Steady-State Responses and Stability Analyses of the Duffing's Oscillator with the Softening Spring to an External Exciting Force(Special Issue on Nonlinear Dynamics)
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概要
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The steady-state responses which the damped Duffing oscillator with a softening spring property under a harmonically stimulating force exhibited in the main resonant frequency region have been analyzed by using both an approximate analytical procedure;that is, the harmonic balance scheme, and a numerical procedure.With regrad to the structure which the system reveals in this region, there exists another branch which seems to be caused by bifurcation from the resonant branch at a certain frequency as well as to the usual resonant and nonresonant branchs.It has been verified that many kinds of periodic solutions exist in the frequency region of interest between this new branch and the resonant one.In addition to the traditional harmonic solutions;that is, resonant and nonresonant solutions and the new branch, there appears a third harmonic solution branch.However, it is absolutely unstable.This unstable solution enables us to explain reasonably the constitution of attractors in this resonant frequency region.Furthermore, an approximate stability analysis of these new branches, including the usual resonant and nonresonant branches, has been developed and has revealed stability problems of all these branches.It has also been shown that chaotic phenomena, which are related to the fundamental harmonics in the region of interest, arise dur to period doubling bifurcation and develop only along the path of the second new branch.
- 社団法人日本機械学会の論文
- 1998-09-15
著者
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Sueoka Atsuo
Dept.of Mechanical Engineering Faculty Of Engineering Kyushu University
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TSUDA Yoshihiro
Dept.of Mechanical Engineering, Faculty of Engineering, Ohita University
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Miin-nan HUANG
Graduate Student of Ohita University
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Sueoka Atsuo
Dept.of Intelligent Machinery And Systems Faculty Of Eng. Kyushu Univ.
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Tsuda Yoshihiro
Dept. Of Mechanical Engineering Faculty Of Engineering Ohita University
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Tsuda Yoshihiro
Dept.of Mechanical Engineering Faculty Of Engineering Ohita University
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Huang Miin-nan
Graduate Student of Ohita University
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