連続ウェーブレット変換を用いたDuffing系の不規則応答におけるジャンプ現象の解析(<小特集>機械系における非線形力学と解析法)

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Stochastic jump phenomena in the random responses of a Duffing oscillator subjected to narrow band random excitation are investigated. The stochastic jump phenomena correspond to the existence of multiple stationary responses, as well as the nonlinear oscillator subjected to harmonic excitation. The Duffing oscillator subjected to the harmonic excitation has two stable stationary responses in some frequency range. These responses differ in the phase angle between the excitation and the response, as well as the amplitude. In the case of the stochastic excitation, there are two states of the response, and the jump between two states occurs suddenly and multiple times in the long sample function. These two states correspond to two stationary responses to the harmonic excitation. Amplitude and phase angle of each state of response are quite different when the stochastic excitation is narrow band, but the differences become obscurer when the band width of the excitation becomes broader. The purpose of this paper is to propose the criterion that is capable of distinguishing between two states of the response in the case of the broad band random excitation. In this study, we propose the product of each wavelet transform of the excitation and the response to estimate the phase angle between them. Numerical examples show that the product corresponds to the frequency decomposed phase angle between the excitation and the response, and successfully identifies the states of the response.
一般社団法人日本機械学会の論文
2007-04-25

連続ウェーブレット変換を用いたDuffing系の不規則応答におけるジャンプ現象の解析(<小特集>機械系における非線形力学と解析法)

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