Three-dimensional free vibration analysis of functionally graded cylindrical panels with cut-out using Chebyshev–Ritz method

Malekzadeh, P.; Bahranifard, F.; Ziaee, Sima

doi:10.1016/j.compstruct.2013.05.005

Cited by 40 publications

(18 citation statements)

References 34 publications

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“…In this study, the plate is also a square, and for the sake of comparison, the side-to-thickness ratio is chosen as a/h = 100. Four different square cutout sizes, c/a = 0.1, 0.2, 0.3 and 0.5, are considered and in each case our results are compared with those of Malekzadeh et al [45] and Mundkur et al [46]. Malekzadeh et al [45] obtained the frequencies according to a three dimensional elasticity formulation and using the Chebyshev–Ritz formulation, whereas boundary characteristics of orthogonal polynomial functions are invoked into the Ritz formulation by Mundkur et al [46] to obtain the plate frequencies.…”

Section: Resultsmentioning

confidence: 99%

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

Mirzaei¹,

Kiani²

2016

Beilstein J. Nanotechnol.

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SummaryDuring the past five years, it has been shown that carbon nanotubes act as an exceptional reinforcement for composites. For this reason, a large number of investigations have been devoted to analysis of fundamental, structural behavior of solid structures made of carbon-nanotube-reinforced composites (CNTRC). The present research, as an extension of the available works on the vibration analysis of CNTRC structures, examines the free vibration characteristics of plates containing a cutout that are reinforced with uniform or nonuniform distribution of carbon nanotubes. The first-order shear deformation plate theory is used to estimate the kinematics of the plate. The solution method is based on the Ritz method with Chebyshev basis polynomials. Such a solution method is suitable for arbitrary in-plane and out-of-plane boundary conditions of the plate. It is shown that through a functionally graded distribution of carbon nanotubes across the thickness of the plate, the fundamental frequency of a rectangular plate with or without a cutout may be enhanced. Furthermore, the frequencies are highly dependent on the volume fraction of carbon nanotubes and may be increased upon using more carbon nanotubes as reinforcement.

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Section: Resultsmentioning

confidence: 99%

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

Mirzaei¹,

Kiani²

2016

Beilstein J. Nanotechnol.

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“…They showed that this method had high accuracy, stable computation and rapid convergence. The computational efficiency and accuracy of this method for the three-dimensional free vibration analyses of the FG plates and shells were demonstrated too [62,63]. Based on the results of these research works, one can conclude that the Chebyshev-Ritz method is a computationally efficient and accurate approximate method for solving the complicated plate and shell problems.…”

Section: The Msgt and Fsdt Of Platesmentioning

confidence: 96%

“…The temperature-dependent coefficients of material properties of ceramic (Si 3 N 4 ) and metals (SUS304)[63].Table 1. The values of i  in the functions i f and i g (i=1,2) for the different boundary conditions.…”

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confidence: 99%

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Thermal environmental effects on free vibration of functionally graded isosceles triangular microplates

Shenas

Malekzadeh

2016

Mechanics of Advanced Materials and Structures

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The free vibration of the functionally graded (FG) isosceles triangular microplates in thermal environment is investigated. The modified strain gradient theory (MSGT) together with the firstorder shear deformation theory (FSDT) of plates is adopted to formulate the problem. The material properties are assumed to be graded in the thickness direction. The Chebyshev-Ritz method is chosen as the solution procedure. After demonstrating the fast rate of convergence and accuracy of the method, the effects of temperature rise, length scale parameters, material gradient index, different boundary conditions, apex angle and width-to-thickness ratio on the free vibration of triangular microplates are studied.

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“…On the other hand, it is shown that one can reduce the complexity of the mechanical behavior modelling of structures with cut-outs by combining the construction of energy functional with the Ritz method (Malekzadeh et al, 2013). Therefore, in this study, the Ritz method is employed to derive discrete equations of motion which yield the eigenvalue problem.…”

Section: Introductionmentioning

confidence: 99%

Linear free vibration of graphene sheets with nanopore via Aifantis theory and Ritz method

Ziaee

2017

jtam

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This article aims to study the natural frequency of defective graphene sheets since the existence of cut-outs in plates may be essential on the basis of their desired functionality. A combination of the Aifantis theory and Kirchhoff thin plate hypothesis is used to derive governing equations of motion. The Ritz method is employed to derive discrete equations of motion. The molecular structural mechanics method is also employed to specify the effective length scale parameter. In the 'numerical results' Section, the effects of different parameters such as boundary conditions and diameter of the hole-to-side length ratio on the fundamental frequency of graphene sheets are studied.

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Three-dimensional free vibration analysis of functionally graded cylindrical panels with cut-out using Chebyshev–Ritz method

Cited by 40 publications

References 34 publications

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

Thermal environmental effects on free vibration of functionally graded isosceles triangular microplates

Linear free vibration of graphene sheets with nanopore via Aifantis theory and Ritz method

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