The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonanc...The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.展开更多
Nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua.The nonlinear non-autonomous governing e...Nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua.The nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by employing the harmonic balance method.The nonlinear normal modes are constructed by the invariant manifold method on the state space and a numerical iterative approach is adopted to obtain numerical solutions,in which two types of initial conditions for the modal coefficients are employed.The results show that both initial conditions can lead to fast convergence.The frequency-amplitude responses with some modal motions in phase space are obtained by the present iterative method.Quadrature phase difference and traveling waves are found in the time-domain complex modal analysis.展开更多
Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation t...Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For nonresonances, it is analytically presented that a single-mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1 : 1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.展开更多
We report on a theoretical and experimental study of an all-normal-dispersion （ANDi） Yb-doped mode-locked fiber laser, in which nonlinear polarization rotation （NPR） is used to realize mode-locking without any dis...We report on a theoretical and experimental study of an all-normal-dispersion （ANDi） Yb-doped mode-locked fiber laser, in which nonlinear polarization rotation （NPR） is used to realize mode-locking without any dispersion compensation. Based on the coupled nonlinear Schr6dinger （CNLS） equation, a model simulating the mode-locked process of an all-normal-dispersion ring fiber laser is developed, which shows that the achievement of stable mode-locking depends on the alignment of the polarization controller （PC） along the fast-polarization axis of the fiber, the birefringence intensity, and the net cavity dispersion. According to the theoretical analysis, stable mode-locked pulses with pulse duration 300 ps and average output power 33.9 mW at repetition rate 36 MHz are obtained.展开更多
文摘The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.
基金This study was partially funded by the National Natural Science Foundation of China(Grant Nos.11672189,11672007)the postdoctoral fund of Beijing Chaoyang District(Grant No.Q5001015201602)+3 种基金the Program Funded by Liaoning Province Education Administration(Grant No.L2016010)Prof.X.-D.Yang was founded by the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education,Northeastern University(VCAME201601)Prof.Melnik was funded by the Natural Sciences and Engineering Research Council(NSERC)of Canada,the Canada Research Chair(CRC)program,and the Bizkaia Talent Grant under the Basque Government through the BERC 2014-2017 programas well as Spanish Ministry of Economy and Competitiveness MINECO:BCAM Severo Ochoa excellence accreditation SEV-2013-0323.
文摘Nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua.The nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by employing the harmonic balance method.The nonlinear normal modes are constructed by the invariant manifold method on the state space and a numerical iterative approach is adopted to obtain numerical solutions,in which two types of initial conditions for the modal coefficients are employed.The results show that both initial conditions can lead to fast convergence.The frequency-amplitude responses with some modal motions in phase space are obtained by the present iterative method.Quadrature phase difference and traveling waves are found in the time-domain complex modal analysis.
文摘Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For nonresonances, it is analytically presented that a single-mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1 : 1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.
文摘We report on a theoretical and experimental study of an all-normal-dispersion （ANDi） Yb-doped mode-locked fiber laser, in which nonlinear polarization rotation （NPR） is used to realize mode-locking without any dispersion compensation. Based on the coupled nonlinear Schr6dinger （CNLS） equation, a model simulating the mode-locked process of an all-normal-dispersion ring fiber laser is developed, which shows that the achievement of stable mode-locking depends on the alignment of the polarization controller （PC） along the fast-polarization axis of the fiber, the birefringence intensity, and the net cavity dispersion. According to the theoretical analysis, stable mode-locked pulses with pulse duration 300 ps and average output power 33.9 mW at repetition rate 36 MHz are obtained.
