Stochastic Vibration Analysis of Functionally Graded Plates with Material Randomness Using Cell-Based Smoothed Discrete Shear Gap Method

Kumaraian, Mohitrajhu Lingan; Rebbagondla, Jayamanideep; Mathew, Tittu Varghese; Natarajan, Sundararajan

doi:10.1142/s0219455419500378

Cited by 14 publications

(2 citation statements)

References 21 publications

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“…Kumaraian et al. 11 analyzed the stochastic natural vibration of P-FG plate employing cell-based smoothed FEM with a discrete shear gap technique. Parida and Mohanty 12 used FEM to carry out the dynamic analysis and the stability analysis of P-FG plate supported on an elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

Ali

Azam

2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

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Section: Introductionmentioning

confidence: 99%

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

Ali

Azam

2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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“…However, a subtle drawback of this approach is that it is limited to small input variance, typically less than 20% [16]. Kumaraian et al [17] employed a cell-based smoothed discrete shear gap method to study the stochastic free vibration characteristics of functionally graded material plates. The input random field was represented by using the Karhunen-Loéve (KL) expansion, and a polynomial chaos expansion was used to represent the stochastic output response.…”

Section: Introductionmentioning

confidence: 99%

A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty

Dsouza

Varghese

Budarapu

et al. 2020

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A non-intrusive approach coupled with non-uniform rational B-splines based isogeometric finite element method is proposed here. The developed methodology was employed to study the stochastic static bending and free vibration characteristics of functionally graded material plates with inhered material randomness. A first order shear deformation theory with an artificial shear correction factor was used for spatial discretization. The output randomness is represented by polynomial chaos expansion. The robustness and accuracy of the framework were demonstrated by comparing the results with Monte Carlo simulations. A systematic parametric study was carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol’ indices. Functionally graded plates made up of Aluminium (Al) and Zirconium Oxide (ZrO2) were considered in all the numerical examples.

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Size-dependent stochastic vibration response of compositionally graded nanoplates with system randomness using nonlocal continuum model with partial support

Kumar

Gupta

2022

Arch Appl Mech

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Stochastic Vibration Analysis of Functionally Graded Plates with Material Randomness Using Cell-Based Smoothed Discrete Shear Gap Method

Cited by 14 publications

References 21 publications

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty

Size-dependent stochastic vibration response of compositionally graded nanoplates with system randomness using nonlocal continuum model with partial support

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