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
采用级数展开形式的Melnikov函数解决高余维分岔问题。通过研究一类5次项和3次项共存,具有异宿轨的Duffing-Van der Pol方程的余维4全局分岔问题,得到了该系统的分岔方程及全局拓扑结构,说明了该方法的可行性。。研究结果表明,该系统有单个极限环、单个异宿轨、异宿轨和极限环共存、两个极限环共存等情况。最后通过数值模拟验正了理论分析结果的正确性。
