In the paper the nonlinear dynamic equation of a harmonically forced elliptic plate is derived, with the effects of large deflection of plate and thermoelasticity taken into account. The Melnikov function method is us...In the paper the nonlinear dynamic equation of a harmonically forced elliptic plate is derived, with the effects of large deflection of plate and thermoelasticity taken into account. The Melnikov function method is used to give the critical condition for chaotic motion. A demonstrative example is discussed through the Poincaré mapping, phase portrait and time history. Finally the path to chaotic motion is also discussed. Through the theoretical analysis and numerical computation some beneficial conclusions are obtained.展开更多
This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different ...This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.展开更多
基金the National Natural Science Foundation of Chinathe Natural Scie
文摘In the paper the nonlinear dynamic equation of a harmonically forced elliptic plate is derived, with the effects of large deflection of plate and thermoelasticity taken into account. The Melnikov function method is used to give the critical condition for chaotic motion. A demonstrative example is discussed through the Poincaré mapping, phase portrait and time history. Finally the path to chaotic motion is also discussed. Through the theoretical analysis and numerical computation some beneficial conclusions are obtained.
文摘This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.
