Abstract
In this research study, free vibration of homogeneous and functionally graded skew plates resting on Winkler-Pasternak elastic foundation is investigated. The elastic foundation is assumed to be a combination of Winkler and Pasternak elastic support with linearly or parabolically variable stiffness coefficients along the directions. Plate skewness is obtained by using a transformation from Cartesian coordinate to oblique coordinate system. The energy of the functionally graded skew plate and the elastic foundation is derived, and the natural frequency of the plate is calculated by the Rayleigh-Ritz method. The results are compared with available results in the literature, showing an excellent agreement. Furthermore, a parametric study is carried out to thoroughly investigate the effects of different boundary conditions, skew angles, inhomogeneity factors, and variable elastic foundation stiffness on the free vibration of skew plates.
Highlights
Composite materials are manufactured based on different industrial needs to optimize the response to external loads and reduce the residual and thermal stresses at desired regions of structures
Free vibration of thin rectangular plates resting on Winkler-Pasternak elastic foundation was studied by Civalek using differential quadrature method in 2007 [6]
Atmane et al [8] used a new shear deformation theory for Functionally graded materials (FGMs) rectangular plates resting on elastic Winkler-Pasternak foundation, in 2010
Summary
Composite materials are manufactured based on different industrial needs to optimize the response to external loads and reduce the residual and thermal stresses at desired regions of structures. Graded materials (FGMs) were first introduced by the Japanese researchers in 1984 [1] They are relatively new composites with spatially continuous variation of mechanical properties along one or more directions. Free vibration of thin rectangular plates resting on Winkler-Pasternak elastic foundation was studied by Civalek using differential quadrature method in 2007 [6]. Atmane et al [8] used a new shear deformation theory for FGM rectangular plates resting on elastic Winkler-Pasternak foundation, in 2010. A number of researches have been performed to thoroughly investigate the vibration characteristics of such structures According to this literature survey and best knowledge of the authors, not a single research has been carried out on free vibration of skew homogeneous or FGM plates on Winkler-Pasternak foundation, with variable foundation characteristics which are more practical in industry.
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