "An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-021-01498-1.