Restricted accessResearch articleFirst published online 2015-3
Nonlinear dynamic response of imperfect symmetric thin sigmoid-functionally graded material plate with metal-ceramic-metal layers on elastic foundation
This paper presents a first proposal to investigate the nonlinear dynamic response of imperfect symmetric thin sigmoid-functionally graded material (S-FGM) plate resting on an elastic foundation and subjected to mechanical loads. The formulations use classical plate theory taking into account geometrical nonlinearity, initial geometrical imperfection of the S-FGM plate and stress function. The volume fractions of metal and ceramic are applied by sigmoid-law distribution (S-FGM) with metal-ceramic-metal layers. The nonlinear equations are solved by the Runge-Kutta and Bubnov-Galerkin methods using stress function. The obtained results show the effects of material, imperfection and elastic foundations on the dynamical response of S-FGM plate.
AllahverdizadehANaeiMHBahramiMN (2008) Nonlinear free and forced vibration analysis of thin circular functionally graded plates. Journal of Sound and Vibration310: 966–984.
BrushDDAlmrothBO (1975) Buckling of Bars, Plates and Shells, New York: McGraw-Hill.
4.
DarabiMDarvizehMDarvizehA (2008) Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading. Composite Structures83: 201–211.
5.
DucND (2013) Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation. Journal of Composite Structures99: 88–96.
6.
Duc ND and Cong PH (2012) Nonlinear dynamic response of FGM plate. In Proceeding of the Second International Conference on Engineering Mechanics and Automation ICEMA2, Hanoi, Vietnam, August 16–17, 2012, pp.271–278.
7.
FakhariVOhadiA (2011) Nonlinear vibration control of functionally graded plate with piezoelectric layers in thermal environment. Journal of Vibration and Control17(3): 449–469.
8.
FerreiraAJMBatraRCRoqueCMC (2006) Natural frequencies of FGM plates by meshless method. Journal of Composite Structures75: 593–600.
9.
IbrahimHHTawfikM (2010) Limit-cycle oscillations of functionally graded material plates subject to aerodynamic and thermal loads. Journal of Vibration and Control16(14): 2147–2166.
10.
KadoliRGanesanN (2006) Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition. Journal of Sound and Vibration289: 450–480.
11.
LiewKMHuGYNgTYZhaoX (2006a) Dynamic stability of rotating cylindrical shells subjected to periodic axial loads. International Journal of Solids and Structures43: 7553–7570.
12.
LiewKMYangJWuYF (2006b) Nonlinear vibration of a coating-FGM-substrate cylindrical panel subjected to a temperature gradient. Computer Methods in Applied Mechanics and Engineering195: 1007–1026.
13.
MatsunagaH (2008) Free vibration and stability of FGM plates according to a 2-D high order deformation theory. Journal of Composite Structures82: 499–512.
14.
Miao RuanZhong-Min WangYan Wang (2012) Dynamic stability of functionally graded materials skew plates subjected to uniformly distributed tangential follower forces. Journal of Vibration and Control18(7): 913–923.
15.
MohammadTSinghBN (2010) Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Applied Mathematical Modeling34(12): 3991–4011.
16.
MollaraziHRForoutanMMoradi-DastjerdiR (2012) Analysis of free vibration of functionally graded material cylinders by a meshless method. Journal of Composite Materials46(5): 507–515.
17.
NajafovASofiyevAOzyigitPYucelKT (2012) Vibration and stability of axially compressed truncated conical shells with functionally graded middle layer surrounded by elastic medium. Journal of Vibration and Control. DOI: 1077546312461025, first published on October 25, 2012.
18.
NayfehAHPaiPF (2004) Linear and Nonlinear Structural Mechanics, New Jersey: Wiley-Interscience.
19.
PrakashTSundararajanNGanapathiM (2007) On the nonlinear axisymmetric dynamic buckling behavior of clamped functionally graded spherical caps. Journal of Sound and Vibration299: 36–43.
20.
ShariyatM (2008a) Dynamic thermal buckling of suddenly heated temperature-dependent FGM cylindrical shells under combined axial compression and external pressure. International Journal of Solids and Structures45: 2598–2612.
21.
ShariyatM (2008b) Dynamic buckling of suddenly loaded imperfect hybrid FGM cylindrical with temperature-dependent material properties under thermo-electro-mechanical loads. International Journal of Mechanical Sciences50: 1561–1571.
22.
Shen Hui-Shen (2009) Functionally Graded materials, Nonlinear Analysis of plates and shells, London, New York: CRC Press, Taylor & Francis Group.
23.
SofiyevAH (2004) The stability of functionally graded truncated conical shells subjected to a periodic impulsive loading. International Journal of Solids and Structures41: 3411–3424.
24.
SofiyevAH (2007) The buckling of functionally graded truncated conical shells under dynamic axial loading. Journal of Sound and Vibration305: 808–826.
25.
SofiyevAH (2009) The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure. Composite Structures89: 356–366.
26.
SofiyevAH (2011) On the vibration and stability of clamped FGM conical shells under external loads. Journal of Composite Materials45(7): 771–788.
27.
SofiyevAHSchnackE (2004) The stability of functionally graded cylindrical shells under linearly increasing dynamic tensional loading. Engineering Structures26: 1321–1331.
28.
VelSSBatraRC (2004) Three dimensional exact solution for the vibration of FGM rectangular plates. Journal of Sound and Vibration272(3): 703–730.
29.
VolmirAS (1972) Non-linear Dynamics of Plates and Shells, Science edn. Moscow: Scientific Totals.
30.
WooJMeguidSAOngLS (2006) Nonlinear free vibration behavior of functionally graded plates. Journal of Sound and Vibration289: 595–611.
31.
Wu Tsung-LinShuklaKKHuangHJ (2006) Nonlinear static and dynamic analysis of functionally graded plates. International Journal of Applied Mechanics and Engineering11: 679–698.
32.
ZhangJLiS (2010) Dynamic buckling of FGM truncated conical shells subjected to non-uniform normal impact load. Composite Structures92: 2979–2983.
33.
ZhaoXLiQLiewKMNgTY (2006) The element-free kp-Ritz method for free vibration analysis of conical shell panels. Journal of Sound and Vibration295: 906–922.
34.
ZhaoXNgTYLiewKM (2004) Free vibration of two-sided simply-supported laminated cylindrical panel via the mesh-free kp-Ritz method. International Journal of Mechanical Sciences46: 123–142.
