Stochastic free vibration of composite plates with temperature-dependent properties under spatially varying stochastic high thermal gradient

References

• Anitescu, C., E. Atroshchenko, N. Alajlan, and T. Rabczuk. 2019. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials & Continua 59 (1):345–59. doi:10.32604/cmc.2019.06641.
   Web of Science ®Google Scholar
• Bassamzadeh, N., and R. Ghanem. 2017. Multiscale stochastic prediction of electricity demand in smart grids using Bayesian networks. Applied Energy 193:369–80. doi:10.1016/j.apenergy.2017.01.017.
   Web of Science ®Google Scholar
• Bohlooly, M., and B. Mirzavand. 2016. A closed-form solution for thermal buckling of cross-ply piezolaminated plates. International Journal of Structural Stability and Dynamics 16 (3):1450112. doi:10.1142/S0219455414501120.
   Web of Science ®Google Scholar
• Burton, W. S. 1992. Three-dimensional solutions for the thermal buckling and sensitivity derivatives of temperature-sensitive muitilayered angle-ply plates. Journal of Applied Mechanics 59:849.
   Web of Science ®Google Scholar
• Chandra, S., K. Sepahvand, V. A. Matsagar, and S. Marburg. 2019. Stochastic dynamic analysis of composite plate with random temperature increment. Composite Structures 111159
   Google Scholar
• Chandrashekhar, M., and R. Ganguli. 2010. Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties. International Journal of Mechanical Sciences 52 (7):874–91. doi:10.1016/j.ijmecsci.2010.03.002.
   Web of Science ®Google Scholar
• Chen, C. S., C. W. Chen, W. R. Chen, and Y. C. Chang. 2013. Thermally induced vibration and stability of laminated composite plates with temperature-dependent properties. Meccanica 48 (9):2311–23. doi:10.1007/s11012-013-9750-7.
   Web of Science ®Google Scholar
• Chen, L. W., and L. Y. Chen. 1989. Thermal buckling behavior of laminated composite plates with temperature-dependent properties. Composite Structures 13 (4):275–87. doi:10.1016/0263-8223(89)90012-3.
   Web of Science ®Google Scholar
• Chiba, R. 2009. Stochastic thermal stresses in an FGM annular disc of variable thickness with spatially random heat transfer coefficients. Meccanica 44 (2):159–76. doi:10.1007/s11012-008-9158-y.
   Web of Science ®Google Scholar
• Chiba, R. 2012. Stochastic analysis of heat conduction and thermal stresses in solids: A review. In Heat Transfer Phenomena and Applications, 243–66.
   Google Scholar
• Dey, S., T. Mukhopadhyay, H. H. Khodaparast, and S. Adhikari. 2015. Stochastic natural frequency of composite conical shells. Acta Mechanica 226 (8):2537–53. doi:10.1007/s00707-015-1316-4.
   Web of Science ®Google Scholar
• Dey, S., T. Mukhopadhyay, H. H. Khodaparast, and S. Adhikari. 2015. Stochastic natural frequency of composite conical shells. Acta Mechanica 226 (8):2537–53. doi:10.1007/s00707-015-1316-4.
   Web of Science ®Google Scholar
• Dey, S., T. Mukhopadhyay, H. H. Khodaparast, P. Kerfriden, and S. Adhikari. 2015. Rotational and ply-level uncertainty in response of composite shallow conical shells. Composite Structures 131:594–605. ‏ doi:10.1016/j.compstruct.2015.06.011.
   Web of Science ®Google Scholar
• Dey, S., T. Mukhopadhyay, S. K. Sahu, G. Li, H. Rabitz, and S. Adhikari. 2015. Thermal uncertainty quantification in frequency responses of laminated composite plates. Composites Part B: Engineering 80:186–97. doi:10.1016/j.compositesb.2015.06.006.
   Web of Science ®Google Scholar
• Fakoor, M., and H. Parviz. 2020. Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach. Frontiers of Structural and Civil Engineering 14 (6):1359–71. doi:10.1007/s11709-020-0658-8.
   Web of Science ®Google Scholar
• Fakoor, M., H. Parviz, and A. Abbasi. 2019. Uncertainty propagation analysis in free vibration of uncertain composite plate using stochastic finite element method. Amirkabir Journal of Mechanical Engineering 52 (12):3503–20.
   Google Scholar
• Fish, J., and W. Wu. 2011. A nonintrusive stochastic multiscale solver. International Journal for Numerical Methods in Engineering 88 (9):862–79. doi:10.1002/nme.3201.
   Web of Science ®Google Scholar
• Ghanem, R. G., and P. D. Spanos. 1991. Stochastic finite element method: response statistics. In Stochastic finite elements: A spectral approach, 101–19. New York, NY: Springer.‏
   Google Scholar
• Graham-Brady, L. L., S. R. Arwade, D. J. Corr, M. A. Gutierrez, D. Breysse, M. Grigoriu, and N. Zabaras. 2006. Probability and materials: From nano-to macro-scale: A summary. Probabilistic Engineering Mechanics 21 (3):193–9. doi:10.1016/j.probengmech.2005.10.005.
   Web of Science ®Google Scholar
• Guilleminot, J., A. Noshadravan, C. Soize, and R. G. Ghanem. 2011. A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures. Computer Methods in Applied Mechanics and Engineering 200 (17–20):1637–48. doi:10.1016/j.cma.2011.01.016.
   Web of Science ®Google Scholar
• Guilleminot, J., and C. Soize. 2013. Stochastic model and generator for random fields with symmetry properties: Application to the mesoscopic modeling of elastic random media. Multiscale Modeling & Simulation 11 (3):840–70. doi:10.1137/120898346.
   Web of Science ®Google Scholar
• Guo, H., X. Zhuang, and T. Rabczuk. 2021. A deep collocation method for the bending analysis of Kirchhoff plate. arXiv Preprint arXiv:2102.02617.
   Google Scholar
• Hamdia, K. M., H. Ghasemi, X. Zhuang, N. Alajlan, and T. Rabczuk. 2018. Sensitivity and uncertainty analysis for flexoelectric nanostructures. Computer Methods in Applied Mechanics and Engineering 337:95–109. doi:10.1016/j.cma.2018.03.016.
   Web of Science ®Google Scholar
• Hoang, T. D., and N. Takano. 2019. First-order perturbation-based stochastic homogenization method applied to microscopic damage prediction for composite materials. Acta Mechanica 230 (3):1061–76. doi:10.1007/s00707-018-2337-6.
   Web of Science ®Google Scholar
• Jiang, M., K. Alzebdeh, I. Jasiuk, and M. Ostoja-Starzewski. 2001. Scale and boundary conditions effects in elastic properties of random composites. Acta Mechanica 148 (1–4):63–78. doi:10.1007/BF01183669.
   Web of Science ®Google Scholar
• Kim, Y. W. 2005. Temperature dependent vibration analysis of functionally graded rectangular plates. Journal of Sound and Vibration 284 (3-5):531–49. ‏ doi:10.1016/j.jsv.2004.06.043.
   Web of Science ®Google Scholar
• Lal, A., and B. N. Singh. 2009. Stochastic nonlinear free vibration of laminated composite plates resting on elastic foundation in thermal environments. Computational Mechanics 44 (1):15–29. doi:10.1007/s00466-008-0352-5.
   Web of Science ®Google Scholar
• Lal, A., B. N. Singh, and R. Kumar. 2008. Nonlinear free vibration of laminated composite plates on elastic foundation with random system properties. International Journal of Mechanical Sciences 50 (7):1203–12. doi:10.1016/j.ijmecsci.2008.04.002.
   Web of Science ®Google Scholar
• Lal, A., B. N. Singh, and R. Kumar. 2009. Effects of random system properties on the thermal buckling analysis of laminated composite plates. Computers & Structures 87 (17–18):1119–28. doi:10.1016/j.compstruc.2009.06.004.
   Web of Science ®Google Scholar
• Malekzadeh, P., A. R. Vosoughi, M. Sadeghpour, and H. R. Vosoughi. 2014. Thermal buckling optimization of temperature-dependent laminated composite skew plates. Journal of Aerospace Engineering 27 (1):64–75. doi:10.1061/(ASCE)AS.1943-5525.0000220.
   Web of Science ®Google Scholar
• Mishra, B. B., A. Kumar, and U. Topal. 2020. Stochastic normal mode frequency analysis of hybrid angle ply laminated composite skew plate with opening using a novel approach. Mechanics Based Design of Structures and Machines 1–35. doi:10.1080/15397734.2020.1840393.
   Web of Science ®Google Scholar
• Mukhopadhyay, T., S. Naskar, P. K. Karsh, S. Dey, and Z. You. 2018. Effect of delamination on the stochastic natural frequencies of composite laminates. Composites Part B: Engineering 154:242–56. doi:10.1016/j.compositesb.2018.07.029.
   Web of Science ®Google Scholar
• Oh, D. H., and L. Librescu. 1997. Free vibration and reliability of composite cantilevers featuring uncertain properties. Reliability Engineering & System Safety 56 (3):265–72. doi:10.1016/S0951-8320(96)00038-5.
   Web of Science ®Google Scholar
• Ostoja-Starzewski, M. 2002. Microstructural randomness versus representative volume element in thermomechanics. Journal of Applied Mechanics 69 (1):25–35. doi:10.1115/1.1410366.
   Web of Science ®Google Scholar
• Pandit, M. K., B. N. Singh, and A. H. Sheikh. 2010. Stochastic free vibration response of soft core sandwich plates using an improved higher-order zigzag theory. Journal of Aerospace Engineering 23 (1):14–23. ‏ doi:10.1061/(ASCE)0893-1321(2010)23:1(14).
   Web of Science ®Google Scholar
• Parhi, A., and B. N. Singh. 2014. Stochastic response of laminated composite shell panel in hygrothermal environment. Mechanics Based Design of Structures and Machines 42 (4):454–82. doi:10.1080/15397734.2014.888006.
   Web of Science ®Google Scholar
• Parviz, H., and M. Fakoor. 2020. Free vibration of a composite plate with spatially varying Gaussian properties under uncertain thermal field using assumed mode method. Physica A: Statistical Mechanics and Its Applications 559:125085. doi:10.1016/j.physa.2020.125085.
   Web of Science ®Google Scholar
• Paudel, D., and S. Hostikka. 2019. Propagation of model uncertainty in the stochastic simulations of a compartment fire. Fire Technology 55 (6):2027–8. doi:10.1007/s10694-019-00841-9.
   Web of Science ®Google Scholar
• Piovan, M. T., and R. Sampaio. 2015. Parametric and non-parametric probabilistic approaches in the mechanics of thin-walled composite curved beams. Thin-Walled Structures 90:95–106. doi:10.1016/j.tws.2014.12.018.
   Web of Science ®Google Scholar
• Piovan, M. T., J. M. Ramirez, and R. Sampaio. 2013. Dynamics of thin-walled composite beams: Analysis of parametric uncertainties. Composite Structures 105:14–28. ‏ doi:10.1016/j.compstruct.2013.04.039.
   Web of Science ®Google Scholar
• Samaniego, E., C. Anitescu, S. Goswami, V. M. Nguyen-Thanh, H. Guo, K. Hamdia, X. Zhuang, and T. Rabczuk. 2020. An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering 362:112790. doi:10.1016/j.cma.2019.112790.
   Web of Science ®Google Scholar
• Sepahvand, K. 2016. Spectral stochastic finite element vibration analysis of fiber-reinforced composites with random fiber orientation. Composite Structures 145:119–28. doi:10.1016/j.compstruct.2016.02.069.
   Web of Science ®Google Scholar
• Sepahvand, K. 2017. Stochastic finite element method for random harmonic analysis of composite plates with uncertain modal damping parameters. Journal of Sound and Vibration 400:1–12. doi:10.1016/j.jsv.2017.04.025.
   Web of Science ®Google Scholar
• Sepahvand, K., M. Scheffler, and S. Marburg. 2015. Uncertainty quantification in natural frequencies and radiated acoustic power of composite plates: Analytical and experimental investigation. Applied Acoustics 87:23–9. ‏ doi:10.1016/j.apacoust.2014.06.008.
   Web of Science ®Google Scholar
• Sepahvand, K., S. Marburg, and H. J. Hardtke. 2012. Stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion. Journal of Sound and Vibration 331 (1):167–79. ‏ doi:10.1016/j.jsv.2011.08.012.
   Web of Science ®Google Scholar
• Shaker, A., W. G. Abdelrahman, M. Tawfik, and E. Sadek. 2007. Stochastic finite element analysis of the free vibration of laminated composite plates. Computational Mechanics 41 (4):493–501. ‏ doi:10.1007/s00466-007-0205-7.
   Web of Science ®Google Scholar
• Shariyat, M. 2007. Thermal buckling analysis of rectangular composite plates with temperature-dependent properties based on a layerwise theory. Thin-Walled Structures 45 (4):439–52. doi:10.1016/j.tws.2007.03.004.
   Web of Science ®Google Scholar
• Shen, H. S. 2001. Thermal postbuckling behavior of imperfect shear deformable laminated plates with temperature-dependent properties. Computer Methods in Applied Mechanics and Engineering 190 (40–41):5377–90. doi:10.1016/S0045-7825(01)00172-4.
   Web of Science ®Google Scholar
• Shen, H. S., J. J. Zheng, and X. L. Huang. 2003. Dynamic response of shear deformable laminated plates under thermomechanical loading and resting on elastic foundations. Composite Structures 60 (1):57–66. ‏ doi:10.1016/S0263-8223(02)00295-7.
   Web of Science ®Google Scholar
• Singh, B. N., A. K. S. Bisht, M. K. Pandit, and K. K. Shukla. 2009. Nonlinear free vibration analysis of composite plates with material uncertainties: A Monte Carlo simulation approach. Journal of Sound and Vibration 324 (1-2):126–38. ‏ doi:10.1016/j.jsv.2009.01.046.
   Web of Science ®Google Scholar
• Singh, B. N., D. Yadav, and N. G. R. Iyengar. 2001. Natural frequencies of composite plates with random material properties using higher-order shear deformation theory. International Journal of Mechanical Sciences 43 (10):2193–214. doi:10.1016/S0020-7403(01)00046-7.
   Web of Science ®Google Scholar
• Soares, C. G. 1997. Reliability of components in composite materials. Reliability Engineering & System Safety 55 (2):171–7. doi:10.1016/S0951-8320(96)00008-7.
   Web of Science ®Google Scholar
• Swain, P. R., P. Dash, and B. N. Singh. 2021. Stochastic nonlinear bending analysis of piezoelectric laminated composite plates with uncertainty in material properties. Mechanics Based Design of Structures and Machines 49 (2):194–216.
   Web of Science ®Google Scholar
• Tomar, S. S., S. Zafar, M. Talha, W. Gao, and D. Hui. 2018. State of the art of composite structures in non-deterministic framework: A review. Thin-Walled Structures 132:700–16. doi:10.1016/j.tws.2018.09.016.
   Web of Science ®Google Scholar
• Tootkaboni, M., and L. Graham‐Brady. 2010. A multi‐scale spectral stochastic method for homogenization of multi‐phase periodic composites with random material properties. International Journal for Numerical Methods in Engineering 83 (1):59–90. doi:10.1002/nme.2829.
   Web of Science ®Google Scholar
• Vosoughi, A. R., P. Malekzadeh, M. R. Banan, and M. R. Banan. 2011. Thermal postbuckling of laminated composite skew plates with temperature-dependent properties. Thin-Walled Structures 49 (7):913–22. doi:10.1016/j.tws.2011.02.017.
   Web of Science ®Google Scholar
• Vu-Bac, N., T. Lahmer, X. Zhuang, T. Nguyen-Thoi, and T. Rabczuk. 2016. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software 100:19–31. doi:10.1016/j.advengsoft.2016.06.005.
   Web of Science ®Google Scholar
• Wen, P., N. Takano, and S. Akimoto. 2018. General formulation of the first-order perturbation-based stochastic homogenization method using many random physical parameters for multi-phase composite materials. Acta Mechanica 229 (5):2133–47. doi:10.1007/s00707-017-2096-9.
   Web of Science ®Google Scholar
• Whiteside, M. B., S. T. Pinho, and P. Robinson. 2012. Stochastic failure modelling of unidirectional composite ply failure. Reliability Engineering & System Safety 108:1–9. doi:10.1016/j.ress.2012.05.006.
   Web of Science ®Google Scholar