Free vibration analysis of moderately thick functionally graded skew plates

This paper is concerned with the vibration and stability analysis of thick rectangular plates resting on elastic foundation, which is distributed over the particular area of the plate. A twoparameter (Pasternak) model is considered to describe the elastic foundation. The eigenvalue problem in 3-D domain is numerically solved by a combination of the finite element and differential quadrature method (DQM). The energy principle is employed to derive the governing equations in the framework of three-dimensional, linear and small strain theory of elasticity. The in-plane domain of the problem is discretized using two-dimensional finite elements and spatial derivatives of equations in the thickness direction are discretized in strongform using DQM. As a first endeavor, the mixed FE-DQ method has been employed for 3-D buckling and free vibration analysis of rectangular thick plates partially supported by an elastic foundation. The accuracy of obtained results is validated by comparing to the few analytical solutions in the literature.

Section: Introductionmentioning

confidence: 99%

An effective combination of finite element and differential quadrature method for analyzing of plates partially resting on elastic foundation

Dehghan¹,

Nejad²,

Moosaie³

2016

“…Liang et al (2007) extended a new method using the limited finite element method (FEM) for the analysis of the natural frequencies of circular/annular plates of polar orthotropy, stepped and variable thickness. Moreover, free vibration analysis of different geometries and materials have also been studied numericaly or theoretically in recent years (Torabi et al 2013;Nia et al 2014;Vimal et al 2014;Yadav et al 2015;Bhardwaj et al 2015;Samaei et al 2015). In this paper, the effects of different radii ratio, with nine possible combinations of free, clamped and simply supported boundary conditions at the inner and outer edges of plates on the free vibration responses are discussed in detail.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of thin circular and annular plate with general boundary conditions

Khare¹,

Mittal²

2015

This paper presents a numerical analysis of free vibration of thin circular and annular plate using finite element method. The first five natural frequencies are presented for uniform annular plates of various inner-to-outer radius ratios, with nine possible combinations of free, clamped and simply supported boundary conditions at the inner and outer edges of plates. The accuracy of the method is established by comparing the results available in the literature. Results show that natural frequency parameter increases as the inner-to-outer radius ratio increases except in case of free boundary condition, for which it decreases with the inner-toouter radius ratio. This result provides benchmark values that can be used to validate result obtained by other approximate approaches such as finite difference method, differential quadrature method and boundary element method.

“…In order to design and analysis of structures made of FGM, various simulation methods including numerical and analytical approaches have been proposed so far (Aihara et al, 1998;Salavati et al, 2014;Vimal et al, 2014). Most of the studies have focused on assessing thermal stresses and also the deformation of the domain, such as the use of FGMs for controlling of thermal deformations (Wetherhold et al, 1996), the investigation of thermal stresses and deformation in shells made of FGM under thermal loads (Takezono et al, 1996;Zhang et al, 1994).…”

Section: Introductionmentioning

confidence: 99%

Thermomechanical transient analysis of a thick-hollow FGM cylinder

Takabi

2016

This paper presents an analytical and a numerical thermomechanical investigation of a thickwalled cylinder made of the functionally graded materials (FGMs). The hollow cylinder is subjected to a pressure and a thermal load and the properties of this material are varying across the thickness from the inner face that is a ceramic to the outer one which is a metal. After validating the current results by the analytical results, the thermomechanical behavior of the cylinder in the transient condition is investigated and the hoop and radial stresses and also temperature distribution are reported. The results reveal that the use of FG material causes a decrease in the stress; thus, it significantly improves thermomechanical behavior of the domain, thanks to using FG materials.