Complex dynamics of the simply-supported functionally graded(FG)rectangular plates with thermal load is investigated.Based on Reddy's third-order shear deformation theory and the von Karman nonlinear strain-displacement relations,ordinary differential equations(ODEs)of the plate's transversal oscillation are derived by using Hamilton's principle and Galerkin's approach.Solutions'classification of the equations in 1:2 internal resonance is analyzed.Particular results of a simplysupported aluminum-alumina rectangular FG plate are given.Effects of temperature and volume fraction on the responses' stabilities are discussed.
DING Ran 1 &WU ZhiQiang 1,2 1 Department of Mechanics,Tianjin University,Tianjin 300072,China
If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.
