2002 Fiscal Year Final Research Report Summary
Chaos in a Forced Vibratory System with an Asymmetric Restoring Force
| Project/Area Number |
13650249
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Dynamics/Control
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
NAKAI Mikio Kyoto University, Precision Engineering, Associate Professor, 工学研究科, 助教授 (50026043)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Piecewise Linear System / Chaos / Gear Vibration / Contact Vibration / Interval Analysis / Conley Index |
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| Research Abstract |
(1) A generalized solution methodology based on piecewise linear vector fields has been proposed for piecewise linear systems with boundaries for both displacement and time. This methodology is applied in analyzing dynamic responses of torsional vibration through bilinear spring stiffness with changing hysteretie torque in the rotating machinery system, which has boundaries for both displacement and velocity. For asymmetric torque with hysteresis. two cases exist when restoring torque changes smoothly and discontinuously. Our present method can be applied to dynamic responses of piecewise linear systems having velocity and displacement boundaries.
(2) In rolling contact vibration of two discs, their dynamic responses can be predicted employing the second-order averaging method of which validity has been confirmed for nonlinear vibrations.
(3) Topological methods are employed to extract unstable fixed points in phase space from numerical and experimental time series data. Conley index of
… More
an isolated invariant subset and the R-B method can determine unstable fixed points contained in strange attractor from numerical time series data. For experimental time series, the theorem for the relationship between index pair and Conley index enables one to predicted unstable fixed points with acceptable accuracy.
(4) For the experimental model, a driven disc with smoothed surface is in rolling contact with another driving disc having wavy roughness. As a driving disc with wavy surface, a spur gear, 0.5 module, was used. Accelerations in the radial direction of the disc were measured at different rotational speeds and contact loads. As a result, non-linear responses including additional and differential harmonic resonances and chaotic motion occur in connection with the corrugation frequency, contact resonance frequency and the natural frequencies of the disc. It was found that the topological method (3) can find an unstable fixed point contained in Poincare map obtained from measured time series data. Less
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Research Products
(17 results)
