Dynamic analysis of a functionally graded thick truncated cone with finite length
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Dynamic analysis of a functionally graded thick truncated cone with finite length Kamran Asemi • Manouchehr Salehi Mehdi Akhlaghi
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Received: 29 November 2010 / Accepted: 23 December 2010 / Published online: 6 January 2011 Ó Springer Science+Business Media, B.V. 2011
Abstract In this article dynamic analysis of a functionally graded thick truncated cone with finite length under axisymmetric internal impact loading is studied. The cone is made of a combined ceramic– metal material and the material composition varying continuously along its thickness according to the power law distribution. Finite Element Method based on Rayleigh–Ritz energy formulation and Newmark direct integration methods are applied to find the responses in time and space domain. The time histories of displacements, stresses, wave propagation in two directions and natural frequencies for various values of volume fraction exponent and semi-vertex angle of the cone for a cone with clamped end conditions have been studied. The results obtained in the present paper are compared with the result of an infinite FG thick hollow cylinder.
K. Asemi M. Akhlaghi Mechanical Engineering Department, Amirkabir University of Technology, 1591634311 Tehran, Iran e-mail: [email protected] M. Akhlaghi e-mail: [email protected] M. Salehi (&) Mechanical Engineering Department and Concrete Technology and Durability Research Centre, Amirkabir University of Technology, Hafez Ave., 1591634311 Tehran, Iran e-mail: [email protected]
Keywords Thick truncated cone FGM Finite element method Elasticity Dynamical analysis
1 Introduction Functionally graded materials (FGMs) are important nonhomogeneous materials designed to maximize strengths and integrities of different engineering structures. The concept of FGMs was first introduced in 1984 by a group of materials scientists in Japan (Koizumi 1993; Yamanouchi et al. 1990). The advantage of using FGMs is their superior resistance to interfacial failure. By increasing the use of FGMs in structures under the dynamic loading, the study of FG thick truncated cone under the time dependent mechanical loading and also the condition of stress wave propagation in it has became very essential. Some research has been done related to response of FG structures under dynamic loads are limited in number. Bruck (2000) studied a one-dimensional model for designing FGMs to manage stress waves. Wave propagation in FGMs and layered materials using space–time discontinuous Galerkin method is investigated by Aksoy and Senocak (2009). Zhang and Batra (2007) used the modified smoothed particle hydrodynamics (MSPH) method to study the propagation of elastic waves in FGMs. Berezovski et al. (2001) studied the propagation of stress waves in FGMs numerically by means of the composite
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wave-propagation algorithm. One-dimensional wave propagation in a functionally graded elastic slab is investigated by Chiu and Erdogan (1999). Santare et al. (2003) used finite elements with graded properties to simulate elastic wave propagati
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