Free Vibration Analysis of Functionally Graded Skew Plate in Thermal Environment Using Higher Order Theory

Parida, S.; Mohanty, Sukesh Chandra

doi:10.1142/s1758825118500072

Cited by 14 publications

(4 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Four noded tetragonal plate element with eleven degrees of freedom is used. Then Smita [18] used a higher order shear deformation theory to develop finite element model of a skew functionally graded plate in thermal environment with a free vibration effect. Eight noded isoparametric element with seven degrees of freedom is considered for this model and showed that frequency of plate decrease with increase in volume fraction index, aspect ratio and side thickness ratio.…”

Section: B Numerical Methods 1) Static Analysis A)mentioning

confidence: 99%

Static and Vibration Analysis of FGM Plates: A Critical Review

Deshpande¹,

More²,

Parekar³

2023

IJRASET

View full text Add to dashboard Cite

Recently a new material has been emerged with variation of material properties particularly across the thickness. Such class of materials is called functionally graded materials. The concept of functionally graded material was proposed in 1984 by materials scientists as a means of preparing thermal barrier materials. Since then functionally graded materials are being increasingly used in the aeronautical and aerospace industry as well as in other fields of modern technology. This paper presents a comprehensive review of the various methods used to study the static and dynamic behaviour of functionally graded material plates. Both analytical and numerical methods are considered. The effect of variation of material properties through the thickness, type of load case, boundary conditions, edge ratio and side-to thickness ratio on the behaviour of functionally graded material plates are discussed. The main objective of this paper is to serve the interests of researchers and engineers already involved in the analysis and design of functionally graded material structures

show abstract

Section: B Numerical Methods 1) Static Analysis A)mentioning

confidence: 99%

Static and Vibration Analysis of FGM Plates: A Critical Review

Deshpande¹,

More²,

Parekar³

2023

IJRASET

View full text Add to dashboard Cite

show abstract

“…In recent decades, scientists have focused their efforts on studying the structural behavior of the perfect [8][9][10][11][12][13][14] and the porous functionally graded (FG) structures, [15][16][17][18][19][20][21][22][23][24][25][26] to name a few. Further, several authors have described the kinematics of the FG plates using various shear deformation theories to achieve the required exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials

Shivaramaiah

Kattimani

Shariati

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

This article investigates the influence of porosity distributions on the nonlinear behavior of two-directional functionally graded porous plates (TDFGPP) made from four distinct materials for the first time. A simple and effectual approach is established based on the improved generalized shear deformation plate theory (GSDPT) and von Karman’s assumptions. The GSDPT incorporates transverse shear strains with a higher order polynomial to avoid shear locking. The TDFGPP constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both transverse and longitudinal directions. The governing equations are obtained using a nonlinear finite element approach in conjunction with Hamilton’s principle. Then, the direct iterative and Newmark’s methods are incorporated to accomplish the numerical results. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, thickness ratio, and aspect ratio for different support conditions provides a thorough insight into the linear and nonlinear responses of the porous plate. In addition, this study emphasizes the influence of the volume fraction gradation profiles with four different materials on the linear frequency, nonlinear frequency, and deflections of the TDFGPP. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in specified directions with appropriate materials. Hence, two-directional functionally graded materials panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.

show abstract

“…Analytical solutions based on plate theories and the three-dimensional elasticity theory have been proposed for the vibration of rectangular plates with two simply supported opposite edges and four simply supported faces, respectively [5][6][7][8][9][10][11]. Moreover, solutions for the vibration of rectangular plates under different boundary conditions have been reported using various numerical approaches, such as the Ritz method [12][13][14], differential quadrature method [15][16][17], mesh-free method [18][19][20], and finite-element method (FEM) [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method

Huang

Lee

et al. 2021

Materials

View full text Add to dashboard Cite

In this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of the three-dimensional elasticity theory. Sets of crack functions are proposed to enrich a set of polynomial functions for constructing admissible functions that represent displacement and slope discontinuities across a crack and appropriate stress singularity behaviors near a crack front. These crack functions enhance the Ritz method in terms of its ability to identify a crack in a plate. Convergence studies of frequencies and comparisons with published results were conducted to demonstrate the correctness and accuracy of the proposed solutions. The proposed approach was also employed for accurately determining the frequencies of cantilevered and simply supported side-cracked rectangular FGM plates and cantilevered internally cracked skewed rhombic FGM plates under uniaxial normal traction. Moreover, the effects of the volume fractions of the FGM constituents, crack configurations, and traction magnitudes on the vibration frequencies of cracked FGM plates were investigated.

show abstract

Free Vibration Analysis of Functionally Graded Skew Plate in Thermal Environment Using Higher Order Theory

Cited by 14 publications

References 33 publications

Static and Vibration Analysis of FGM Plates: A Critical Review

Static and Vibration Analysis of FGM Plates: A Critical Review

Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials

Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method

Contact Info

Product

Resources

About