Prediction of dynamic behaviour of FGM shells under arbitrary boundary conditions R. Ansari, M. Darvizeh * Department of Mechanical Engineering, Guilan University, P.O. Box 3756, Rasht, Iran Available online 4 November 2007 Abstract In this study, a general analytical approach is presented to investigate vibrational behavior of functionally graded shells. Theoretical formulations, based on first order shear deformation shell theory, take into consideration transverse shear deformation and rotary inertia effects. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stoke’s transformation. Material properties are assumed to be temperature-dependent and graded in the thickness direction according to different volume fraction functions. These functions are assumed to have power–law, sigmoid and exponential distributions. A FGM cylindrical shell made up of a mixture of ceramic and metal is considered. The Influence of some commonly used boundary conditions, the effect of variations of volume fractions and shell geometrical parameters on the vibration characteristics are studied. The results obtained for a number of particular cases show good agreement with those available in the literature. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Vibration; FGM shells; Exact method; Arbitrary boundary conditions 1. Introduction The idea of the construction of functionally graded materials (FGMs) was first introduced in 1984 by a group of Japanese materials scientists [1,2]. During the past two decades, FGMs have experienced a noteworthy increase in terms of research and development programs. World wide distribution and dissemination of the results through publications, international meetings and exchange pro- grams testifies to this increasing growth. They have many gained applications in rocket engine components, space plan body, nuclear reactor components, first wall of fusion reactor, engine components, turbine blades, hip implant and other engineering and technological applications. A detailed discussion on their design, processing and applica- tions can be found in [3]. FGMs are also promising candi- dates for future intelligent composites [4]. They are multifunctional composite materials, mechanical properties of which vary smoothly and continuously from one side to the other. This is achieved by a continuous change in com- position of the constituent materials. The most well-known FGM is compositionally graded from a ceramic to a metal to incorporate such diverse prop- erties as heat, wear and oxidation resistance of ceramics with the toughness, strength, machinability and bending capability of metals. Vibration of shells is a well-established branch of research in structural dynamics. Cylindrical shells also have vast range of applications in engineering and technology. A good overview of preliminary work has been given by Leis- sa [5]. There are also some good reviews on vibration of composite shell, which can be found in the literature [6–9]. Loy et al. [10] analyse frequency spectrum of FGM cylindri- cal shells composed of stainless steel and nickel with simply supported boundary conditions. It is found that frequency characteristics are similar to those as observed for homoge- neous isotropic shells and are altered by the constituent vol- ume fractions and the configurations of the constituent material. Pradhan et al. [11] study vibration characteristics of a FGM cylindrical shell made up of stainless steel and zirconia for various boundary conditions. This analysis is 0263-8223/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2007.10.037 * Corresponding author. Tel./fax: +98 131 6690276. E-mail address: Darvizeh@Guilan.ac.ir (M. Darvizeh). www.elsevier.com/locate/compstruct Available online at www.sciencedirect.com Composite Structures 85 (2008) 284–292