Abstract
This paper presents the stability and bifurcation analysis of a simply-supported functionally graded materials (FGMs) rectangular plate subject to the transversal and in-plane excitations. A two-degree-of-freedom nonlinear system of the FGM plate is obtained via the Hamilton’s principle and the Galerkin approach. The case of primary parametric resonance and 1:2 internal resonance is considered. The asymptotic perturbation method is utilized to obtain four-dimensional nonlinear averaged equation. With the aid of Matlab and normal form theory, the various types of dynamical behavior in the neighborhood of a kind of degenerated equilibrium point are investigated. It was found that static bifurcation and Hopf bifurcation exist for the FGM rectangular plate under certain conditions.
Highlights
The functionally graded materials (FGMs) are a kind of microscopically composite materials
Based on the theoretical model for the nonlinear oscillations of the FGM plate subjected to the transversal and in-plane excitations, the normal form theory and bifurcation theory are applied to discuss the local dynamical behaviors of the FGMs rectangular plate
We investigate the case of 1:2 internal resonance and primary parametric resonance for the FGMs rectangular plate, Z1
Summary
The functionally graded materials (FGMs) are a kind of microscopically composite materials Their properties can be spatially varied to achieve the desired structural, electrical functions, or thermal. Gunes and Reddy [7] investigated the geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads. Hao [8] investigated the nonlinear dynamics of a -supported FGM rectangular plate with the parametric and forcing excitations. This paper focuses on research on the bifurcation and stability analysis of the FGM rectangular plate deflection with variation of material properties. Based on the theoretical model for the nonlinear oscillations of the FGM plate subjected to the transversal and in-plane excitations, the normal form theory and bifurcation theory are applied to discuss the local dynamical behaviors of the FGMs rectangular plate
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