In this paper, a finite element study is conducted using the Green Lagrange strain field based on vonKarman assumptions for the geometric nonlinear static and dynamic response of the laminated functionally graded CNT reinforced (FG-CNTRC) composite plate. The governing equations for determining the nonlinear static and dynamic behavior of the FG-CNTRC plate are derived using the Lagrange equation of motion based on Reddy's higher order theory. Using the direct iteration technique, the nonlinear eigenvalues for analyzing the free vibration response are obtained and the nonlinear dynamic responses of the FG-CNTRC plate are encapsulated based on the nonlinear Newmark integration scheme. The impact of the amplitude of vibration on mode switching phenomena and the consequence of the duration of the pulse on the free vibration regime of the plate are outlined. Also, the effect of time dependent loads is studied on the normal stresses of the plate. Furthermore, the impact on the nonlinear static and dynamic response of the laminated FG-CNTRC plate of various parameters such as span-thickness ratio (b/h ratio), aspect ratio (a/b ratio), different edge constraints, CNT fiber gradation, etc. are also studied.
WangZ-XShenH-S.Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments. Nonlinear Dyn2012; 70: 735–754.
2.
MalekzadehPZareiAR.Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers. Thin-Walled Struct2014; 82: 221–232.
3.
AdhikariBSinghBN.Dynamic response of functionally graded plates resting on two-parameter-based elastic foundation model using a quasi-3D theory. Mech Based Des Struct Mach2019; 47: 399–331.
PhanNDReddyJN.Analysis of laminated composite plates using a higher-order shear deformation theory. Int J Numer Methods Eng1985; 21: 2201–2219.
6.
SathyamoorthyM.Nonlinear vibration analysis of plates: a review and survey of current developments. Appl Mech Rev1987; 40: 1553–1561.
7.
AmabiliMPaïdoussisMP.Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl Mech Rev2003; 56: 349–381.
8.
AlhazzaKAAlhazzaAA.A review of the vibrations of plates and shells. Shock Vib Dig2004; 36: 377–395.
9.
AmabiliM.Nonlinear vibrations and stability of shells and plates. New York: Cambridge University Press, 2008.
10.
SwainPRAdhikariBDashP.A higher-order polynomial shear deformation theory for geometrically nonlinear free vibration response of laminated composite plate. Mech Adv Mater Struct2019; 26: 129–138.
AmabiliM.Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections. J Sound Vib2006; 291: 539–565.
13.
AmabiliMCarraS.Thermal effects on geometrically nonlinear vibrations of rectangular plates with fixed edges. J Sound Vib2009; 321: 936–954.
14.
KapoorHKapaniaRK.Geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates. Compos Struct2012; 94: 3434–3447.
15.
LiewKMWangJTanMJ, et al. Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT. Comput Methods Appl Mech Eng2004; 193: 4763–4779.
16.
AdhikariBDashP.Geometrically nonlinear free vibration analysis of laminated composite plates: a finite element assessment of a higher order non-polynomial shear deformation theory. Mech Adv Mater Struct2021; 28: 200–211.
17.
AndradeLGAwruchAMMorschIB.Geometrically nonlinear analysis of laminate composite plates and shells using the eight-node hexahedral element with one-point integration. Compos Struct2007; 79: 571–580.
18.
KazancıZMecitoğluZ.Nonlinear dynamic behavior of simply supported laminated composite plates subjected to blast load. J Sound Vib2008; 317: 883–897.
19.
KazancıZKazanciZ.Dynamic response of composite sandwich plates subjected to time-dependent pressure pulses. Int J Non-Linear Mech2011; 46: 807–817.
20.
ShenHS.Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Compos Struct2009; 91: 9–19.
21.
GolmakaniMEZeighamiV.Nonlinear thermo-elastic bending of functionally graded carbon nanotube-reinforced composite plates resting on elastic foundations by dynamic relaxation method. Mech Adv Mater Struct2018; 25: 868–880.
22.
LeiZXLiewKMYuJL.Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method. Comput Methods Appl Mech Eng2013; 256: 189–199.
23.
LeiZXZhangLWLiewKM.Meshless modeling of geometrically nonlinear behavior of CNT-reinforced functionally graded composite laminated plates. Appl Math Comput2017; 295: 24–46.
KianiY.Analysis of FG-CNT reinforced composite conical panel subjected to moving load using Ritz method. Thin-Wall Struct2017; 119: 47–57.
28.
KianiY.Dynamics of FG-CNT reinforced composite cylindrical panel subjected to moving load. Thin-Wall Struct2017; 111: 48–57.
29.
KianiYDimitriRTornabeneF.Free vibration study of composite conical panels reinforced with FG-CNTs. Eng Struct2018; 172: 472–482.
30.
KianiY.Free vibration of carbon nanotube reinforced composite plate on point supports using Lagrangian multipliers. Meccanica2017; 52: 1353–1367.
31.
DatNDThanhNVanMinhanhV.Vibration and nonlinear dynamic analysis of sandwich FG-CNTRC plate with porous core layer. Mech Adv Mater Struct2020; 0: 1–18. DOI: 10.1080/15376494.2020.1822476
32.
ManhDTAnhVTTNguyenPD, et al. Nonlinear post-buckling of CNTs reinforced sandwich-structured composite annular spherical shells. Int J Str Stab Dyn2020; 20: 2050018.
33.
ThanhNVan KhoaNDTuanND, et al. Nonlinear dynamic response and vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shear deformable plates with temperature-dependent material properties and surrounded on elastic foundations. J Therm Stress2017; 40: 1254–1274.
34.
Nguyen DinhDNguyenP.The dynamic response and vibration of functionally graded carbon Nanotube-Reinforced composite (FG-CNTRC) truncated conical shells resting on elastic foundations. Materials2017; 10: 1194.
35.
DucND. Nonlinear thermo- dynamic response of shear deformable piezoelectric sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations. Epub Ahead of Print 2018. DOI: 10.1177/1099636216653266.
36.
DucNDQuanTQLuatVD.Nonlinear dynamic analysis and vibration of shear deformable piezoelectric FGM double curved shallow shells under damping-thermo-electro-mechanical loads. Compos Struct2015; 125: 29–40.
37.
DuongHMGongFLiuP, et al. Advanced fabrication and properties of aligned carbon nanotube composites: experiments and modeling. In: Berber MHafez IH (eds) Carbon nanotubes – current progress of their polymer composites. InTech, 2016, p. 13.
38.
WangJNLuoXGWuT, et al. High-strength carbon nanotube fibre-like ribbon with high ductility and high electrical conductivity. Nat Commun2014; 5: 3848.
39.
LiWZhaoJXueY, et al. Merge multiple carbon nanotube fibers into a robust yarn. Carbon2019; 145: 266–272.
40.
ZhuPLeiZXLiewKM.Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Compos Struct2012; 94: 1450–1460.
41.
ReddyJN.Mechanics of laminated composite plates and shells: theory and analysis. Boca Raon, FL: CRC Press, 2004.
42.
AdhikariBSinghBN.An efficient higher order non-polynomial quasi 3-D theory for dynamic responses of laminated composite plates. Compos Struct2018; 189: 386–397.
43.
LiuC-FHuangC.Free vibration of composite laminated plates subjected to temperature changes. Comput Struct1996; 60: 95–101.
44.
NaiduNVSSinhaPK.Nonlinear free vibration analysis of laminated composite shells in hygrothermal environments. Compos Struct2007; 77: 475–483.
45.
GanapathiMPatelBPMakhechaDP.Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higher-order theory. Compos Part B: Eng2004; 35: 345–355.
46.
SinghaMKGanapathiM.Large amplitude free flexural vibrations of laminated composite skew plates. Int J Non-Linear Mech2004; 39: 1709–1720.
47.
TranLVLeeJNguyen-VanH, et al. Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory. Int J Non-Linear Mech2015; 72: 42–52.
