We introduce a method to compute the girth of knots, defined by Herne^ndez and Lin, using the Jones and Brandt-Lickorish-Millett-Ho polynomial. We determine the girth of all knots up to 10 crossings.
We focus on the hysteretic characteristics of the varying compliance(VC) principal resonance in a ball bearing. The branches of the periodic VC response are traced by the harmonic balance method and the alternating fr...We focus on the hysteretic characteristics of the varying compliance(VC) principal resonance in a ball bearing. The branches of the periodic VC response are traced by the harmonic balance method and the alternating frequency/time domain technique(HB-AFT) embedding Arc-length continuation, and the stability of these solutions is investigated by using Floquet theory. We find that the resonant response displays a swallow-tail structure due to the coupling nonlinearities between the Hertzian contact and the bearing clearance, which differs from the soft hysteresis of the non-loss Hertzian contact resonances. Furthermore, we find that period-1 VC branch cannot completely characterize the response of the system for a large bearing clearance, because multiple instability regions may occur from the cyclic fold, the secondary Hopf bifurcations, supercritical and subcritical period doubling bifurcations, in which case co-existences of period-1, period-2, and even quasi-periodic VC motions emerge in the hysteretic resonant range.展开更多
Obvious resonance peak will be generated when parallel photovoltaic grid-connected inverters are connected to the weak grid with high grid impedance, which seriously affects the stability of grid-connected operation o...Obvious resonance peak will be generated when parallel photovoltaic grid-connected inverters are connected to the weak grid with high grid impedance, which seriously affects the stability of grid-connected operation of the photovoltaic system. To overcome the problems mentioned above, the mathematical model of the parallel photovoltaic inverters is established. Several factors including the impact of the reference current of the grid-connected inverter, the grid voltage interference and the current disturbance between the photovoltaic inverters in parallel with the grid-connected inverters are analyzed. The grid impedance and the LCL filter of the photovoltaic inverter system are found to be the key elements which lead to existence of resonance peak. This paper presents the branch voltage and current double feedback suppression method under the premise of not changing the topological structure of the photovoltaic inverter, which effectively handles the resonance peak, weakens the harmonic content of the grid current of the photovoltaic grid-connected inverter and the voltage at the point of common coupling, and improves the stability of the parallel operation of the photovoltaic grid-connected inverters in weak grid. At last, the simulation model is established to verify the reliability of this suppression method.展开更多
文摘We introduce a method to compute the girth of knots, defined by Herne^ndez and Lin, using the Jones and Brandt-Lickorish-Millett-Ho polynomial. We determine the girth of all knots up to 10 crossings.
基金supported by the National Basic Research Program of China("973"Project)(Grant No.2015CB057400)the China Postdoctoral Science Foundation(Grant No.2013M541360)the National Natural Science Foundation of China(Grant Nos.10632040 and 11302058)
文摘We focus on the hysteretic characteristics of the varying compliance(VC) principal resonance in a ball bearing. The branches of the periodic VC response are traced by the harmonic balance method and the alternating frequency/time domain technique(HB-AFT) embedding Arc-length continuation, and the stability of these solutions is investigated by using Floquet theory. We find that the resonant response displays a swallow-tail structure due to the coupling nonlinearities between the Hertzian contact and the bearing clearance, which differs from the soft hysteresis of the non-loss Hertzian contact resonances. Furthermore, we find that period-1 VC branch cannot completely characterize the response of the system for a large bearing clearance, because multiple instability regions may occur from the cyclic fold, the secondary Hopf bifurcations, supercritical and subcritical period doubling bifurcations, in which case co-existences of period-1, period-2, and even quasi-periodic VC motions emerge in the hysteretic resonant range.
基金supported by National Natural Science Foundation of China (No. 61573303)Natural Science Foundation of Hebei Province (No. E2016203092)
文摘Obvious resonance peak will be generated when parallel photovoltaic grid-connected inverters are connected to the weak grid with high grid impedance, which seriously affects the stability of grid-connected operation of the photovoltaic system. To overcome the problems mentioned above, the mathematical model of the parallel photovoltaic inverters is established. Several factors including the impact of the reference current of the grid-connected inverter, the grid voltage interference and the current disturbance between the photovoltaic inverters in parallel with the grid-connected inverters are analyzed. The grid impedance and the LCL filter of the photovoltaic inverter system are found to be the key elements which lead to existence of resonance peak. This paper presents the branch voltage and current double feedback suppression method under the premise of not changing the topological structure of the photovoltaic inverter, which effectively handles the resonance peak, weakens the harmonic content of the grid current of the photovoltaic grid-connected inverter and the voltage at the point of common coupling, and improves the stability of the parallel operation of the photovoltaic grid-connected inverters in weak grid. At last, the simulation model is established to verify the reliability of this suppression method.
