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Propagation of waves and chaos in transmission line with strongly anharmonic dangling resonator |
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| Authors: | P. Zieliński A. Kułak L. Dobrzyński B. Djafari-Rouhani |
| Affiliation: | (1) The H. Niewodniezański Institute of Nuclear Physics, ul. Radzikowskiego 152, 30-342 Kraków, Poland, PL;(2) Department of Electronics, Academy of Mining and Metallurgy, Al. Mickiwicza 30, 30-059, Kraków, Poland, PL;(3) Laboratoire de Dynamique et Structure des Matériaux Moléculaires, UFR de Physique, Université de Lille I, 59655 Villeneuve d'Ascq Cedex, France, FR |
| Abstract: | Delayed differential equation of motion with multiple lags is derived for an anharmonic stub resonator coupled to a monomode transmission line. Transmission and reflection coefficients are found analytically in the harmonic approximation. Nonlinear response of the system is analysed by an electric circuit obeying the same equations of motion. Enhanced second harmonic generation is found at the frequencies, which in the harmonic approximation correspond to the zeros of transmission. An aperiodic (chaotic) response is found mainly in the frequency range close to the resonance of the dangling resonator. Zeros of transmission and total transmissions are shown to be lifted by the anharmonicity nearly in the same frequency region. Higher harmonics are preferentially transmitted at the zero transmission points in the presence of anharmonicity. Received 14 March 2002 / Received in final form 25 November 2002 Published online 14 March 2003 |
| Keywords: | PACS. 43.25.+y Nonlinear acoustics – 05.45.Tp Time series analysis – 68.35.Ja Surface and interface dynamics and vibrations |
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