In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.
LoyCTLamKYReddyJN.Vibration of functionally graded cylindrical shells. Int J Mech Sci1999; 41: 309–324.
2.
PradhanSCLoyCTLamKY, et al. Vibration characteristics of functionally graded cylindrical shells under various boundary conditions. Appl Acoust2000; 61: 111–129.
3.
ArshadSHNaeemMN andSultanaN.Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws. J Mech Eng Sci2007; 221: 1483–1495.
4.
ZhangLXiangY andWeiGW.Local adaptive differential quadrature for free vibration analysis of cylindrical shells with various boundary conditions. International Journal of Mechanical Sciences2006; 48: 1126–1138.
5.
GhamkharMNaeemMNImranM, et al. Vibration frequency analysis of three-layered cylinder shaped shell with effect of FGM central layer thickness. Sci Rep2019; 9: 1566.
6.
ZhongBFLiCF andLiPY.Modeling and vibration analysis of sectional-laminated cylindrical thin shells with arbitrary boundary conditions. Appl Acoust2020; 162: 107184.
7.
HussainMNaeemMNShahzadA, et al. Vibrations of rotating cylindrical shells with functionally graded material using wave propagation approach. J Mech Eng Sci2018; 232: 4342–4356.
8.
KadoliR andGanesanN.Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition. J Sound Vib2006; 289: 450–480.
9.
HaddadpourHMahmoudkhaniS andNavaziHM.Free vibration analysis of functionally graded cylindrical shells including thermal effects. Thin-Walled Struct2007; 45: 591–599.
10.
MalekzadehP andHeydarpourY.Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment. Compos Struct2012; 94: 2971–2981.
11.
LiangXZhaXYuYet al. Semi-analytical vibration analysis of FGM cylindrical shells surrounded by elastic foundations in a thermal environment. Compos Struct2019; 223: 110997.
12.
LiSRFuXH andBatraRC.Free vibration of three-layer circular cylindrical shells with functionally graded middle layer. Mech Res Commun2010; 37: 577–580.
13.
LiCFLiPYZhongBFet al. Large-amplitude vibrations of thin-walled rotating laminated composite cylindrical shell with arbitrary boundary conditions. Thin-Walled Struct2020; 156: 106966.
14.
QinZYYangZBZuJ, et al. Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates. Int J Mech Sci2018; 142–143: 127–139.
15.
LiCFQiaoRHTangQS, et al. Investigation on the vibration and interface state of a thin-walled cylindrical shell with bolted joints considering its bilinear stiffness. Appl Acoust2021; 172: 107580.
16.
TangQSLiCFSheHXet al. Nonlinear response analysis of bolted joined cylindrical–cylindrical shell with general boundary condition. J Sound Vib2019; 443: 788–803.
17.
QinZYChuFL andZuJ.Free vibrations of cylindrical shells with arbitrary boundary conditions: a comparison study. Int J Mech Sci2017; 133: 91–99.
18.
LiCFLiPYZhongBF, et al. Geometrically nonlinear vibration of laminated composite cylindrical thin shells with non-continuous elastic boundary conditions. Nonlinear Dyn2019; 95: 1903–1921.
19.
TangQSLiCFSheHX, et al. Analysis of frequency and mode shape of rotating-flexible disk–drum coupled structure with non-continuous connections. Int J Mech Sci2021; 190: 106004.
20.
LiPYLiCFQiaoRH, et al. Sensitivity on the non-continuous supported laminated cylindrical shell to boundary conditions and lamination schemes. Arch Appl Mech2019; 89: 2245–2264.
21.
PuneraD andKantT.Free vibration of functionally graded open cylindrical shells based on several refined higher order displacement models. Thin-Walled Struct2017; 119: 707–726.
22.
MatsunagaH.Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory. Compos Struct2009; 88: 519–531.
23.
FrikhaAZghalSDammakF.Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis. Comput Methods Appl Mech Eng2018; 329: 289–311.
24.
TrabelsiSZghalS andDammakF.Thermo-elastic buckling and post-buckling analysis of functionally graded thin plate and shell structures. J Braz Soc Mech Sci Eng2020; 42: 233.
25.
ShahbaztabarAIzadiASadeghianM, et al. Free vibration analysis of FGM circular cylindrical shells resting on the Pasternak foundation and partially in contact with stationary fluid. Appl Acoust2019; 153: 87–101.
AnhVTTBichDHDucND.Nonlinear stability analysis of thin FGM annular spherical shells on elastic foundations under external pressure and thermal loads. Eur J Mech A Solid2015; 50: 28–38.
28.
WangZX andShenHS.Nonlinear vibration of sandwich plates with FG-GRC face sheets in thermal environments. Compos Struct2018; 192: 642–653.
29.
QinZYPangXJSafaeiB, et al. Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions. Compos Struct2019; 220: 847–860.
30.
SetoodehARShojaeeM andMalekzadehP.Vibrational behavior of doubly curved smart sandwich shells with FG-CNTRC face sheets and FG porous core. Compos Part B Eng2019; 165: 798–822.
31.
AsgariMAkhlaghiM.Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations. Eur J Mech A Solid2011; 30: 72–81.
32.
BahadoriR andNajafizadehMM.Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler–Pasternak elastic foundation by first-order shear deformation theory and using Navier-differential quadrature solution methods. Appl Math Model2015; 39: 4877–4894.
33.
TornabeneFFantuzziNBacciocchiM, et al. A numerical investigation on the natural frequencies of FGM sandwich shells with variable thickness by the local generalized differential quadrature method. Appl Sci2017; 7: 131–139.
34.
LiHCKeLLYangJet al. Free vibration of variable thickness FGM beam submerged in fluid. Compos Struct2020; 233: 111582.
35.
Duc NDKimSEVuTAT, et al. Vibration and nonlinear dynamic analysis of variable thickness sandwich laminated composite panel in thermal environment. J Sandw Struct Mater2020; DOI: 10.1177/1099636219899402.
36.
QatuMS.Recent research advances in the dynamic behavior of shells: 1989–2000, part 1: laminated composite shells. Appl Mech Rev2002; 55: 325–350.
