In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and ...In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.展开更多
Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W...Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W function, this paper presents a simple algorithm for locating the rightmost characteristic root of periodic solutions of some nonlinear oscillators with large time delay. As application, the proposed algorithm is used to study the primary resonance and 1/3 subharmonic resonance of the Duffing oscillator under harmonic excitation and delayed feedback, as well as the control problem of the van der Pol oscillator under harmonic excitation by using delayed feedback, with a number of case studies. The main advantage of this algorithm is that though very simple in implementation, it works effectively with high accuracy even if the delay is large.展开更多
The system state trajectory, Poincard maps, largest Lyapunov exponents, frequency spectra and bifurcation diagrams were used to investigate the non-linear dynamic behaviors of a rotor-bearing-seal coupled system and t...The system state trajectory, Poincard maps, largest Lyapunov exponents, frequency spectra and bifurcation diagrams were used to investigate the non-linear dynamic behaviors of a rotor-bearing-seal coupled system and to analyze the influence of the seal and bearing on the nonlinear characteristics of the rotor sys- tem. Various nonlinear phenomena in the rotor-bearing-seal system, such as periodic motion, double-periodic motion, multi-periodic motion and quasi-periodic motion were investigated. The results may contribute to a further understanding of the non-linear dynamics of the rotor-bearing-seal coupled system.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 Nature Science Foundation of Jining(JB10)
文摘In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10825207, 11032009)by Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0968)
文摘Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W function, this paper presents a simple algorithm for locating the rightmost characteristic root of periodic solutions of some nonlinear oscillators with large time delay. As application, the proposed algorithm is used to study the primary resonance and 1/3 subharmonic resonance of the Duffing oscillator under harmonic excitation and delayed feedback, as well as the control problem of the van der Pol oscillator under harmonic excitation by using delayed feedback, with a number of case studies. The main advantage of this algorithm is that though very simple in implementation, it works effectively with high accuracy even if the delay is large.
基金the National Natural Science Foundation of China (No. 10572087)the National High Technology Research and Development Program (863) of China (No. 2002AA526138)
文摘The system state trajectory, Poincard maps, largest Lyapunov exponents, frequency spectra and bifurcation diagrams were used to investigate the non-linear dynamic behaviors of a rotor-bearing-seal coupled system and to analyze the influence of the seal and bearing on the nonlinear characteristics of the rotor sys- tem. Various nonlinear phenomena in the rotor-bearing-seal system, such as periodic motion, double-periodic motion, multi-periodic motion and quasi-periodic motion were investigated. The results may contribute to a further understanding of the non-linear dynamics of the rotor-bearing-seal coupled system.
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.
