A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates

Fekrar, Abdelkader; Houari, Mohammed Sid Ahmed; Tounsi, Abdelouahed; Mahmoud, S.R.

doi:10.1007/s11012-013-9827-3

Cited by 74 publications

(19 citation statements)

References 33 publications

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“…It has to be mentioned that the classical plate theory cannot capture the influence of shear deformations which severely affects the vibrational behavior of the plate especially when the thickness is comparable to one of the plate's dimensions. In addition, it is seen that the Mindlin plate theory produces desirable results which are comparable to other more exact higher order plate theories [53][54][55][56][57][58][59][60][61][62][63][64] which are much more complicated in the theory and calculations. In Eqs.…”

Section: Formulationmentioning

confidence: 82%

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

Anjomshoa

Tahani

2016

J Mech Sci Technol

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In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded orthotropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.

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Section: Formulationmentioning

confidence: 82%

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

Anjomshoa

Tahani

2016

J Mech Sci Technol

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“…It should be mentioned that the neutral plane location is different from the mid plane location in plates with material changes along the thickness [20,21], the thing which is not true for plates with inplane changes.…”

Section: Plate Constitutive Equationmentioning

confidence: 95%

Transverse vibration analysis of FGM plates with in-plane exponentially non-homogeneous material

Boreyri

Ketabdari

Mohtat³

et al. 2016

IJPR

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In this research, free vibration of rectangular functionally graded (FG) plates with in-plane exponentially non-homogeneous material is investigated. Young's modulus and mass density are assumed to vary between a metal-rich and a ceramic-rich zone along one in-plane direction of the plate. The governing differential equation is derived for the case, and a truncated Taylor series expansion technique is utilized to calculate natural frequencies. A Levy-type solution is obtained for plates having two simply supported edges parallel with the material gradient direction. Results for normalized natural frequency are compared with the 4th order Runge-Kutta method, and when possible with exact solution, showing an accurate agreement. Furthermore, a comprehensive parametric study is carried out to determine the effects of different boundary conditions, aspect ratios, and material variations on the free vibration of FGM plates. Nomenclature

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“…Neves et al [45], Vidoli and Batra [46], Thai and Choi [47] assumed polynomial expansion of w in the thickness coordinate. Trigonometric functions in the thickness coordinate for w assumed by Fekrar et al [48] and Sid Ahmed Houari et al [49]. Hyperbolic functions were considered by Belabed et al [50] and Hebali et al [51].…”

Section: 1mentioning

confidence: 99%

Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution

Jahwari

Naguib

2016

Applied Mathematical Modelling

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A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates

Cited by 74 publications

References 33 publications

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

Transverse vibration analysis of FGM plates with in-plane exponentially non-homogeneous material

Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution

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