Structural Engineering and Mechanics, Vol. 50, No. 1 (2014) 53-71 DOI: http://dx.doi.org/10.12989/sem.2014.50.1.053 53 Copyright © 2014 Techno-Press, Ltd. http://www.techno-press.org/?journal=sem&subpage=8 ISSN: 1225-4568 (Print), 1598-6217 (Online) Dynamic behavior of a functionally graded plate resting on Winkler elastic foundation and in contact with fluid Ali A. Shafiee 1 , Farhang Daneshmand 2a , Ehsan Askari 3b and Mojtaba Mahzoon 1c 1 Faculty of Mechanical Engineering, Shiraz University, Shiraz 71348-51154, Iran 2 Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street W., Montreal, Québec H3A 2K6, Canada 3 Australian School of Advanced Medicine, Macquarie University, Sydney, Australia (Received April 5, 2013, Revised July 29, 2013, Accepted February 1, 2014) Abstract. A semi-analytical method is developed to consider free vibrations of a functionally graded elastic plate resting on Winkler elastic foundation and in contact with a quiescent fluid. Material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The fluid is considered to be incompressible and inviscid. In the analysis, the effect of an in-plane force in the plate due to the weight of the fluid is taken into account. By satisfying the compatibility conditions along the interface of fluid and plate, the fluid-structure interaction is taken into account and natural frequencies and mode shapes of the coupled system are acquired by employing energy methods. The results obtained from the present approach are verified by those from a finite element analysis. Besides, the effects of volume fractions of functionally graded materials, Winkler foundation stiffness and in-plane forces on the dynamic of plate are elucidated. Keywords: dynamic behavior; fluid-structure interaction; functionally graded material; Winkler elastic foundation; in-plane forces 1. Introduction Free vibration analysis of circular plates made of composite materials such as functionally graded materials (FGM) is of interest in practical applications. Functionally graded materials have appeal properties of high strength, minimum weight and ultra-high temperature resistance and were first introduced by a group of Japanese scientists (Shen 2009). A typical FGM, is an inhomogeneous composite made of different phases of material constituents usually metal and ceramic with a high bending-stretching coupling effect was reported by Shen (2009). By gradually varying the volume fraction of constituent materials, the material properties of functionally graded materials vary smoothly and change continuously between different layers. This advantage eliminates interface problems of composite materials and the stress distribution becomes smooth. Corresponding author, Ph.D. Student, E-mail: aa.shafiee@me.iut.ac.ir, aa.shafiee@yahoo.com a Professor, E-mail: farhang.daneshmand@mcgill.ca b Ph.D. Student, E-mail: ehsanaskary@gmail.com c Professor, E-mail: mahzoon@shirazu.ac.ir