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One-to-Two Internal Resonance in Two-Degrees-of-Freedom Nonlinear System with Narrow-Band Excitations |
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| Authors: | Wei Xu Qun He Haiwu Rong Tong Fang |
| Affiliation: | (1) Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710072, P. R. China;(2) Department of Mathematics, Foshan University, Guangdong, 528000, P. R. China;(3) Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an, 710072, P. R. China |
| Abstract: | Response of two-degrees-of-freedom nonlinearsystem to narrow-band random parametric excitation isinvestigated. The method of multiple scales is used todetermine the equations of modulation of amplitude andphase. The effect of detunings and amplitude areanalyzed. Theoretical analyses and numerical simulationsshow that the nontrivial steady-state solution may changeform a limit cycle to a diffused limit cycle as theintensity of the random excitation increase. Under someconditions, the system may have two steady-statesolutions. |
| Keywords: | two-degrees-of-freedom nonlinear system one-to-two internal resonance narrow-band excitations multiple scales method |
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