Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method

Farid, Muhammad; Zahedinejad, P.; Malekzadeh, P.

doi:10.1016/j.matdes.2009.07.025

Cited by 94 publications

(28 citation statements)

References 43 publications

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“…The results are prepared for with different thickness-to-mean radius ratios, panel angle φ and different values of the GDQ grid points in the radial direction and are shown in Table 3. Also, one can see that excellent agreement exists between the results of this method and those of Farid et al [17].…”

Section: Numerical Results and Discussionsupporting

confidence: 76%

“…15,16,17. It is observed the non-dimensional natural frequency decreases with increasing the R/L ratio and then remains almost unaltered for R/L >4.…”

Section: Numerical Results and Discussionmentioning

confidence: 92%

“…The shells are discretized into cylindrical finite elements, and the distribution of the foundation in the circumferential direction is defined by the expansion of Fourier series. Farid et al [17] have studied three-dimensional temperature-dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation subjected in thermal environment. The curved panels was made of isotropic material, and in order to discretize the governing equations, the differential quadrature method in the thickness direction and the trigonometric functions in longitudinal and tangential directions in conjunction of the three-dimensional form of the Hamilton's principle have been used.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional free vibration analysis of four-parameter continuous grading fiber reinforced cylindrical panels resting on Pasternak foundations

Aragh

Yas

2011

Arch Appl Mech

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This research investigates three-dimensional free vibration analysis of four-parameter continuous grading fiber reinforced (CGFR) cylindrical panels resting on Pasternak foundations by using generalized power-law distribution. The functionally graded orthotropic panel is simply supported at the edges, and it is assumed to have an arbitrary variation of matrix volume fraction in the radial direction. A four-parameter power-law distribution presented in literature is proposed. Symmetric and asymmetric volume fraction profiles are presented. Suitable displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which are solved by generalized differential quadrature method, and natural frequency is obtained. The fast rate of convergence of the method is demonstrated, and to validate the results, comparisons are made with the available solutions for functionally graded isotropic shells with/without elastic foundations. The effect of the elastic foundation stiffness parameters and various geometrical parameters on the vibration behavior of the CGFR cylindrical panels is investigated. This work mainly contributes to illustrate the influence of the four parameters of power-law distributions on the vibration behavior of functionally graded orthotropic cylindrical panels resting on elastic foundation. This paper is also supposed to present useful results for continuous grading of matrix volume fraction in the thickness direction of a cylindrical panel on elastic foundation and comparison with similar discrete laminated composite cylindrical panel.

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Section: Numerical Results and Discussionsupporting

confidence: 76%

“…15,16,17. It is observed the non-dimensional natural frequency decreases with increasing the R/L ratio and then remains almost unaltered for R/L >4.…”

Section: Numerical Results and Discussionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Three-dimensional free vibration analysis of four-parameter continuous grading fiber reinforced cylindrical panels resting on Pasternak foundations

Aragh

Yas

2011

Arch Appl Mech

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“…The results of the presented formulations are given in the form of convergence studies with respect to N r and N z , the number of discrete points distributed along the radial and axial directions, respectively. The obtained natural frequencies based on the threedimensional elasticity formulation are compared with those of the power series expansion method for both FGM curved panels with and without elastic foundations [14,22,23]. In these studies the material properties of functionally graded materials are assumed as follows -Metal (Aluminum, Al): E c 5380 Ã 10 9 Pa; q c 53800Kg=m 3 ; t c 50:3…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Using eshelby–mori–tanaka scheme for 3D free vibration analysis of sandwich curved panels with functionally graded nanocomposite face sheets and finite length

Tahouneh

Naei

2016

Polymer Composites

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This article deals with free vibration analysis of thick nanocomposite laminated curved panels with finite length resting on two‐parameter elastic foundations, based on the three‐dimensional elasticity theory. The main objective of this research paper is to present a 3D elasticity solution for free vibration analysis of thick laminated curved panels with continuously graded carbon nanotube‐reinforced sheets. The structure is supported by an elastic foundation with Winkler's (normal) and Pasternak's (shear) coefficients. The volume fractions of oriented, straight single‐walled carbon nanotubes are assumed to be a three‐parameter power‐law distribution which is graded in the radial direction of the panels. An equivalent continuum model based on the Eshelby‐Mori‐Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes. Because of using two‐dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. The convergence of the method is demonstrated and comparisons are made between the present results and results reported by well‐known references and have confirmed accuracy and efficiency of the present approach. This study serves as a benchmark for assessing the validity of numerical methods or two‐dimensional theories used to analysis of laminated curved panels. POLYM. COMPOS., 38:E563–E576, 2017. © 2016 Society of Plastics Engineers

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“…Only a few references can be found that consider the effect of MWCNTs on the vibrational behavior of structures [38]. Farid et al [39] studied three-dimensional (3-D) temperature dependent free vibration analysis of FGM curved panels resting on two parameter elastic foundation by using a hybrid semi-analytic, DQM. Jam et al [40] used the new version of Rule of mixture to show the effect of waviness of CNT on the vibrational behavior of nanocomposite cylindrical panel.…”

Section: Introductionmentioning

confidence: 99%

An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-walled Carbon Nanotubes

Tahouneh

2017

Period. Polytech. Mech. Eng.

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In the present work, vibration characteristics of functionally graded (FG) Keywords multiwalled carbon nanotubes, vibration, sandwich plates, modified Halpin-Tsai equation, three-dimensional elasticity solution IntroductionNowadays, the use of carbon nanotubes in polymer/carbon nanotube composites has attracted wide attention [1]. A high aspect ratio, low weight of CNTs and their extraordinary mechanical properties (strength and flexibility) provide the ultimate reinforcement for the next generation of extremely lightweight but highly elastic and very strong advanced composite materials. On the other hand, by using of the polymer/CNT composites in advanced composite materials, we can achieve structures with low weight, high strength and high stiffness in many structures of civil, mechanical and space engineering.Several researches have recently investigated the elastic properties of multiwalled carbon nanotube (MWCNT) and their composites [2,3]. Gojny et al. [4] focused on the evaluation of the different types of the CNTs applied, their influence on the mechanical properties of epoxy-based nanocomposites and the relevance of surface functionalization. Therefore, the study of the mechanical performance of CNT-based composites and the discovery of possible innovative applications has recently attracted the interest of many researchers.Several researchers have reported that mechanical properties of polymeric matrices can be drastically increased [5,6] by adding a few weight percent (wt%) MWCNTs. Montazeri et al. [5] showed that modified Halpin-Tsai equation with exponential Aspect ratio can be used to model the experimental result of MWCNT composite samples. They also demonstrated that reduction in Aspect ratio (L/d) and nanotube length cause a decrease in aggregation and above 1.5 wt%, nanotubes agglomerate causing a reduction in Young's modulus values. Thus, it is important to determine the effect Aspect ratio and arrangement of CNTs on the effective properties of carbon nanotube-reinforced composite (CNTRC). Yeh et al. [6] used the Halpin-Tsai equation to shows the effect of MWCNT shape factor (L/d) on the mechanical properties. They showed that the mechanical properties of nanocomposite samples with the higher shape factor (L/d) values were better than the ones with the lower shape factor. The reinforcement effect of MWCNTs with different aspect ratio in an epoxy matrix has been carried out by Martone et al. [7]. They showed that progressive reduction of

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Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method

Cited by 94 publications

References 43 publications

Three-dimensional free vibration analysis of four-parameter continuous grading fiber reinforced cylindrical panels resting on Pasternak foundations

Three-dimensional free vibration analysis of four-parameter continuous grading fiber reinforced cylindrical panels resting on Pasternak foundations

Using eshelby–mori–tanaka scheme for 3D free vibration analysis of sandwich curved panels with functionally graded nanocomposite face sheets and finite length

An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-walled Carbon Nanotubes

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