Three-dimensional exact solution for the vibration of functionally graded rectangular plates

By S. Vel, Romesh C. Batra. 2004

614 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/1ecb82dc8d3499033497c5db1ccd44f04dd0bd8d

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory (2008, methodology): “A three-dimensional solution has been presented for free and forced vibrations of simply supported rectangular plates by Vel and Batra [8].”
Higher-order shear and normal deformable theory for functionally graded incompressible linear elastic plates (2007, neutral): “Vel and Batra [15–17] and Lee and Yu [12] have employed expansions (31) and the assumptions of Caijkl and r a being independent of x1 and x2 to solve problems for plates made of functionally graded materials with material properties varying only in the z-direction.”
Buckling analysis of sandwich plates with functionally graded skins using a new quasi‐3D hyperbolic sine shear deformation theory and collocation with radial basis functions (2012, background): “[23] Z. Q. Cheng and R. C. Batra, Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates, J. Sound Vib.”
An efficient shear deformation theory for vibration of functionally graded plates (2013, methodology): “3-D [29] 0.”
Advanced mixed theories for bending analysis of functionally graded plates (2010, background): “Vel and Batra [3] consider the Mori–Tanaka scheme [4] for the variation of the material properties, a three-dimensional solution is proposed for a plate in case of free vibration problems.”
NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter (2012, methodology): “Matsunaga [21] presented analytical solutions for simply supported rectangular FGM plates based on secondorder shear deformation theory, whereas, three dimensional solutions are proposed in [22, 23] for vibrations of simply supported rectangular FGM plates.”
An isogeometric finite element formulation for thermal buckling analysis of functionally graded plates (2013, background): “Vel and Batra [9,10] provided an analytical solution for thermo-mechanical deformations of FGM plates.”
Natural frequencies of sandwich plates with FGM core via variable-kinematic 2-D Ritz models (2013, methodology): “Vel and Batra [4] have proposed an exact three-dimensional solution for free and forced vibrations of rectangular simply-supported FGM plates.”
TRANSIENT THERMOELASTIC DEFORMATIONS OF A THICK FUNCTIONALLY GRADED PLATE (2004, background): “Analytical solutions of 3D thermoelasticity equations for simply supported FG plates subjected to either timeindependent mechanical and=or thermal loads or transient thermal loads with mechanical inertia neglected have been given by Vel and Batra [11, 12]; they [13] have also given an analytical sol”
Analysis of functionally graded plates using an edge-based smoothed finite element method (2011, methodology): “With the advantageous features of FGMs in many practical applications and the limitations of analytical methods [9–11], practical and effective numerical methods have been devised to analyze and simulate the behavior of FGMs in the structural components.”
Stress, vibration and buckling analyses of FGM plates—A state-of-the-art review (2015, methodology): “ity solution provided by Vel and Batra [201] and MLPG formulation provided by Qian et al.”