Abstract
In this scientific work, a new shear deformation theory for free vibration analysis of simply supported rectangular functionally graded plate embedded in an elastic medium is presented. Due to technical problems during the fabrication, porosities can be created in side FGM plate which may lead to reduction in strength of materials. In this investigation the FGM plate are assumed to have a new distribution of porosities according to the thickness of the plate. The elastic medium is modeled as Winkler-Pasternak two parameter models to express the interaction between the FGM plate and elastic foundation. The four unknown shear deformation theory is employed to deduce the equations of motion. The Hamilton’s principle is used to derive the governing equations of motion. The accuracy of this theory is verified by compared the developed results with those obtained using others plate theory. Some examples are performed to demonstrate the effect of changing gradient material, elastic parameters, porosity index, and length to thickness ratios on the fundamental frequency of functionally graded plate.
Highlights
Graded materials (FGMs) are a type of heterogeneous composite materials that exhibits a continuous variation of mechanical properties from one point to another
In this investigation the Functionally graded materials (FGMs) plate are assumed to have a new distribution of porosity according to the thickness of the plate
The four unknown shear deformation theory is employed to deduce the equations of motion from Hamilton’s principle
Summary
Graded materials (FGMs) are a type of heterogeneous composite materials that exhibits a continuous variation of mechanical properties from one point to another. For FG thick and moderately thick plates; the first-order shear deformation theory (FSDT) has been employed [24,25,26,27]. The purpose of this work to propose a new higher-order shears deformation theory for free vibration response of FG plates with porosity embedded in elastic medium. In this investigation the FGM plate are assumed to have a new distribution of porosity according to the thickness of the plate. Some examples are performed to demonstrate the effect of changing gradient material, elastic parameters, porosity index, and length to thickness ratios on the fundamental frequency of functionally graded plate
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