The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load

Sofiyev, A.H.; Deniz, A.; Akçay, İsmail Hakkı; Yusufoğlu, Elçin

doi:10.1007/s00707-006-0328-5

Cited by 36 publications

(19 citation statements)

References 38 publications

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“…(33) and (34) are for inner and outer FGM layers of the cylindrical shell which vary from −h/2 to 0 and from 0 to +h/2 respectively. From these relations, one can conclude that at z = −h/2, the effective material properties become E = E 1 , ν = ν 1 , ρ = ρ 1 for inner layer, for z = 0, Variation of volume fractions V 1 ,V 2 and V 3 for constituent materials M 1 ,M 2 and M 3 placed at the inner, middle and the outer shell surfaces in both the FGM layers are sketched in Fig.…”

Section: Functionally Graded Materialsmentioning

confidence: 99%

“…No study is reported on multi-layered or bi-layered FGM cylindrical shells except very few studies are available on sandwich technology. Sofiyev et al [33] have analyzed the vibration and stability analysis of a three-layered conical shell with middle layer of functionally graded material. They applied Galerkin method to transform governing equations of motion to a pair of time dependent partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Vibration analysis of bi-layered FGM cylindrical shells

et al. 2010

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In the present study, a vibration frequency analysis of a bi-layered cylindrical shell composed of two independent functionally graded layers is presented. The thickness of the shell layers is assumed to be equal and constant. Material properties of the constituents of bi-layered functionally graded cylindrical shell are assumed to vary smoothly and continuously through the thickness of the layers of the shell and are controlled by volume fraction power law distribution. The expressions for strain-displacement and curvature-displacement relationships are utilized from Love's first approximation linear thin shell theory. The versatile Rayleigh-Ritz approach is employed to formulate the frequency equations in the form of eigenvalue problem. Influence of material distribution in the two functionally graded layers of the cylindrical shells is investigated on shell natural frequencies for various shell parameters with simply supported end conditions. To check the validity, accuracy and efficiency of the present methodology, results obtained are compared with those available in the literature.

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Section: Functionally Graded Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration analysis of bi-layered FGM cylindrical shells

et al. 2010

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“…Very few studies are available on sandwich technology. Sofiyev et al [8] analyzed the vibration and stability analysis of a threelayered conical shell, with the middle layer made up of FGM. Shi-Rong and Batra [9] studied the buckling of a simply supported three-layered circular cylindrical shell under axial compressive load, in which the inner and outer layers of the shell were composed of isotropic materials and the middle layer was composed of FGMs.…”

Section: Introductionmentioning

confidence: 99%

Vibration of bilayered cylindrical shells with layers of different materials

et al. 2010

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In this analysis, a comparative study for natural frequencies of two-layered cylindrical shells was presented with one layer composed of functionally graded material and the other layer of isotropic material. Love's thin shell theory was exploited for the straindisplacement and curvature-displacement relationships. For governing frequency equations, the Rayleigh-Ritz method was utilized to minimize the Lagrangian functional in the form of an eigenvalue problem. Frequency spectra were computed for long, short, thick, and thin cylindrical shells by varying the nondimensional geometrical parameters, length-to-radius and thickness-to-radius ratios for a simply supported end condition. Influence of different configurations of cylindrical shells on the shell frequencies was studied. For validity, the results obtained were compared with some results of isotropic and single-layered functionally graded cylindrical shells from the literature.

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“…The governing equations were obtained using energy functional with the Rayleigh Ritz method. Sofiyev et al [23] studied the vibration and stability analysis of a three-layered conical shell with middle layer composed of functionally graded material. They applied Galerkin numerical technique to transform the governing equations of motion into a pair of time dependent partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Vibration of Three-Layered FGM Cylindrical Shells with Middle Layer of Isotropic Material for Various Boundary Conditions

Khan¹,

Arshad²,

Shah³

et al. 2014

WJM

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In the present study, vibration analysis of a three-layered cylindrical shell is performed whose inner and outer layers are composed of functionally graded materials whereas the middle one is assumed to be of isotropic material. This formation of a cylindrical shell influences stiffness modulii and the resultant material properties. The shell problem is formulated from the constitutive relations of stresses and strains with the displacement deformations and they are taken from Love's thin shell theory. This problem is transformed into the integral form by evaluating the expressions for the strain and kinetic energies of the shell. Rayleigh-Ritz method is employed to solve the shell dynamic equations. Vibration characteristics of these cylindrical shells are investigated for a number of physical parameters and configurations of the fabrication of shells. The axial modal dependence is approximated by the characteristic beam functions that satisfy the boundary conditions. Results evaluated, show good agreement with the open literature.

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The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load

Cited by 36 publications

References 38 publications

Vibration analysis of bi-layered FGM cylindrical shells

Vibration analysis of bi-layered FGM cylindrical shells

Vibration of bilayered cylindrical shells with layers of different materials

Vibration of Three-Layered FGM Cylindrical Shells with Middle Layer of Isotropic Material for Various Boundary Conditions

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