A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations

Alipour, M.M.; Shariyat, M.; Shaban, M.

doi:10.1007/s10999-010-9134-2

Cited by 56 publications

(25 citation statements)

References 26 publications

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“…Moreover, Figs. 2, 3, and 4 reveal that due to changes in the material properties distributions caused by changing the α value, locations of the vibration nodes and antinodes and subsequently, the overall mode shapes have been changed [28]. Indeed, since the stiffness of the plate decreases when value of the α parameter is negative, as one proceeds from the center of the plate to the edge of the plate, the extrema of the mode shapes shift outward for negative values of the α parameters.…”

Section: Resultsmentioning

confidence: 99%

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Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations

Shariyat

Alipour

2010

Arch Appl Mech

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In the present paper, the differential transformation method is employed to develop a semi-analytical solution for free vibration and modal stress analyses of two-dimensional functionally graded circular plates resting on two-parameter elastic foundations. Simultaneous variations of the material properties in the radial and transverse directions are described by a general function. Some comprehensive sensitivity analyses are performed, and the natural frequencies and the modal stresses are extracted for free, simply supported, and clamped boundary conditions and different combinations of the geometric, material, and foundation parameters. Therefore, very complex combinations of the material properties, boundary conditions, and parameters of the elastic foundation are considered in the present semi-analytical solution approach. Thus, many novelties are included in the present research. Comparisons made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. Moreover, the paper treats some interesting problems, for the first time.

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Section: Resultsmentioning

confidence: 99%

“…The frequency equations may be derived by incorporating the transformed boundary conditions (27,28,29) simultaneously. As it has been mentioned before, three kinds of edge conditions are considered in the present research: free, simply supported, and clamped.…”

Section: The Solution Proceduresmentioning

confidence: 99%

Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations

Shariyat

Alipour

2010

Arch Appl Mech

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“…There are very few studies on the static and dynamic behaviors of shear deformable heterogeneous structural elements resting on elastic foundations. Alipour et al (2010) presented a semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations based on FOSDT. Atmane et al (2011) investigated free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Stability of EG cylindrical shells with shear stresses on a Pasternak foundation

Najafov

Sofiyev²,

Hui³

et al. 2014

Steel Compos. Struct.

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This article is the result of an investigation on the influence of a Pasternak elastic foundation on the stability of exponentially graded (EG) cylindrical shells under hydrostatic pressure, based on the first-order shear deformation theory (FOSDT) considering the shear stresses. The shear stresses shape function is distributed parabolic manner through the shell thickness. The governing equations of EG orthotropic cylindrical shells resting on the Pasternak elastic foundation on the basis of FOSDT are derived in the framework of Donnell-type shell theory. The novelty of present work is to achieve closed-form solutions for critical hydrostatic pressures of EG orthotropic cylindrical shells resting on Pasternak elastic foundation based on FOSDT. The expressions for critical hydrostatic pressures of EG orthotropic cylindrical shells with and without an elastic foundation based on CST are obtained, in special cases. Finally, the effects of Pasternak foundation, shear stresses, orthotropy and heterogeneity on critical hydrostatic pressures, based on FOSDT are investigated.

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“…Many papers that have dealt with nonlinear algebraic governing equations may be found in the literature. The homotopy perturbation method (HPM) was proposed for the first time by He [14,15] for solving linear and nonlinear differential and integral equations and has been the subject of extensive analytical and numerical studies [16][17][18][19][20]. The method is a coupling between the traditional perturbation method and the homotopy method that is commonly used in topology analysis.…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate

Shariyat

Ghajar

2011

J Eng Math

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An analytical solution for a low velocity impact between a thin transversely isotropic plate made of a strain-hardening material supported by a rigid substrate and a rigid sphere is presented. One of the novelties of this work is employing a linear strain-hardening model for investigating the indentation phenomenon in the plastic zone, rather than the traditional perfectly plastic model. Another novelty of this work is employing the homotopy perturbation method to derive analytical solutions for the highly nonlinear governing equations of contact. Since it is very important to accurately predict the contact force and its time history, the three stages of the indentation process, i.e., (1) the elastic indentation, (2) the plastic indentation, and (3) the elastic unloading stages, are investigated in detail. Comparison of the present results with results obtained from the iterative numerical time integration method confirms the accuracy and efficiency of the present solution.

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A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations

Cited by 56 publications

References 26 publications

Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations

Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations

Stability of EG cylindrical shells with shear stresses on a Pasternak foundation

An analytical solution for a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate

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