Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution

Tornabene, Francesco

doi:10.1016/j.cma.2009.04.011

Cited by 502 publications

(143 citation statements)

References 54 publications

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“…In contrast to the extensive researches accomplished on displacement analysis, vibration (Nie and Zhong, 2007;Tornabene, 2009;Setoodeh et al, 2011;Shariyat and Alipour, 2011;Shariyat, 2012;Tahani et al, 2013;Duc, 2013;Mercan et al, 2016) or buckling (Sofiyev, 2007;Shariyat, 2008;Shariyat, 2011, 2013;Shariyat and Asgari, 2013;Sun et al, 2014) of the FGM circular/annular plates and cylindrical/conical shells, limited works have been published on the stress analysis of the mentioned structures. A semi-inverse series elasticity solution was presented by Pelletier and Vel (2006) for thermoelastic analysis of a transversely graded orthotropic cylindrical shell.…”

Section: Introductionmentioning

confidence: 99%

Analytical Bending and Stress Analysis of Variable Thickness FGM Auxetic Conical/Cylindrical Shells with General Tractions

Shariyat

2017

Lat. Am. j. solids struct.

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Section: Introductionmentioning

confidence: 99%

Analytical Bending and Stress Analysis of Variable Thickness FGM Auxetic Conical/Cylindrical Shells with General Tractions

Shariyat

2017

Lat. Am. j. solids struct.

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“…Tornabene and Viola [1][2][3] studied the free vibration of the moderately thick four-parameter functionally graded conical, cylindrical shells and annular plates under some classical boundary conditions by means of the generalized differential quadrature method on the basis of the first-order shear deformation theory. Zhao and Liew [4,5] presented the element-free kp-Ritz method to investigate the free vibration analysis of mechanical and thermal buckling of functionally graded conical shell panels with classical boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In order to check the present method, the numerical results reported by Su et al [7][8][9], Qu et al [27], and Tornabene et al [1,3,52] are also given in the above tables for comparison. From the comparisons, we can see a consistent agreement of present results taken from the current proposed unified approach and referential data.…”

mentioning

confidence: 99%

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Pang

et al. 2017

Mathematical Problems in Engineering

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The aim of this paper is to extend the modified Fourier-Ritz approach to evaluate the free vibration of four-parameter functionally graded moderately thick cylindrical, conical, spherical panels and shells of revolution with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. In the modified Fourier-Ritz approach, the admissible functions of the structure elements are expanded into the improved Fourier series which consist of two-dimensional (2D) Fourier cosine series and auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions and then solve the natural frequencies by means of the Ritz method. As one merit of this paper, the functionally graded cylindrical, conical, spherical shells are, respectively, regarded as a special functionally graded cylindrical, conical, spherical panels, and the coupling spring technology is introduced to ensure the kinematic and physical compatibility at the common meridian. The excellent accuracy and reliability of the unified computational model are compared with the results found in the literatures.

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“…Therefore, a unified analytical model is developed to study the vibration characteristics of varying FG shallow shell structures. Tornabene [24][25][26] focused on the free vibration and dynamic behavior of FG conical, cylindrical shells and annular plates with a four-parameter power-law distribution based on the 2D GDM and FSDT. Besides, Tornabene et al [27] applied higher-order equivalent single layer theories to study free vibrations of free-form FG doubly curved shells.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Shi

Zha

Zhang

et al. 2017

Shock and Vibration

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The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and RayleighRitz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

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Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution

Cited by 502 publications

References 54 publications

Analytical Bending and Stress Analysis of Variable Thickness FGM Auxetic Conical/Cylindrical Shells with General Tractions

Analytical Bending and Stress Analysis of Variable Thickness FGM Auxetic Conical/Cylindrical Shells with General Tractions

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

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