Meccanica (2012) 47:1441–1453 DOI 10.1007/s11012-011-9527-9 Dynamic analysis of thick short length FGM cylinders Kamran Asemi · Mehdi Akhlaghi · Manouchehr Salehi Received: 8 August 2010 / Accepted: 10 November 2011 / Published online: 8 December 2011 © Springer Science+Business Media B.V. 2011 Abstract In this paper a thick short length hol- low cylinder made of functionally graded materials (FGMs) under internal impact loading is considered. The inner surface of the cylinder is pure ceramic, the outer surface is pure metal, and the material compo- sition varies continuously along its thickness. Finite Element Method based on Rayleigh-Ritz energy for- mulation has been applied to study the propagation of elastic waves in FG thick hollow cylinders. The New- mark direct integration method is applied to solve the time dependent equations. The time histories of dis- placements, stresses, wave propagation in two direc- tions and velocities of radial stress wave propagation for various values of volume fraction exponent have been investigated. Also by using fast Fourier trans- form, the first natural frequencies for FG cylinders with simply-simply and clamped-clamped ends con- ditions are illustrated. The model has been compared with result of a plane strain FG thick hollow cylinder which is subjected to an internal impact loading, and it shows very good agreement. K. Asemi · M. Akhlaghi ( ) Mechanical Engineering Department, Amirkabir University of Technology, Tehran, 1591634311, Iran e-mail: makhlagi@aut.ac.ir M. Salehi Mechanical Engineering Department and Concrete Technology and Durability Research Centre, Amirkabir University of Technology, Tehran, 1591634311, Iran Keywords Functionally graded materials · Short length cylinder · 2D-wave propagation · Internal impact loading 1 Introduction Functionally Graded Materials (FGMs) are composite materials, microscopically inhomogeneous, in which the mechanical properties vary smoothly and continu- ously from one surface to the other. The applications of FGMs in engineering designs were first started by Lee et al. [1]. These materials are increasingly used in various applications to maximize strengths and in- tegrities of different engineering structures. Therefore, analysis of FG thick hollow cylinder under impact loading is necessary for practical purposes in order to optimize their resistance to failure. However investiga- tions into wave propagation and dynamic analysis for FG structures by using numerical and analytical meth- ods are presented in [1–16]. Hosseini and Abolbashari [17] proposed an ana- lytical method for the dynamic response analysis of infinite functionally graded thick hollow cylinders un- der impact loading. Some works can be found in the literature on numerical determination of wave prop- agation in FG cylinders. Houillon et al. [18] studied the characterization of propagation constants of re- alistic thin-walled structures with any cross-section. They proposed a propagative approach using finite