Exact modal analysis of multilayered FG-CNT plate assemblies using the dynamic stiffness method

References

• W. H. Wittrick and F. W. Williams, Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings, Int. J. Mech. Sci., vol. 16, no. 4, pp. 209–239, 1974. DOI: 10.1016/0020-7403(74)90069-1.
   Web of Science ®Google Scholar
• M. Boscolo and J. R. Banerjee, Dynamic stiffness formulation for composite Mindlin plates for exact modal analysis of structures. Part I: Theory, Comput. Struct., vol. 96-97, pp. 61–73, 2012. DOI: 10.1016/j.compstruc.2012.01.002.
   Web of Science ®Google Scholar
• F. A. Fazzolari, M. Boscolo, and J. R. Banerjee, An exact dynamic stiffness element using a higher order shear deformation theory for free vibration analysis of composite plate assemblies, Compos. Struct., vol. 96, pp. 262–278, 2013. DOI: 10.1016/j.compstruct.2012.08.033.
   Web of Science ®Google Scholar
• I. Chopra, Vibration of stepped thickness plates, Int. J. Mech. Sci., vol. 16, no. 6, pp. 337–344, 1974. DOI: 10.1016/0020-7403(74)90007-1.
   Web of Science ®Google Scholar
• S. J. Guo, A. J. Keane, and M. Moshrefi-Torbati, Vibration analysis of stepped thickness plates, J. Sound Vib., vol. 204, no. 4, pp. 645–657, 1997. DOI: 10.1006/jsvi.1997.0955.
   Web of Science ®Google Scholar
• J. Yuan and S. M. Dickinson, The flexural vibration of rectangular plate systems approached by using artificial springs in the Rayleigh-Ritz method, J. Sound Vib., vol. 159, no. 1, pp. 39–55, 1992. DOI: 10.1016/0022-460X(92)90450-C.
   Web of Science ®Google Scholar
• Y. Xiang and G. W. Wei, Exact solutions for buckling and vibration of stepped rectangular Mindlin plates, Int. J. Solids Struct., vol. 41, no. 1, pp. 279–294, 2004. DOI: 10.1016/j.ijsolstr.2003.09.007.
   Web of Science ®Google Scholar
• A. Samanta and M. Mukhopadhyay, Finite element static and dynamic analyses of folded plates, Eng. Struct., vol. 21, no. 3, pp. 277–287, 1999. DOI: 10.1016/S0141-0296(97)90172-3.
   Web of Science ®Google Scholar
• S. Y. Lee and S. C. Wooh, Finite element vibration analysis of composite box structures using the high order plate theory, J. Sound Vib., vol. 277, no. 4-5, pp. 801–814, 2004. DOI: 10.1016/j.jsv.2003.09.024.
   Web of Science ®Google Scholar
• L. X. Peng, Free vibration analysis of symmetrically laminated folded plate structures using an element-free Galerkin method, Math. Prob. Eng., vol. 2015, pp. 1–13, 2015. DOI: 10.1155/2015/124296.
   Web of Science ®Google Scholar
• S. Kumar and P. Jana, Application of dynamic stiffness method for accurate free vibration analysis of sigmoid and exponential functionally graded rectangular plates, Int. J. Mech. Sci., vol. 163, p. 105105, 2019. DOI: 10.1016/j.ijmecsci.2019.105105.
   Web of Science ®Google Scholar
• S. Iijima, Helical microtubules of graphitic carbon, Nature, vol. 354, no. 6348, pp. 56–58, 1991. DOI: 10.1038/354056a0.
   Web of Science ®Google Scholar
• E. T. Thostenson, Z. Ren, and T. W. Chou, Advances in the science and technology of carbon nanotubes and their composites: A review, Compos. Sci. Technol., vol. 61, no. 13, pp. 1899–1912, 2001. DOI: 10.1016/S0266-3538(01)00094-X.
   Web of Science ®Google Scholar
• P. J. F. Harris, Carbon Nanotubes and Related Structures: New Materials for the Twenty-First Century, Am. J. Phys., vol. 72, pp. 414–416, 2004.
   Google Scholar
• B. Fiedler, F. H. Gojny, M. H. G. Wichmann, M. C. M. Nolte, and K. Schulte, Fundamental aspects of nano-reinforced composites, Compos. Sci. Technol., vol. 66, no. 16, pp. 3115–3125, 2006. DOI: 10.1016/j.compscitech.2005.01.014.
   Web of Science ®Google Scholar
• L. Ci and J. Bai, The reinforcement role of carbon nanotubes in epoxy composites with different matrix stiffness, Compos. Sci. Technol., vol. 66, no. 3–4, pp. 599–603, 2006. DOI: 10.1016/j.compscitech.2005.05.020.
   Web of Science ®Google Scholar
• P. C. Ma, S. Y. Mo, B. Z. Tang, and J. K. Kim, Dispersion, interfacial interaction and re-agglomeration of functionalized carbon nanotubes in epoxy composites, Carbon., vol. 48, no. 6, pp. 1824–1834, 2010. DOI: 10.1016/j.carbon.2010.01.028.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• P. Maji, M. Rout, and A. Karmakar, The free vibration response of temperature-dependent carbon nanotube-reinforced composite stiffened plate, Mech. Adv. Mater. Struct., vol. 29, pp. 2555–2569, 2021. DOI: 10.1080/15376494.2020.1870782.
   PubMed Web of Science ®Google Scholar
• H. Cheng and LiC Jiang, Y, Free vibration analysis of rotating pre-twisted ceramic matrix carbon nanotubes reinforced blades, Mech. Adv. Mater. Struct., vol. 29, pp. 2040–2052, 2020. DOI: 10.1080/15376494.2020.1849881.
   Web of Science ®Google Scholar
• J. Gou, B. Minaie, B. Wang, Z. Liang, and C. Zhang, Computational and experimental study of interfacial bonding of single-walled nanotube reinforced composites, Comput. Mater. Sci., vol. 31, no. 3–4, pp. 225–236, 2004. DOI: 10.1016/j.commatsci.2004.03.002.
   Web of Science ®Google Scholar
• H. S. Shen, Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Compos. Struct., vol. 91, no. 1, pp. 9–19, 2009. DOI: 10.1016/j.compstruct.2009.04.026.
   Web of Science ®Google Scholar
• Z. X. Lei, K. M. Liew, and J. L. Yu, Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment, Compos. Struct., vol. 106, pp. 128–138, 2013. DOI: 10.1016/j.compstruct.2013.06.003.
   Web of Science ®Google Scholar
• L. W. Zhang, W. C. Cui, and K. M. Liew, Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges, Int. J. Mech. Sci., vol. 103, pp. 9–21, 2015. DOI: 10.1016/j.ijmecsci.2015.08.021.
   Web of Science ®Google Scholar
• L. W. Zhang, Z. X. Lei, and K. M. Liew, Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method, Int. J. Mech. Sci., vol. 120, pp. 189–199, 2015. DOI: 10.1016/j.compstruct.2014.10.009.
   Google Scholar
• P. Zhu, Z. X. Lei, and K. M. Liew, Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory, Compos. Struct., vol. 94, no. 4, pp. 1450–1460, 2012. DOI: 10.1016/j.compstruct.2011.11.010.
   Web of Science ®Google Scholar
• P. Phung-Van, M. Abdel-Wahab, K. M. Liew, S. P. A. Bordas, and H. Nguyen-Xuan, Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory, Compos. Struct., vol. 123, pp. 137–149, 2015. DOI: 10.1016/j.compstruct.2014.12.021.
   Web of Science ®Google Scholar
• N. D. Duc, J. Lee, T. Nguyen-Thoi, and P. T. Thang, Static response and free vibration of functionally graded carbon nanotube-reinforced composite rectangular plates resting on Winkler–Pasternak elastic foundation, Aerosp. Sci. Technol., vol. 68, pp. 391–402, 2017. DOI: 10.1016/j.ast.2017.05.032.
   Web of Science ®Google Scholar
• R. Ansari, J. Torabi, and A. H. Shakouri, Vibration analysis of functionally graded carbon nanotube-reinforced composite elliptical plates using a numerical strategy, Aerosp. Sci. Technol., vol. 60, pp. 152–161, 2017. DOI: 10.1016/j.ast.2016.11.004.
   Web of Science ®Google Scholar
• P. Malekzadeh and A. R. Zarei, Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers, Thin-Walled Struct., vol. 82, pp. 221–231, 2014. DOI: 10.1016/j.tws.2014.04.016.
   Web of Science ®Google Scholar
• M. H. Yas, A. Pourasghar, S. Kamarian, and M. Heshmati, Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube, Mater. Des., vol. 49, pp. 583–590, 2013. DOI: 10.1016/j.matdes.2013.01.001.
   Web of Science ®Google Scholar
• Z. X. Lei, L. W. Zhang, and K. M. Liew, Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method, Compos. Struct., vol. 127, pp. 245–259, 2015. DOI: 10.1016/j.compstruct.2015.03.019.
   Web of Science ®Google Scholar
• D. Onvani, A. Jafari, and M. B. Dehkordi, Carrera unified formulation for bending and free vibration analysis of sandwich plate with FG-CNT faces considering the both soft and stiff cores, Mech. Adv. Mater. Struct., pp. 1–15, 2021. DOI: 10.1080/15376494.2021.1983899.
   Google Scholar
• J. R. Banerjee, Dynamic stiffness formulation for structural elements: A general approach, Comput. Struct., vol. 63, no. 1, pp. 101–103, 1997. DOI: 10.1016/S0045-7949(96)00326-4.
   Web of Science ®Google Scholar
• A. Pagani, M. Boscolo, J. R. Banerjee, and E. Carrera, Exact dynamic stiffness elements based on one-dimensional higher-order theories for free vibration analysis of solid and thin-walled structures, J. Sound Vib., vol. 332, no. 23, pp. 6104–6127, 2013. DOI: 10.1016/j.jsv.2013.06.023.
   Web of Science ®Google Scholar
• M. Boscolo and J. R. Banerjee, Dynamic stiffness elements and their applications for plates using first order shear deformation theory, Comput. Struct., vol. 89, no. 3–4, pp. 395–410, 2011. DOI: 10.1016/j.compstruc.2010.11.005.
   Web of Science ®Google Scholar
• A. Pagani, E. Carrera, M. Boscolo, and J. R. Banerjee, Refined dynamic stiffness elements applied to free vibration analysis of generally laminated composite beams with arbitrary boundary conditions, Compos. Struct., vol. 110, pp. 305–316, 2014. DOI: 10.1016/j.compstruct.2013.12.010.
   Web of Science ®Google Scholar
• A. Pagani, E. Carrera, J. R. Banerjee, P. H. Cabral, G. Caprio, and A. Prado, Free vibration analysis of composite plates by higher-order 1D dynamic stiffness elements and experiments, Compos. Struct., vol. 118, pp. 654–663, 2014. DOI: 10.1016/j.compstruct.2014.08.020.
   Web of Science ®Google Scholar
• S. Kumar, V. Ranjan, and P. Jana, Free vibration analysis of thin functionally graded rectangular plates using the dynamic stiffness method, Compos. Struct., vol. 197, pp. 39–53, 2018. DOI: 10.1016/j.compstruct.2018.04.085.
   Web of Science ®Google Scholar
• W. H. Wittrick and F. W. Williams, A general algorithm for computing natural frequencies of elastic structures, Q. J. Mech. Appl. Math., vol. 24, no. 3, pp. 263–284, 1971. DOI: 10.1093/qjmam/24.3.263.
   Web of Science ®Google Scholar
• Y. Han and J. Elliott, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Comput. Mater. Sci., vol. 39, no. 2, pp. 315–323, 2007. DOI: 10.1016/j.commatsci.2006.06.011.
   Web of Science ®Google Scholar
• A. A. Daikh, M. S. A. Houari, M. O. Belarbi, S. A. Mohamed, and M. A. Eltaher, Static and dynamic stability responses of multilayer functionally graded carbon nanotubes reinforced composite nanoplates via quasi 3D nonlocal strain gradient theory, Def. Technol., 2021. DOI: 10.1016/j.dt.2021.09.011.
   Web of Science ®Google Scholar
• J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, London, 2003.
   Google Scholar
• C. L. Zhang and H. S. Shen, Temperature-dependent elastic properties of single-walled carbon nanotubes: Prediction from molecular dynamics simulation, Appl. Phys. Lett., vol. 89, no. 8, p. 081904, 2006. DOI: 10.1063/1.2336622.
   Web of Science ®Google Scholar