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
In this paper,determination of the characteristics of futures market in China is presented by the method of the phase-randomized surrogate data.There is a significant difference in the obtained critical values when this method is used for random timeseries and for nonlinear chaotic timeseries.The singular value decomposition is used to reduce noise in the chaotic timeseries.The phase space of chaotic timeseries is decomposed into range space and null noise space.The original chaotic timeseries in range space is restructured.The method of strong disturbance based on the improved general constrained randomized method is further adopted to re-deternination.With the calculated results,an analysis on the trend of futures market of commodity is made in this paper.The results indicate that China's futures market of commodity is a complicated nonlinear system with obvious nonlinear chaotic characteristic.
