Effect of Boundary Conditions and Taper Patterns on Geometrically Nonlinear Frequency Response of Axially Graded Beams on Elastic Foundation

Introduction

In the recent years it has emerged that pure homogeneous materials, due to certain insufficiency of their properties, are limited in terms of applications in the more technologically advanced domains, such as aerospace industries. New class of advanced materials, namely, composites and functionally graded materials (FGM) have come to the forefront in case of these applications. FGMs are characterized by continuous variation in properties along the spatial directions. Two or more constituent materials are mixed functionally and continuously to obtain FGMs (Koizumi, 1997). These materials provide unique thermo-mechanical properties which are different from the parent materials. It has excellent thermal resistance, low density and high toughness. FGM is also free from interface problems which are severe in case of laminated composite (Suresh and Mortensen, 1998; Nguyen et al., 2013). Due to excellent properties and increasing demand in various areas, a vast body of researchers is devoted to explore their behavior in different ways.

FG beams can be graded in thickness direction, axial direction and simultaneously along the two directions as well. The thickness directional gradations are most common and have been explored quite comprehensively over the last two decades. Various methodologies like analytical method, semi-analytical method and numerical methods are employed to study the static, dynamic and buckling behavior (Kodali et al., 2008; Yaghoobi and Fereidoon, 2010; Hemmatnezhad et al., 2013; Su et al., 2013; Pradhan and Chakraverty, 2014; Ebrahimi and Salari, 2015; Chen et al., 2015; Jin and Wang, 2015; Jia et al, 2015; Ebrahimi and Zia, 2015) of beams which are graded in the thickness direction. On the other hand, recent years has seen quite a few research works on axially graded beams.