Equations of currents in an electric nonlinear vibrator excited by biharmonic ideal EMF
DOI:
https://doi.org/10.3103/S0735272704060032Abstract
The paper describes a new mathematical model of a thin rectilinear electric vibrator driven with biharmonic ideal electromotive force. The EMF is applied to a cut filled with a substance having nonlinear properties with respect to electric field. The field in the cut is investigated. Integral equations of spectral components of the vibrator current are derived. It is shown that dispersive characteristics of the vibrator are dictated by electrophysical properties of the substance in the cut, and by the vibrator’s electric dimensions.References
KAPITSA, P.L.; FOK, V.A.; VAINSHTEIN, L.A. "Waves of current in a thin cylindrical conductor. Symmetric electric oscillations of an ideally conducting hollow cylinder of a finite length," in: VAINSHTEIN, L.A. The Diffraction Theory [in Russian]. Moscow: Radio i Svyaz’, 1995, p.65-125.
MITTRA, R. (ed.), Computer Techniques for Electromagnetics. Pergamon Press, 1973.
EMINOV, S.I. "Ob odnom eksperimente v oblasti vibratornykh antenn," Antenny, n.12, p.9-10, 2002.
FRANCESCHETTI, Giorgio; PINTO, Innocenzo. "Nonlinearly loaded antennas," in: USLENGHI, Piergiorgio L. E. Nonlinear Electromagnetics. Academic Press, 1980. DOI: https://doi.org/10.1016/B978-0-12-709660-5.50015-3.
PETROV, B.M.; SEMENIKHINA, D.V. "Effekt nelineinogo rasseianiia elektromagnitnykh voln," Elektrodinamika i Tekhnika SVCh i KVCh, v.7, n.7, p.52-71, 1999.
SCHMUTZER, E. Grundprinzipien der klassischen Mechanik und der klassischen Feldtheorie (kanonischer Apparat) [in German]. Berlin: Wissenschaften, 1973.
BOGOLYUBOV, N.N.; MITROPOL’SKII, Y.A. Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian]. Moscow: Nauka, 1974.
PUKHOV, G.Y. Differential Transformations of Functions and Equations [in Russian]. Kiev: Naukova Dumka, 1984.
LEVITAN, B.M. Quasiperiodic Functions [in Russian]. Moscow: GITTL, 1953.
LANDAU, E. Grundlagen der Analysis [in German]. Akademische Verlagsgesellschaft, 1930.
SOBOLEV, S.L. Mathematical Physics Equations [in Russian]. Moscow: Nauka, 1966.
POLYANIN, A.D.; MANZHIROV, A.V. Handbook of Integral Equations [in Russian]. Moscow: Fizmatlit, 2003.
