The effects of the constant excitation on the local bifurcation of the periodic solutions in the 1：2 internal resonant systems were analyzed based on the singularity theory. It is shown that the constant excitation m...The effects of the constant excitation on the local bifurcation of the periodic solutions in the 1：2 internal resonant systems were analyzed based on the singularity theory. It is shown that the constant excitation make influence only when there exist some nonlinear terms, in the oscillator with lower frequency. Besides acting as main bifurcation parameter, the constant excitation, together with coefficients of some nonlinear terms, may change the values of unfolding parameters and the type of the bifurcation. Under the non-degenerate cases, the effect of the third order terms can be neglected.展开更多
The vibration response formulas of the mechanical system under the affect of thevari-frequency exciting force are deduced. It is proved by the theoretical analysis and experimentalresults that the vibration response a...The vibration response formulas of the mechanical system under the affect of thevari-frequency exciting force are deduced. It is proved by the theoretical analysis and experimentalresults that the vibration response amplitude of the mechanical system under the affect of thevari-frequency exciting force is far smaller than that under the affect of the constant frequency exciting force on condition that the exciting force amplitudes are just the same;while the vari-fre-quency rate a increases to 5 Hz per second the vibration amplitude will decrease to 10% only as lowas that under the affect of the constant frequency exciting force. All these conclusions will be of significance for revealing the mechanism of suppressing chatter in van-speed cutting and analyzing theexperimental results of sine-wave scanning exciting test.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos.10472078, 10102014)and the Natural Science Foundation of Tianjin (Nos.043103611, 013604711)
文摘The effects of the constant excitation on the local bifurcation of the periodic solutions in the 1：2 internal resonant systems were analyzed based on the singularity theory. It is shown that the constant excitation make influence only when there exist some nonlinear terms, in the oscillator with lower frequency. Besides acting as main bifurcation parameter, the constant excitation, together with coefficients of some nonlinear terms, may change the values of unfolding parameters and the type of the bifurcation. Under the non-degenerate cases, the effect of the third order terms can be neglected.
文摘The vibration response formulas of the mechanical system under the affect of thevari-frequency exciting force are deduced. It is proved by the theoretical analysis and experimentalresults that the vibration response amplitude of the mechanical system under the affect of thevari-frequency exciting force is far smaller than that under the affect of the constant frequency exciting force on condition that the exciting force amplitudes are just the same;while the vari-fre-quency rate a increases to 5 Hz per second the vibration amplitude will decrease to 10% only as lowas that under the affect of the constant frequency exciting force. All these conclusions will be of significance for revealing the mechanism of suppressing chatter in van-speed cutting and analyzing theexperimental results of sine-wave scanning exciting test.
