Benchmark solution for free vibration of functionally graded moderately thick annular sector plates

Saidi, A.R.; Baferani, A. Hasani; Jomehzadeh, E.

doi:10.1007/s00707-011-0459-1

Cited by 32 publications

(21 citation statements)

References 30 publications

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“…Firstly, the validity of the present method for the moderately thick FG sandwich circular sector plate is studied. The comparisons of the frequency parameters Ω = [38] using the DQ method on the basis of FSDT. The comparison shows that the current results are in good agreement with those of Saidi et al [38].…”

Section: Validation and Some Newmentioning

confidence: 99%

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Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

Pang

Wang

et al. 2017

Shock and Vibration

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The free vibration analysis of moderately thick functionally graded (FG) sector plates resting on two-parameter elastic foundation with general boundary conditions is presented via Fourier-Ritz method, which is composed of the modified Fourier series approach and the Ritz procedure. The material properties are assumed to vary continuously along the thickness according to the powerlaw distribution. The bilayered and single-layered functionally graded sector plates are obtained as the special cases of sandwich plates. The first-order shear deformation theory (FSDT) is adopted to construct the theoretical model. Under current framework, regardless of boundary conditions, each displacement and each rotation of plates is represented by the modified Fourier series consisting of a standard Fourier cosine series and several closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series representation. Then, the accurate solutions are obtained by using the Ritz procedure based on the energy function of sector plates. The present method shows good convergence, reliability, and accuracy by comprehensive investigation with some selected classical boundary conditions. Numerous new vibration results for moderately thick FG sandwich sector plates are provided. The effects of the elastic restraint parameters and so forth on free vibration characteristic of sector plates are presented.

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Section: Validation and Some Newmentioning

confidence: 99%

“…The comparisons of the frequency parameters Ω = [38] using the DQ method on the basis of FSDT. The comparison shows that the current results are in good agreement with those of Saidi et al [38]. Next, the validity of the present method for the moderately thick FG sandwich circular sector plate is studied.…”

Section: Validation and Some Newmentioning

confidence: 99%

Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

Pang

Wang

et al. 2017

Shock and Vibration

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“…First, a verification study is made to validate the accuracy and reliability of the present method. The results reported by Sharma [14] are adopted herein as the reference. And the Numerous new results are presented in Tables 3, 4 and 5 for composite laminated annular sector plates with a variety of boundary conditions including clamped boundary, simple-support boundary, free boundary and their combinations.…”

Section: Composite Laminated Annular Sector Plates With Various Boundmentioning

confidence: 99%

“…To eliminate this deficiency, the FSDT was developed then, which assumes constant states of the transverse shear stresses through the plate thickness. There is also a great deal of research on the plate structure on the basis of FSDTs [11][12][13][14][15][16][17][18][19][20][21][22][23]. Generally, the shear correction factor is used to adjust the transverse shear stiffness as a constant, which differs from the fact that the shear correction factor is determined by the material properties and boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A modified Fourier solution for vibration analysis of moderately thick laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports

Pang

Miao³

et al. 2017

Curved and Layered Structures

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Abstract:In this paper, a modified Fourier solution based on the first-order shear deformation theory is developed for the free vibration problem of moderately thick composite laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports. In this solution approach, regardless of boundary conditions, the displacement and rotation components of the sector plate are written in the form of the trigonometric series expansion in which several auxiliary terms are added to ensure and accelerate the convergence of the series. Each of the unknown coefficients is taken as the generalized coordinate and determined using the RaleighRitz method. The accuracy and reliability of the present solution are validated by the comparison with the results found in the literature, and numerous new results for composite laminated annular sector plates considering various kinds of boundary conditions are presented. Comprehensive studies on the effects of elastic restraint parameters, layout schemes and locations of line/arc supports are also made. New results are obtained for laminated annular sector plates subjected to elastic boundary restraints and arbitrary internal radial line and circumferential arc supports in both directions, and they may serve as benchmark solutions for future researches.

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“…The FSDT [1][2][3][4][5][6][7][8][9] gives acceptable prediction, but requires a shear correction factor which is hard to find out consistently because of dependent on many parameters including geometry, boundary conditions, and loading conditions. The HSDTs [10][11][12][13][14][15][16][17] do not require a shear correction factor, but their equations of motion are more complicated than those of the FSDT.…”

Section: Introductionmentioning

confidence: 99%

A quasi-3D hyperbolic shear deformation theory for functionally graded plates

Thai

Bui

et al. 2013

Acta Mech

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Benchmark solution for free vibration of functionally graded moderately thick annular sector plates

Cited by 32 publications

References 30 publications

Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

A modified Fourier solution for vibration analysis of moderately thick laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports

A quasi-3D hyperbolic shear deformation theory for functionally graded plates

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