STRUCTURAL RESPONSE OF FGM PLATE WITH VARIABLE THICKNESS

Abstract

A new class of advanced composite materials like Functionally Graded Materials (FGM) are very demanding in various engineering applications because these materials have significant importance in designing a component for the different functional requirements. The component made of FG materials comprises a graded pattern of material composition in its microstructure. With a Continuous change in their microstructure, FGM offers differences from other conventional composite materials, which fail due to delamination at the interfaces of two different materials at extreme loadings. The concept of functionally graded material was initially developed in the decade of 1980 in Japan. The three different types of gradation laws are applied in this study to tailor the material properties in thickness direction viz; power Law FGM (P-FGM), exponential FGM (E-FGM) and sigmoidal FGM (S-FGM). The focus of this study is free vibration and buckling response analysis of the FGM plate with variable thickness. In particular, the analysis based on a uniform thick plate for free vibration and buckling response of FG material plate is extensive but little literature has been reported for vibration and buckling analysis of FGM plate made of functionally graded materials. The plate with variable thickness has an advantage over the uniform thickness to reduce the weight of structural elements as well as reduce the requirement of the materials. The present study comprises First-order and Higher-order shear deformation plate theories to derive and formulate the free vibration problem. The formulation of buckling analysis is derived by using FSDT. Different boundary conditions are carefully chosen for the plate to be simply supported, clamped-clamped and a combination of both two conditions. Gelarkin’s-Vlasov method is applied to solve the governing equation of motion and to obtain the free vibration and critical buckling load. The present work consists of three major contributions in which, the first part focuses on the free vibration and buckling response analysis of FGM plate supported with various boundary conditions. The FGM plate based on metal-ceramic compositions is proposed for use in the above analysis. The effect of material gradation, span ratio, aspect ratio and taper ratio on the plate are discussed. In the next part of the study, the effect of elastic foundation on vibration and buckling response of FGM plate with variable thickness is studied by using the FSDT. The various types of elastic foundations are applied and investigated the effect of individual foundations or the combinations of different types of foundations. FGM plate resting on Winkler’s, Pasternak and Kerr foundation model is presented with parametric studies. The effect of Winkler’ elastic foundation ii with a linearly, exponential, parabolic and sinusoidal variation on plate vibration is carried out. In addition, the effect of orthotropy in the Pasternak foundation is investigated with different boundary conditions. The vibration response analysis of FGM plate with bi-linear and parabolic variation in thickness, laying on elastic foundation is presented. The last section of the study covers the effect of porosity on free vibration and buckling analysis of tapered FGM plates. During the manufacturing process, the structural element may possess pores. These pores can affect the vibration and buckling results of the plates. The five different types of porosity viz. even, uneven, centrally enhanced, bottom enhanced and top enhanced distribution are assumed to obtain the analysis. Comprehensive studies have been made to predict the behavior of porous FGM plates with or without elastic foundations. The parametric study including volume exponent index, span ratio, taper ratio, foundation stiffness and porosity volume fraction have been done for different porosity models and boundary conditions.