Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates

Jha, Dhirendra Kumar; Kant, Tarun; Singh, Raj Kumar

doi:10.1016/j.nucengdes.2012.05.001

Cited by 42 publications

(20 citation statements)

References 12 publications

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“…The comparison of the dimensionless fundamental frequencies of present results shows good agreement with analytical solutions of Thai H. T., & Kim S. E. [12] based on simple higher-order theory, and finite element results of Thai H. T., & Choi D.H. [9] based on four unknowns shear deformation theories. Example 2.…”

Section: Numerical Resultssupporting

confidence: 79%

Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite element method

Quoc

Tú

Long³

2016

JST

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In this paper, a new eight-unknown shear deformation theory is developed for bending and free vibration analysis of functionally graded plates by finite element method. The theory based on full twelve-unknown higher order shear deformation theory, simultaneously satisfy zeros transverse stresses at top and bottom surface of FG plates. A four-node rectangular element with sixteen degrees of freedom per node is used. Poisson's ratios, Young's moduli and material densities vary continuously in thickness direction according to the volume fraction of constituents which is modeled as power law functions. Results are verified with available results in the literature. Parametric studies are performed for different power law index, side-tothickness ratios.

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Section: Numerical Resultssupporting

confidence: 79%

Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite element method

Quoc

Tú

Long³

2016

JST

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“…Kim and Reddy (2013) also used acouple of stress-based third-ordertheory with elevenunknowns to analyze the bending, vibration and buckling behaviors of FG plates by analytical method. Based on the higher-order refined theories, Jha et al (2012) presented analytical solutions for free vibration analysis of simply supported rectangular functionally graded plates. This HSDT introduces twelve displacement unknowns, and correctly describes the quadratic distribution of transverse normal strain across the thickness although the values at the top and bottom are non-zero.…”

Section: Latin American Journal Of Solids and Structures 13 (2016) 45mentioning

confidence: 99%

“…The displacement components u (x,y,z), v(x,y,z) and w(x,y,z) at any point in the plate can be expanded in Taylor's series in terms of the thickness coordinate as (Jha -2012) …”

Section: Kinematicsmentioning

confidence: 99%

Vibration and Buckling Analysis of Functionally Graded Plates Using New Eight-Unknown Higher Order Shear Deformation Theory

Thinh

Tú

Quoc

et al. 2016

Lat. Am. j. solids struct.

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In this paper a new eight-unknown higher order shear deformation theory is proposed to study the buckling and free vibration of functionally graded (FG) material plates. The theory bases on full twelve-unknown higher order shear deformation theory, simultaneously satisfies zero transverse shear stress at the top and bottom surfaces of FG plates. Equations of motion are derived from Hamilton's principle. The critical buckling load and the vibration natural frequency are analyzed. The accuracy of present analytical solution is confirmed by comparing the present results with those available in existing literature. The effect of power law index of functionally graded material, side-to-thickness ratio on buckling and free vibration responses of FG plates is investigated.

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“…Liu et al (2010) have analysed the free vibration of FGM rectangular plates with inplane material inhomogeneity using Fourier series expansion and a particular integration technique on the basis of classical plate theory. Navier solution method has been used by Jha et al (2012) to analyse the free vibration of FG rectangular plates employing higher order shear and normal deformation theory. The vibration behaviour of rectangular FG plates with non-ideal boundary conditions has been studied by Najafizadeh et al (2012) using Levy method and Lindstedt-Poincare perturbation technique.…”

Section: Introductionmentioning

confidence: 99%

Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation

Lal

Ahlawat

2015

Lat. Am. j. solids struct.

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An investigation on the effect of uniform tensile in-plane force on the radially symmetric vibratory characteristics of functionally graded circular plates of linearly varying thickness along radial direction and resting on a Winkler foundation has been carried out on the basis of classical plate theory. The non-homogeneous mechanical properties of the plate are assumed to be graded through the thickness and described by a power function of the thickness coordinate. The governing differential equation for such a plate model has been obtained using Hamilton's principle. The differential transform method has been employed to obtain the frequency equations for simply supported and clamped boundary conditions. The effect of various parameters like volume fraction index, taper parameter, foundation parameter and the in-plane force parameter has been analysed on the first three natural frequencies of vibration. By allowing the frequency to approach zero, the critical buckling loads for both the plates have been computed. Threedimensional mode shapes for specified plates have been plotted. Comparison with existing results has been made.

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Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates

Cited by 42 publications

References 12 publications

Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite element method

Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite element method

Vibration and Buckling Analysis of Functionally Graded Plates Using New Eight-Unknown Higher Order Shear Deformation Theory

Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation

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