Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Thermal frequency analysis of FG sandwich structure under variable temperature loading

  • Received : 2020.04.19
  • Accepted : 2020.09.11
  • Published : 2021.01.10
⟨ Previous Next ⟩

Abstract

The thermal eigenvalue responses of the graded sandwich shell structure are evaluated numerically under the variable thermal loadings considering the temperature-dependent properties. The polynomial type rule-based sandwich panel model is derived using higher-order type kinematics considering the shear deformation in the framework of the equivalent single-layer theory. The frequency values are computed through an own home-made computer code (MATLAB environment) prepared using the finite element type higher-order formulation. The sandwich face-sheets and the metal core are discretized via isoparametric quadrilateral Lagrangian element. The model convergence is checked by solving the similar type published numerical examples in the open domain and extended for the comparison of natural frequencies to have the final confirmation of the model accuracy. Also, the influence of each variable structural parameter, i.e. the curvature ratios, core-face thickness ratios, end-support conditions, the power-law indices and sandwich types (symmetrical and unsymmetrical) on the thermal frequencies of FG sandwich curved shell panel model. The solutions are helping to bring out the necessary influence of one or more parameters on the frequencies. The effects of individual and the combined parameters as well as the temperature profiles (uniform, linear and nonlinear) are examined through several numerical examples, which affect the structural strength/stiffness values. The present study may help in designing the future graded structures which are under the influence of the variable temperature loading.

Keywords

References

  1. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A., Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concr., 24, 347-367. http://dx.doi.org/10.12989/cac.2019.24.4.347.
  2. Aghababaei, R. and Reddy, J.N. (2009), "Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates", J. Sound Vib., 326, 277-289. https://doi.org/10.1016/j.jsv.2009.04.044.
  3. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magnetoelastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71, 485-502. http://dx.doi.org/10.12989/sem.2019.71.5.485.
  4. Alipour, M.M. and Shariyat, M. (2014), "An analytical global-local Taylor transformation-based vibration solution for annular FGM sandwich plates supported by non-uniform elastic foundations", Arch. Civil Mech. Eng., 14, 6-24. https://doi.org/10.1016/j.acme.2013.05.006.
  5. Arani, A.G., Kolahchi, R. and Esmailpour, M. (2016), "Nonlinear vibration analysis of piezoelectric plates reinforced with carbon nanotubes using DQM", Smart Struct. Syst., 18, 787-800. https://doi.org/10.12989/sss.2016.18.4.787.
  6. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18, 187-212. https://doi.org/10.12989/scs.2015.18.1.187.
  7. Baferani, A.H., Saidi, A.R. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93, 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020.
  8. Balubaid, M., Tounsi, A., Dakhel, B., Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concr. 24, 579-586. http://dx.doi.org/10.12989/cac.2019.24.6.579.
  9. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, Abdeldjebbar, Bourada, F., Mahmoud, S.R., Bedia, E.A.A., Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34, 643-655. https://doi.org/10.12989/SCS.2020.34.5.643.
  10. Berghouti, H., Bedia, E.A.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7, 351-364. https://doi.org/10.12989/anr.2019.7.5.351
  11. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, Abdeldjebbar, Algarni, A., Bedia, E.A., Tounsi, Abdelouahed, (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concr., 25, 155-166. http://dx.doi.org/10.12989/cac.2020.25.2.155
  12. Bui, T.Q., Khosravifard, A., Zhang, Ch., Hematiyan, M.R. and Golub, M.V. (2013), "Dynamic analysis of sandwich beams with functionally graded core using a truly mesh free radial point interpolation method", Eng. Struct., 47, 90-104, http://dx.doi.org/10.1016/j.engstruct.2012.03.041.
  13. Bui, TQ., Do, T.V., Ton, L.H.T., Doan, D.H., Tanaka, S., Pham. D.T., Bgyyen-Van, T., Yu, T. and Hirose, S. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos. Part B Eng., 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048.
  14. Bui, T.Q., Nguyen, M.N. and Zhang, C. (2011), "An efficient mesh free method for vibration analysis of laminated composite plates", Comput. Mech., 48, 175-193. https://doi.org/10.1007/s00466-011-0591-8.
  15. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, Abdeldjebbar, Derras, A., Bousahla, A.A. and Tounsi, Abdelouahed (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71, 185-196. https://doi.org/10.12989/SEM.2019.71.2.185.
  16. Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Technol., 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005.
  17. Cook, R.D., Malkus, D.S. and Plesha, M.E. (2000), Concepts and Applications of Finite Element Analysis, 3rd edition, John Willey and Sons, Singapore.
  18. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2019), "Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel", Earthq. Struct., 16, 55-67. https://doi.org/10.12989/scs.2018.28.5.629.
  19. Draiche, K., Bousahla, A.A., Tounsi, Abdelouahed, Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concr., 24, 369-378. http://dx.doi.org/10.12989/cac.2019.24.4.369.
  20. Ghannadpour, S.A.M. and Alinia, M.M. (2009), "Nonlinear analysis of pressure loaded FGM plates", Compos. Struct., 88(3), 354-359. https://doi.org/10.1016/j.compstruct.2008.04.013.
  21. Ghannadpour, S.A.M. and Kiani, P. (2018), "Nonlinear spectral collocation analysis of imperfect functionally graded plates under end-shortening", Struct. Eng. Mech., 66, 557-568. https://doi.org/10.12989/sem.2018.66.5.557.
  22. Ghannadpour, S.A.M. and Mehrparvar, M. (2020), "Nonlinear and post-buckling responses of FGM plates with oblique elliptical cut-outs using plate assembly technique", Steel Compos. Struct. 34(2), 227-239. https://doi.org/10.12989/scs.2020.34.2.227.
  23. Gupta, A. and Talha, M. (2018), "Influence of porosity on the flexural and free vibration responses of functionally graded plates in thermal environment", J. Struct. Stability Dynam., 18(1), 1850013. https://doi.org/10.1142/S021945541850013X.
  24. Hosseini-Hashemi, S.H. Fadaee, M. and Atashipour, S.R. (2011), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93, 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007.
  25. Hussain, M., Naeem, M.N., Taj, M., Tounsi, A. (2020), "Simulating vibration of single-walled carbon nanotube using Rayleigh-Ritz's method", Adv. Nano Res., 8, 215-228. https://doi.org/10.12989/anr.2020.8.3.215
  26. Hussain, M., Nawaz, N.M., Tounsi, A., Muhammad, T. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7, 431-442. https://doi.org/10.12989/ANR.2019.7.6.431.
  27. Jin, G., Su, Z., Shi, S., Ye, T. and Gao, S. (2013), "Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions", Compos. Struct., 108, 565-577. http://doi.org/10.1016/j.compositesb.2018.09.107.
  28. Joseph, S.V. and Mohanty, S.C. (2017), "Temperature effects on buckling and vibration characteristics of sandwich plate with viscoelastic core and functionally graded material constraining layer", J. Sandwich Struct. Mater., 21. https://doi.org/10.1177/1099636217722309.
  29. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, Abdelouahed, Bourada, F., Tounsi, Abdeldjebbar, Bedia, E.A., Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi3D model: Bending and free vibration analysis", Comput. Concr., 25, 37-57. http://dx.doi.org/10.12989/cac.2020.25.1.037.
  30. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/ different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  31. Kant, T. and Swaminathan, K. (2002), "Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos Struct., 56, 329-344. https://doi.org/10.1016/S0263-8223 (02)00017-X.
  32. Karami, B., Janghorban, M., Tounsi, A. (2019b), "On pre-stressed functionally graded anisotropic nanoshell in magnetic field", J. Brazilian Soc. Mech. Sci. Eng., 41, 495. https://doi.org/10.1007/s40430-019-1996-0.
  33. Khalili, S.M.R. and Mohammadi, Y. (2012), "Free vibration analysis of sandwich plates with functionally graded face sheets and temperature dependent material properties: a new approach", Eur. J. Mech., A(35), 61-74, https://doi.org/10.1007/978-3-642-31497-1_13.
  34. Kima, J., Zur, K.K. and Reddy, J.N. (2019), "Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates", Compos. Struct., 209, 879-888. https://doi.org/10.1016/j.compstruct.2018.11.023.
  35. Kolahchi, R., Bidgoli, A.M.M. and Heydari, M.M. (2015), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., 55, 1001-1014. https://doi.org/10.12989/sem.2015.55.5.1001.
  36. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016.
  37. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J Sound Vib., 311(1), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018.
  38. Li, Q., Iu, V.P. and Kou, K.P. (2009), "Three-dimensional vibration analysis of functionally graded material plates in thermal environment", J. Sound Vib., 324, 733-750. https://doi.org/10.1016/j.jsv.2009.02.036.
  39. Liu, B., Xing, Y.F. and Reddy, J.N. (2014) "Exact compact characteristic equations and new results for free vibrations of orthotropic rectangular Mindlin plates", Compos. Struct., 118, 31-321. https://doi.org/10.1016/j.compstruct.2014.07.051.
  40. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Exact solutions free vibrations of functionally graded thick plates on elastic foundations", Mech. Adv. Mater. Struct., 16, 576-584. https://doi.org/10.1080/15376490903138888.
  41. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21, 1906-1929. https://doi.org/10.1177/1099636217727577.
  42. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2D higher-order deformation theory", Compos. Struct., 82, 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030.
  43. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, Abdelouahed, Bousahla, A.A., Tounsi, Abdeldjebbar, Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32, 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  44. Mehar, K. and Panda, S.K. (2017), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polym. Compos., 39, 2751-2764. http://dx.doi.org/10.1002/pc.24266.
  45. Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017), "Nonlinear thermo elastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Therm. Stress, 40(7), 1-18. https://doi.org/10.1080/01495739.2017.1318689
  46. Moussa, A., Abdelbaki, C., Habib, H., Abdelhakim, K., Abdeldjebbar, T., Anis, B.A., Abdelouahed, T. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concr., 24, 489-498. https://doi.org/10.12989/CAC.2019.24.6.489.
  47. Muhammad, T., Afnan, M., Muzamal, H., N., N.M., Muhammad, S., Manzoor, A., Ullah, K.H. and Abdelouahed, T. (2020), "Non-local orthotropic elastic shell model for vibration analysis of protein microtubules", Comput. Concr., 25, 245-253. https://doi.org/10.12989/CAC.2020.25.3.245
  48. Nasrine, B., Kada, D., Anis, B.A., Mohamed, B., Abdelouahed, T. and Mohammadimehr, M. (2019), "Bending analysis of antisymmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33, 81-92. https://doi.org/10.12989/SCS.2019.33.1.081
  49. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B, 43, 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009
  50. Nguyen, T.K., Vo, T.P. and Thai, H.T. (2014), "Vibration and buckling analysis of functionally graded sandwich plates with improved transverse shear stiffness based on the first-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 228, 2110-2131. https://doi.org/10.1177/0954406213516088.
  51. Panda, S.K. and Singh, B.N. (2013), "Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre", Aerosp. Sci. Technol., 29, 47-57. https://doi.org/10.1016/j.ast.2013.01.007.
  52. Pandey, S. and Pradyumna, S. (2015), "Free vibration of functionally graded sandwich plates in thermal environment using a layer wise theory", European J. Mech. A Solids, 51, 55-66. https://doi.org/10.1016/j.euromechsol.2014.12.001.
  53. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, Abdeldjebbar, Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comput. Concr., 25, 225-244. http://dx.doi.org/10.12989/cac.2020.25.3.225.
  54. Reddy, J.N. and Chin, C.D. (1998), "Thermo mechanical analysis of functionally graded cylinders and plates", J. Therm. Stresses, 21, 593-626. https://doi.org/10.1080/01495739808956165.
  55. Sahla, M., Saidi, H., Draiche, K., Anis, B.A., Bourada, F. and Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33, 663-679. https://doi.org/10.12989/scs.2019.33.5.663
  56. Sehar, A., Naeem, M.N., Hussain, M., Taj, M. and Tounsi, A. (2020), "Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis", Comput. Concr., 25, 133-144. https://doi.org/10.12989/CAC.2020.25.2.133.
  57. Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D.L.A. (2011), "Free vibration analysis of solar functionally graded plates with temperature dependent material properties using second order shear deformation theory", J. Mech. Sci. Technol., 25, 2195-2209. https://doi.org/10.1007/s12206-011-0610-x.
  58. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.
  59. Tounsi, Abdelouahed, Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermomechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct. 34, 511. http://dx.doi.org/10.12989/scs.2020.34.4.511.
  60. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Bedia E.A.A. (2013), "A refined trigonometric shear deformation theory for thermo elastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009.
  61. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547.
  62. Trinh, L.C., Vo, T.P., Thai, H.T., Nguyen, T.K. and Keerthan, P. (2018), "State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates", Composites Part B, 149, 144-164. https://doi.org/10.1016/j.compositesb.2018.05.017.
  63. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., 69, 637-649. http://dx.doi.org/10.12989/sem.2019.69.6.637.
  64. Ungbhakorn, V. and Wattanasakulpong, N. (2013), "Thermoelastic vibration analysis of third-order shear deformable functionally graded plates with distributed patch mass under thermal environment", Appl. Acoust., 74, 1045-1059. https://doi.org/10.1016/j.apacoust.2013.03.010.
  65. Wattanasakulpong, N., Prusty, G.B. and Kelly, D.W. (2013), "Free and forced vibration analysis using improved third-order shear deformation theory for functionally graded plates under high temperature loading", J. Sandwich Struct. Mater., 15, 583-606, https://doi.org/10.1177/2F1099636213495751.
  66. Zenkour, A.M. and Alghamdi, N.A. (2010), "Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal Loads bending analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 17, 419-432. https://doi.org/10.1080/15376494.2010.483323.
  67. Zenkour, A.M. and Sobhy, M. (2010), "Thermal buckling of various types of FGM sandwich plates", Compos. Struct., 93, 93-102. https://doi.org/10.1016/j.compstruct.2010.06.012.
  68. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319, 918-939. https://doi.org/10.1016/j.jsv.2008.06.025.
  69. Zhu, P. and Liew, K.M. (2011), "Free vibration analysis of moderately thick functionally graded plates by local Kriging mesh less method", Compos. Struct., 93, 2925-2944. https://doi.org/10.1016/j.compstruct.2011.05.011.
  70. Zur, K.K. (2016), "Green's function for frequency analysis of thin annular plates with nonlinear variable thickness", Appl. Math. Modelling, 40, 3601-3619. https://doi.org/10.1016/j.apm.2015.10.014.

Cited by

  1. Thermoelastic response of functionally graded sandwich plates using a simple integral HSDT vol.91, pp.7, 2021, https://doi.org/10.1007/s00419-021-01973-7