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Free vibration of functionally graded sandwich plates with stiffeners based on the third-order shear deformation theory

In this paper, the free vibration of functionally sandwich grades plates with stiffeners is investigated by using the finite element method. The material properties are assumed to be graded in the thickness direction by a power-law distribution. Based on the third-order shear deformation theory, the governing equations of motion are derived from the Hamilton’s principle. | Vietnam Journal of Mechanics, VAST, Vol. 38, No. 2 (2016), pp. 103 – 122 DOI:10.15625/0866-7136/38/2/6730 FREE VIBRATION OF FUNCTIONALLY GRADED SANDWICH PLATES WITH STIFFENERS BASED ON THE THIRD-ORDER SHEAR DEFORMATION THEORY Pham Tien Dat, Do Van Thom∗ , Doan Trac Luat Le Quy Don Technical University, Hanoi, Vietnam ∗ E-mail: promotion6699@gmail.com Received August 11, 2015 Abstract. In this paper, the free vibration of functionally sandwich grades plates with stiffeners is investigated by using the finite element method. The material properties are assumed to be graded in the thickness direction by a power-law distribution. Based on the third-order shear deformation theory, the governing equations of motion are derived from the Hamilton’s principle. A parametric study is carried out to highlight the effect of material distribution, stiffener parameters on the free vibration characteristics of the plates. Keywords: Stiffened plate, sandwich, vibration, functionally graded materials. 1. INTRODUCTION Functionally graded materials (FGMs) made of two constituents, mainly metal and ceramic are widely used. The composition is varied continuously along certain directions according to volume fration from a ceramic-rich surface to a metal-rich surface. Many researchers in past have worked upon to understand behavior of functionally graded plates. Reddy [1] carried out nonliear finite element static and dynamic analyses of functionally graded plates using Navier’s solution, Vel and Batra [2] presented threedimendional exact solutions for free and forced vibrations of simply supported functionally graded rectangular plates, Tinh Quoc Bui et al [3] used finite element method to study static bending and vibration of heated FG plates. Dao Huy Bich et al [4, 5], Nguyen Dinh Duc et al [6, 7] used analytical method to study vibration, nonlinear respones of eccentrically stiffened functionally graded cylindrical panels [4, 5] and nonlinear postbucking of FGM plate and .