A unified formulation for vibration analysis of functionally graded shells of revolution with arbitrary boundary conditions

Qu, Yegao; Long, Xinhua; Yuan, Guangyin; Meng, Guang

doi:10.1016/j.compositesb.2013.02.028

Cited by 143 publications

(45 citation statements)

References 60 publications

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“…Su et al [32] presented a unified solution for vibration analysis of FG cylindrical, conical shells and annular plates with general boundary conditions by applying the FSDT and Rayleigh-Ritz procedure. Qu et al [33] described a unified formulation for free, steady-state, and transient vibration analyses of FG shells with arbitrary boundary conditions on the basis of the FSDT. In this paper, the free vibrations of functionally graded cylindrical, conical, and spherical shells with different combinations of free, shear-diaphragm, simply supported, clamped, and elasticsupported boundary conditions were discussed.…”

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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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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“…First order shear deformation theory and Love's first approximation theory are utilized in the equilibrium equations. Qu et al (2013) studied vibrational response of FG shells of revolution with arbitrary boundary conditions. The formulation is derived by means of a modified variational principle in conjunction with a multisegment partitioning procedure on the basis of the first-order shear deformation shell theory.…”

Section: Introductionmentioning

confidence: 99%

Three dimensional Free Vibration and Transient Analysis of Two Directional Functionally Graded Thick Cylindrical Panels Under Impact Loading

Zafarmand

Salehi

Asemi

2015

Lat. Am. j. solids struct.

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In this paper three dimensional free vibration and transient response of a cylindrical panel made of two directional functionally graded materials (2D-FGMs) based on three dimensional equations of elasticity and subjected to internal impact loading is considered. Material properties vary through both radial and axial directions continuously. The 3D graded finite element method (GFEM) based on Rayleigh-Ritz energy formulation and Newmark direct integration method has been applied to solve the equations in space and time domains. The fundamental normalized natural frequency, time history of displacements and stresses in three directions and velocity of radial stress wave propagation for various values of span angel of cylindrical panel and different power law exponents have been investigated. The present results show that using 2D-FGMs leads to a more flexible design than conventional 1D-FGMs. The GFEM solution have been compared with the results of an FG thick hollow cylinder and an FG curved panel, where a good agreement between them is observed.

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“…Neves et al [26] dealt with free vibration problems of functionally graded shells with classical boundary conditions based on the higher-order shear deformation theory and the radial basis functions collocation. Qu et al [27] described a general formulation for free, steady-state, and transient vibration analyses of functionally graded shells of revolution subjected to arbitrary boundary conditions by means of a modified variational principle in conjunction with a multisegment partitioning procedure. Santos et al [28,29] developed a semianalytical axisymmetric finite element model using the 3D linear elastic theory to study the free vibrations of functionally graded cylindrical shells made up of isotropic properties.…”

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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A unified formulation for vibration analysis of functionally graded shells of revolution with arbitrary boundary conditions

Cited by 143 publications

References 60 publications

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

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

Three dimensional Free Vibration and Transient Analysis of Two Directional Functionally Graded Thick Cylindrical Panels Under Impact Loading

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

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