This paper presents the vibration analysis of stiffened plates with initial imperfections, using both conventional and super finite element methods. Von Karman theory was utilized so as to formulate the plate element. Eccentricity of the stiffeners is also taken into account and they are not limited to be placed on nodal lines. Consequently, any configuration of plate and stiffeners can be modelled. Nonlinear finite element equations are solved using arc-length method and backbone curve is extracted accordingly. The accuracy of proposed methodology is established in comparison with previous results. Finally, the effect of geometric imperfection on vibration characteristics of stiffened plates is studied extensively.
RibeiroPPetytM. Nonlinear vibration of plates by the hierarchical finite element and continuation methods. Int J Mech Sci1999; 41(4–5): 437–459.
2.
SuZWangLSunK, et al. Vibration characteristic and flutter analysis of elastically restrained stiffened functionally graded plates in thermal environment. Int J Mech Sci2019; 157: 872–884.
3.
HamedaniSJRanjiAR. Buckling analysis of stiffened plates subjected to non-uniform biaxial compressive loads using conventional and super finite elements. Thin-Walled Struct2013; 64: 41–49.
4.
OlsonMDHazellCR. Vibration studies on some integral rib-stiffened plates. J Sound Vib1977; 50(1): 43–61.
5.
MustafaBAAliR. Prediction of natural frequency of vibration of stiffened cylindrical shells and orthogonally stiffened curved panels. J Sound Vib1987; 113(2): 317–327.
6.
MukherjeeAMukhopadhyayM. Finite element free vibration of eccentrically stiffened plates. Computers & Structures1987; 30(6): 1303–1317.
7.
HamedaniSJKhedmatiMRAzkatS. Vibration analysis of stiffened plates using finite element method. Lat Am J Solids Struct2012; 9(1): 1–20.
8.
KimSEDucNDNamVH, et al. Nonlinear vibration and dynamic buckling of eccentrically oblique stiffened FGM plates resting on elastic foundations in thermal environment. Thin-Walled Struct2019; 142: 287–296.
9.
SinhaLMishraSSNayakAN, et al. Free vibration characteristics of laminated composite stiffened plates: experimental and numerical investigation. Compos Struct2020; 233: 111557.
10.
LeungAYZhuB. Geometric nonlinear vibration of clamped Mindlin plates by analytically integrated trapezoidal p-element. Thin-Walled Struct2004; 42(7): 931–945.
11.
AmabiliM. Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections. J Sound Vib2006; 291(3–5): 539–565.
12.
LiuLLiJMKardomateasGA. Nonlinear vibration of a composite plate to harmonic excitation with initial geometric imperfection in thermal environments. Composite Struct2019; 209: 401–423.
13.
TalebizadehsardariPSalehipourHShahgholian-GhahfarokhiD, et al, Free vibration analysis of the macro-micro-nano plates and shells made of a material with functionally graded porosity: a closed-form solution. Mech Based Des Struct Mach2020; 48: 1–27.
14.
Shahgholian-GhahfarokhiDRahimiG. A sensitivity study of the free vibration of composite sandwich cylindrical shells with grid cores. Iran J Sci Technol Trans Mech Eng2020; 44: 149–162.
15.
Shahgholian-GhahfarokhiDRahimiG. Buckling analysis of composite lattice sandwich shells under uniaxial compression based on the effective analytical equivalent approach. Compos B Eng2019; 174: 106932.
16.
Shahgholian-GhahfarokhiDRahimiG. Buckling load prediction of grid-stiffened composite cylindrical shells using the vibration correlation technique. Compos Sci Technol2018; 167: 470–481.
17.
Shahgholian-GhahfarokhiDRahimiG. An analytical approach for global buckling of composite sandwich cylindrical shells with lattice cores. Int J Solids Struct2018; 146: 69–79.
18.
ChoDSKimBHVladimirN, et al. Natural vibration analysis of vertical rectangular plates and stiffened panels in contact with fluid on one side. Proc Inst Mech Eng M J Eng Marit Environ2014; 230(1): 114–125.
19.
AmabiliM. Nonlinear vibration and stability of shell and plates. 1st ed. Cambridge: Cambridge University Press, 2008.
20.
LiewKMXiangYKitipornchaiS, et al. Vibration of mindlin plates. 1st ed. Oxford: Elsevier Science Ltd., 1998.
21.
PetytM. Introduction to finite element vibration analysis. 1st ed. New York: Cambridge University Press, 1990.
22.
ZienkiewiczOCTaylorRL. The finite element method for solid and structural mechanics. 6th ed. Oxford: Elsevier Ltd., 2005.
23.
CrisfieldMA. Nonlinear finite element analysis of solids and structures. England: John Wiley and Sons Ltd., 2000.
