This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitation...This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy＇s third-order shear deformation plate theory and the model of the yon Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton＇s principle. Then, using the second-order Galerkin dis- cretization, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1：1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The theoretic results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation, which also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.展开更多
Long-term prediction of chaotic time series is very difficult,for the Chaos restricts predictability.in this paper a new method is studied to model and predict chaotic time series based on minimax probability machine ...Long-term prediction of chaotic time series is very difficult,for the Chaos restricts predictability.in this paper a new method is studied to model and predict chaotic time series based on minimax probability machine regression （MPMR）. Since the positive global Lyapunov exponents lead the errors to increase exponentially in modelling the chaotic time series, a weighted term is introduced to compensate a cost function. Using mean square error （MSE） and absolute error （AE） as a criterion, simulation results show that the proposed method is more effective and accurate for multistep prediction. It can identify the system characteristics quite well and provide a new way to make long-term predictions of the chaotic time series.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10732020 and 11072008)the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)
文摘This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy＇s third-order shear deformation plate theory and the model of the yon Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton＇s principle. Then, using the second-order Galerkin dis- cretization, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1：1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The theoretic results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation, which also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.
基金Project supported by the National Natural Science Foundation of China （Grant No 60602034） and the Natural Science Foundation of Jiangxi Province, China （Grant No 0611031）.
文摘Long-term prediction of chaotic time series is very difficult,for the Chaos restricts predictability.in this paper a new method is studied to model and predict chaotic time series based on minimax probability machine regression （MPMR）. Since the positive global Lyapunov exponents lead the errors to increase exponentially in modelling the chaotic time series, a weighted term is introduced to compensate a cost function. Using mean square error （MSE） and absolute error （AE） as a criterion, simulation results show that the proposed method is more effective and accurate for multistep prediction. It can identify the system characteristics quite well and provide a new way to make long-term predictions of the chaotic time series.
