Three-dimensional vibration analysis of laminated functionally graded spherical shells with general boundary conditions

Ye, Tiangui; Jin, Guoyong; Su, Zhu

doi:10.1016/j.compstruct.2014.05.046

Cited by 56 publications

(26 citation statements)

References 53 publications

(84 reference statements)

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“…Fazzolari and Carrera [35] developed a hierarchical trigonometric Ritz formulation and employed the same to perform free vibration analysis of doubly curved shallow and deep shells with single layered FGM and sandwich shells with functionally graded core. Ye et al [36] employed threedimensional shell theory of elasticity and energy based Rayleigh-Ritz procedure to carry out free vibration analysis of laminated functionally graded spherical shells under general boundary conditions. Recently, Jin et al [37] presented a modified Fourier-Ritz approach for free vibration analysis of laminated functionally graded shallow shells with general boundary conditions using first-order shear deformation shallow shell theory.…”

Section: Introductionmentioning

confidence: 99%

A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

Pandey

Pradyumna

2015

Composite Structures

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Section: Introductionmentioning

confidence: 99%

A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

Pandey

Pradyumna

2015

Composite Structures

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“…Tornabene and his team [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] extended the generalized differential quadrature (GDQ) method for the free vibration analysis of functionally graded circular and parabolic panels and shells of revolution with classical boundary conditions. Other related research results with the layered composite parabolic and circular panels can be seen in Refs [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. From the above literature review, it's easy to see that the computational accuracy and the range of application of boundary conditions strongly lie on the shell theories and solution methods for the most of studies on the titled problem.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of functionally graded parabolic and circular panels with general boundary conditions

Zhang

Shi

Wang

et al. 2017

Curved and Layered Structures

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Abstract:The purpose of this content is to investigate the free vibration of functionally graded parabolic and circular panels with general boundary conditions by using the Fourier-Ritz method. The first-order shear deformation theory is adopted to consider the effects of the transverse shear and rotary inertia of the panel structures. The functionally graded panel structures consist of ceramic and metal which are assumed to vary continuously through the thickness according to the power-law distribution, and two types of power-law distributions are considered for the ceramic volume fraction. The improved Fourier series method is applied to construct the new admissible function of the panels to surmount the weakness of the relevant discontinuities with the original displacement and its derivatives at the boundaries while using the traditional Fourier series method. The boundary spring technique is adopted to simulate the general boundary condition. The unknown coefficients appearing in the admissible function are determined by using the Ritz procedure based on the energy functional of the panels. The numerical results show the present method has good convergence, reliability and accuracy. Some new results for functionally graded parabolic and circular panels with different material distributions and boundary conditions are provided, which may serve as benchmark solutions.

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“…Particularly, each of the basic beam variables is mathematically described as a set of modified Fourier series including a standard cosine Fourier series as well as certain auxiliary functions [36][37][38][39][40][41]. The auxiliary terms are introduced for the purpose of removing the entire possible discontinuities with the basic beam variables and their derivatives at the edges to form a mathematically complete set and then ensure the convergence and speed up the calculation [39,[42][43][44][45].…”

Section: Modified Fourier Series Approximation the Modifiedmentioning

confidence: 99%

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

Wang

Miao

et al. 2017

Shock and Vibration

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An efficient modified Fourier series-based sampling surface approach is proposed for the analytical evaluation of the vibration characteristics of thick curved beams subjected to general restraints. The theoretical models of the beams are formulated by the theory of elasticity in two dimensions, which allows arbitrary thickness configurations to be tackled. As an innovation of this work, the approach is based upon the sampling surface method combined with the use of modified Fourier series approximation. In particular, the transverse beam domain is discretized by a set of sampling surfaces with unequal spaces, and the displacement components in beam domain coinciding with these surfaces are mathematically described as a set of modified Fourier series in which certain supplementary functions are included to remove all the relevant discontinuities with the displacements and their derivatives at the boundaries to form a mathematically complete set and guarantee the results convergent to the exact solutions. The final results are numerically solved using a modified variational principle by means of Lagrange multipliers and penalty method for the sake of arbitrary boundary conditions. The influences of transverse normal and shear deformation on the vibration characteristics with respect to the geometrical dimension and boundary conditions are systematically evaluated.

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Three-dimensional vibration analysis of laminated functionally graded spherical shells with general boundary conditions

Cited by 56 publications

References 53 publications

A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

Free vibration of functionally graded parabolic and circular panels with general boundary conditions

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

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