The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
We discuss two classes of solutions to a novel Casimir equation associated with the Ito system,a couplednonlinear wave equation.Both travelling wave solutions and separable self-similar solutions are discussed.In a nu...We discuss two classes of solutions to a novel Casimir equation associated with the Ito system,a couplednonlinear wave equation.Both travelling wave solutions and separable self-similar solutions are discussed.In a numberof cases,explicit exact solutions are found.Such results,particularly the exact solutions,are useful in that they provideus a baseline of comparison to any numerical simulations.Besides,such solutions provide us a glimpse of the behaviorof the Ito system,and hence the behavior of a type of nonlinear wave equation,for certain parameter regimes.展开更多
In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
A new method of catastrophe control is described in one dimension nonlinear system. Catastrophe control based on catastrophe theory is a brand new area for control theory. A certain catastrophe is created at a desired...A new method of catastrophe control is described in one dimension nonlinear system. Catastrophe control based on catastrophe theory is a brand new area for control theory. A certain catastrophe is created at a desired location by appropriate control, which has preferred properties. Washout filter is presented and applied to preserve the original equilibrium of a system. Washout filter aided dynamic feedback controller is developed for the creation of catastrophe, and an example is given to illustrate the process. Catastrophe control may provide a new way of designing warning signals of impending collapse or catastrophe for monitoring and control purposes.展开更多
This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed ...This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed by using theoretical methods.It is shown that the sub-harmonic resonance may occur due to maneuvering flight conditions.The larger the eccentricity E and the maneuver load G,the greater the sub-harmonic resonance.The effects of nonlinear stiffness,damping of the system,maneuver load,and eccentricity on the sub-harmonic resonance region in parameter planes are also investigated.Bifurcation diagrams of the analytical solutions are in good agreement with that of the numerical simulation solutions.These results will contribute to the understanding of the nonlinear dynamic behaviors of maneuvering rotor systems.展开更多
基金＊Supported by the National Natural Science Foundation of China under Grant No. 40876010, the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No. KZCX2-YW-Q03-08, the R ＆： D Special Fund for Public Welfare Industry （Meteorology） under Grant No. GYHY200806010, the LASG State Key Laboratory Special Fund and the Foundation of E-Institutes of Shanghai Municipal Education Commission （E03004）
文摘The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
文摘We discuss two classes of solutions to a novel Casimir equation associated with the Ito system,a couplednonlinear wave equation.Both travelling wave solutions and separable self-similar solutions are discussed.In a numberof cases,explicit exact solutions are found.Such results,particularly the exact solutions,are useful in that they provideus a baseline of comparison to any numerical simulations.Besides,such solutions provide us a glimpse of the behaviorof the Ito system,and hence the behavior of a type of nonlinear wave equation,for certain parameter regimes.
基金Supported by the National Natural Science Foundation of China under Grant No.40876010the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No.KZCX2-YW-Q03-08+2 种基金the LASG State Key Laboratory Special Fundthe Foundation of Shanghai Municipal Education Commission under Grant No.E03004the Natural Science Foundation of Zhejiang Province under Grant No.Y6090164
文摘In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
文摘A new method of catastrophe control is described in one dimension nonlinear system. Catastrophe control based on catastrophe theory is a brand new area for control theory. A certain catastrophe is created at a desired location by appropriate control, which has preferred properties. Washout filter is presented and applied to preserve the original equilibrium of a system. Washout filter aided dynamic feedback controller is developed for the creation of catastrophe, and an example is given to illustrate the process. Catastrophe control may provide a new way of designing warning signals of impending collapse or catastrophe for monitoring and control purposes.
基金supported by the National Natural Science Foundation of China(Grant No.10632040)
文摘This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed by using theoretical methods.It is shown that the sub-harmonic resonance may occur due to maneuvering flight conditions.The larger the eccentricity E and the maneuver load G,the greater the sub-harmonic resonance.The effects of nonlinear stiffness,damping of the system,maneuver load,and eccentricity on the sub-harmonic resonance region in parameter planes are also investigated.Bifurcation diagrams of the analytical solutions are in good agreement with that of the numerical simulation solutions.These results will contribute to the understanding of the nonlinear dynamic behaviors of maneuvering rotor systems.
