不規則外乱を受ける非線形振動系のカオス的挙動 : スケーリング構造の評価

概要

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This paper studies a random vibration of chaotic mechanical system with stochastic excitation. To dates, studies of mechanical chaotic vibrations have mainly focused on their deterministic properties. However, stochastic properties of mechanical system are sometimes unavoidable especially in practical situations. In the previous paper, we investigated a random vibration similar to deterministic chaos, which we call SCB (Stochastic Chaotic Behavior), and showed that the SCB may have a negative largest Liapunov exponent despite of its chaotic properties and chaotic aspect of the SCB can be characterized by a probability density function of local expansion rates. The result was in good agreement with that of an experimental mechanical chaos. This paper focuses on scaling structures of the SCB and investigates whether the SCB gives an more adequate model of the experimental chaos than the deterministic chaos. Correlation integrals, information dimensions, and spectral distribution functions of the SCB are in good agreement with those of the experimental chaos. Furthermore, an attractor of the SCB exhibits a scaling relation similar to strange nonchaotic attractors.
1999-04-25