In the recent years, functionally gradient materials (FGMs) have gained considerable attention with possible applications in several engineering fields, especially in a high-temperature or hazardous environment. In this work, the nonlinear vibrations of a simply supported fluid-filled functionally graded cylindrical shell subjected to a lateral time-dependent load and axial static preload are analyzed. To model the shell, the Donnell nonlinear shell theory is used. The fluid is assumed to be incompressible, nonviscous, and irrotational. A new function to describe the variation in the volume fraction of the constituent material through the shell thickness is proposed, extending the concept of sandwich structures to a functionally graded material. Material properties are graded along the shell thickness according to the proposed volume fraction power law distribution. A consistent reduced order model derived from a perturbation technique is used to describe the displacements of the shell and, the Galerkin method is applied to derive a set of coupled nonlinear ordinary differential equations of motion. Results show the influence of the variation of the two constituent materials along the shell thickness, internal fluid, static preload, and shell geometry on the natural frequencies, nonlinear frequency–amplitude relation, resonance curves, and bifurcation scenario of the FG cylindrical shell.
MoussaouiFBenamarR. Non-linear vibrations of shell-type structures: A review with bibliography. J Sound Vib2002; 255: 161–184.
2.
AmabiliMPaïdoussisMP. Review of studies on geometrically non-linear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl Mech Rev2003; 56: 655–699.
3.
AlhazzaKAAlhazzaAA. A review of vibrations of plates and shells. Shock Vib Dig2004; 36: 377–395.
4.
AlijaniFAmabiliM. Non-linear vibrations of shells: A literature review from 2003 to 2013. Int J Non-Linear Mech2014; 58: 233–257.
5.
KanaDDLindholmUSAbramsonHN. An experimental study of liquid instability in a vibrating elastic tank. J Spacecraft1966; 3: 1183–1188.
6.
ChuWHKanaDD. A theory for nonlinear transverse vibrations of a partially filled elastic tank. AIAA J1967; 5: 1828–1835.
7.
GonçalvesPBBatistaRC. Frequency response of cylindrical shells partially submerged or filled with liquid. J Sound Vib1986; 113: 59–70.
ChibaM. Non-linear hydroelastic vibration of a cantilever cylindrical tank – II. Experiment (liquid-filled case). Int J Non-Linear Mech1993; 28: 601–612.
10.
AmabiliM. Shell–plate interaction in the free vibrations of circular cylindrical tanks partially filled with a liquid: the artificial spring method. J Sound Vib1997; 199: 431–452.
11.
AmabiliMPaïdoussisMPLakisAA. Vibrations of partially filled cylindrical tanks with ring-stiffeners and flexible bottom. J Sound Vib1998; 213: 259–299.
12.
ReddyJN. Mechanics of laminated composite plates and shells: Theory and analysis, Boca Raton: CRC Press, 2004.
13.
VinsonJR. The behavior of sandwich structures of isotropic and composite materials, Boca Raton: CRC Press, 1999.
14.
SoedelW. Vibrations of shells and plates, Boca Raton: CRC Press, 2004.
15.
TanakaKTanakaYWatanabeH. An improved solution to thermoelastic material design in functionally gradient materials: Scheme to reduce thermal stresses. Comput Meth Appl Mech Eng1993; 109: 377–389.
16.
KoizumiM. FGM activities in Japan. Compos Part B: Eng1997; 28: 1–4.
17.
AboudiJPinderaMJArnoldSM. Higher-order theory for functionally graded materials. Compos Part B: Eng1999; 30: 777–832.
18.
ShenHS. Functionally graded materials: Nonlinear analysis of plates and shells, Boca Raton: CRC Press, 2009.
19.
ThaiHTKimSE. A review of theories for the modeling and analysis of functionally graded plates and shells. Compos Struct2015. DOI: http://dx.doi.org/10.1016/j.compstruct. 2015.03.010.
20.
SwaminathanKNaveenkumarDTZenkourAM. Stress, vibration and buckling analyses of FGM plates—A state-of-the-art review. Compos Struct2015; 120: 10–31.
21.
ShahsiahREslamiMR. Functionally graded cylindrical shell thermal instability based on improved Donnell equations. AIAA J2003; 41: 1819–1826.
BahtuiAEslamiMR. Coupled thermoelasticity of functionally graded cylindrical shells. Mech Res Commun2007; 34: 1–18.
24.
LoyCTLamKYReddyJN. Vibration of functionally graded cylindrical shells. Int J Mech Sci1999; 41: 309–324.
25.
PradhanSCLoyCTLamKY. Vibration characteristics of functionally graded cylindrical shells under various boundary conditions. Appl Acoust2000; 61: 111–129.
26.
SepianiHARastgooAKarimipourH. A vibration and buckling investigation of two-layered functionally graded cylindrical structures. Proc IMechE, Part C: J Mechanical Engineering Science2009; 224: 1905–1913.
27.
SofiyevAH. Dynamic buckling of functionally graded cylindrical thin shells under non-periodic impulsive loading. Acta Mech2003; 165: 151–163.
28.
SofiyevAHSchnackE. The stability of functionally graded cylindrical shells under linearly dynamic torsional loading. Eng Struct2004; 26: 1321–1331.
29.
SofiyevAH. The stability of compositionally graded ceramic–metal cylindrical shells under aperiodic axial impulsive loading. Compos Struct2005; 69: 247–257.
30.
ShariyatM. An accurate double-superposition global-local theory for vibration and bending analyses of cylindrical composite and sandwich shells subjected to thermo-mechanical loads. Proc IMechE, Part C: J Mechanical Engineering Science2011; 225: 1816–1832.
31.
TalebianSTTahaniM. A study on dynamic behaviour of functionally graded thick hollow circular cylinders. Proc IMechE, Part C: J Mechanical Engineering Science2012; 226: 498–513.
32.
DucNDThangPTDaoNT. Nonlinear buckling of higher deformable S-FGM thick circular cylindrical shells with metal–ceramic–metal layers surrounded on elastic foundations in thermal environment. Compos Struct2015; 121: 134–141.
33.
DucNDThangPT. Nonlinearbucklingofimperfecteccentricallystiffened metal–ceramic–metal S-FGM thin circular cylindrical shells with temperature-dependent properties in thermal environments. Int J Mech Sci2014; 81: 17–25.
34.
SunJXuXLimCW. Accurate buckling analysis for shear deformable FGM cylindrical shells under axial compression and thermal loads. Compos Struct2015; 123: 246–256.
35.
DucNDThangPT. Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations. Aerosp Sci Technol2015; 40: 115–127.
36.
ZhangWHaoYXYangJ. Nonlinear dynamics of FGM circular cylindrical shell with clamped–clamped edges. Compos Struct2012; 94: 1075–1086.
37.
DungDVNamVH. Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium. Eur J Mech A/Solids2014; 46: 42–53.
DuCLiY. Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments. Compos Struct2013; 102: 164–174.
42.
Evensen DA. Nonlinear flexural vibrations of thin-walled circular cylinders. NASA TN 1967; D4090.
43.
OlsonMD. Some experimental observations on the nonlinear vibrations of cylindrical shells. AIAA J1965; 3: 1775–1777.
44.
CrollJGABatistaRC. Explicit lower bounds for the buckling of axially loaded cylinders. Int J Mech Sci1981; 23: 331–343.
45.
HuntGWWilliamsKAJCowellRG. Hidden symmetry concepts in the elastic buckling of axially-loaded cylinders. Int J Solids Struct1986; 22: 1501–1515.
46.
AmabiliM. Nonlinear vibrations and stability of shells and plates, Cambridge: Cambridge University Press, 2008.
47.
GonçalvesPBSilvaFMAPradoZJGN. Low-dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition. J Sound Vib2008; 315: 641–663.
48.
SilvaFMAGonçalvesPBPradoZJGN. An alternative procedure for the non-linear vibration analysis of fluid-filled cylindrical shells. Nonlinear Dyn2011; 66: 303–333.
49.
ArshadSHNaeemMNSultanaN. Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws. Proc IMechE, Part C: J Mechanical Engineering Science2007; 221: 1483–1495.
50.
GonçalvesPBDel PradoZJGN. Effect of nonlinear modal interaction on the dynamic instability of axially excited cylindrical shells. Comput Struct2004; 82: 2621–2634.
51.
GonçalvesPBDel PradoZJGN. Low-dimensional Galerkin models for nonlinear vibration and instability analysis of cylindrical shells. Nonlinear Dyn2005; 41: 129–145.
52.
KimYWLeeYSKoSH. Coupled vibration of partially fluid-filled cylindrical shells with ring stiffeners. J Sound Vib2004; 276: 869–897.
53.
NayfehAHBalachandranB. Applied nonlinear dynamics: Analytical, computational and experimental methods, New York: John Wiley & Sons, Inc., 1995.
