Nonlinear lumped-parameter force factor Bl(x), stiffness Kms(x) and inductance Le(x) of electrodynamic loudspeakers change frequency responses and generate some nonlinear effects for large stimulus: harmonic and inter...Nonlinear lumped-parameter force factor Bl(x), stiffness Kms(x) and inductance Le(x) of electrodynamic loudspeakers change frequency responses and generate some nonlinear effects for large stimulus: harmonic and intermodulation distortion, DC component in diaphragm displacement, instability of vibration and jumping effects. By modeling the nonlinear system under large-signal conditions, relationship between the nonlinear parameters and large-signal behavior can be revealed and help to provide guidance to diagnose loudspeakers. Agreement between the measured and predicted responses of a real loudspeaker validates the modeling and enables new methods for loudspeaker diagnosis.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
基金supported by the National Natural Science Foundation of China(Grant No. 11274172)
文摘Nonlinear lumped-parameter force factor Bl(x), stiffness Kms(x) and inductance Le(x) of electrodynamic loudspeakers change frequency responses and generate some nonlinear effects for large stimulus: harmonic and intermodulation distortion, DC component in diaphragm displacement, instability of vibration and jumping effects. By modeling the nonlinear system under large-signal conditions, relationship between the nonlinear parameters and large-signal behavior can be revealed and help to provide guidance to diagnose loudspeakers. Agreement between the measured and predicted responses of a real loudspeaker validates the modeling and enables new methods for loudspeaker diagnosis.
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.
