Nonlinear Dynamic Response of Functionally Graded Rectangular Plates under Different Internal Resonances. (2010)

• Record Type: Journal Article
• Authors: Hao, Y. X.; Zhang, W.; Ji, X. L.
• Other Names: Cattani Carlo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2010(2010)
• Publication Date: 2010
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2010/738648
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : The nonlinear dynamic response of functionally graded rectangular plates under combined transverse and in-plane excitations is investigated under the conditions of 1 : 1, 1 : 2 and 1 : 3 internal resonance. The material properties are assumed to be temperature-dependent and vary along the thickness direction. The thermal effect due to one-dimensional temperature gradient is included in the analysis. The governing equations of motion for FGM rectangular plates are derived by using Reddy's third-order plate theory and Hamilton's principle. Galerkin's approach is utilized to reduce the governing differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms, which are then solved numerically by using 4th-order Runge-Kutta algorithm. The effects of in-plane excitations on the internal resonance relationship and nonlinear dynamic response of FGM plates are studied.