Issue 50

H. Saidi et alii, Frattura ed Integrità Strutturale, 50 (2019) 286-299; DOI: 10.3221/IGF-ESIS.50.24 286 Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al 2 O 3 ) embedded in an elastic medium Saidi Hayat, Sahla Meriem Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Laboratory of Materials and Hydrology (LMH), Algeria. hayatsaidi2019@yahoo.fr, meriemsahla@gmail.com A BSTRACT 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. K EYWORDS . Shear deformation theory; Vibration; Functionally graded plate; Porosity; Frequency. Citation: Saidi, H., Sahla, M., Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al 2 O 3 ) embedded in an elastic medium, Frattura ed Integrità Strutturale, 5 0 (2019) 286-299. Received: 2 0.07.2019 Accepted: 19.08.2019 Published: 01.10.2019 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION unctionally graded materials (FGMs) are a type of heterogeneous composite materials that exhibits a continuous variation of mechanical properties from one point to another. The concept of functionally graded material was first considered in Japan in 1984 during a space plane project. Such kind material is produced by mixing two or more materials by a graded distribution of the volume fractions of the constituents [1], the FGM is thus suitable for diverse applications, such as thermal coatings of barrier for ceramic engines, electrical devices, energy transformation, biomedical engineering, optics, etc [2-11]. F