Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2023. ¹5

ContentsFull text in Russian (pdf)

DOI: https://doi.org/10.30898/1684-1719.2023.5.6

NON-STATIONARY VIBRATIONS IN THE SYSTEM

OF TWO CONNECTED OSCILLATORS

IN CONDITIONS OF CUBIC NONLINEARITY AND CUBIC CONNECTION.

PART 1. MULTI-REGIME CHARACTER OF VIBRATIONS

A.P. Ivanov^{1}, V.G. Shavrov^{2}, V.I. Shcheglov^{2}

^{1}Syktyvkar State University, 167001, Russia, Syktyvkar, Oktyabrskiy prosp., 55

^{2}Kotelnikov IRE RAS, 125009, Russia, Moscow, Mokhovaya, 11, b.7

The paper was received March 28, 2023.

Abstract.The task about the excitation of magnetoelastic vibrations in geometry of magnetostriction transducer which contains normal magnetized ferrite plate excited by alternating magnetic field is investigated. It is proposed the model presentation of transducer in the view of two connected oscillators first of its corresponds to magnetic part of structure and the second correspond to elastic its part. The first oscillator is linear and the second is nonlinear. The nonlinearity and connection have cubic character. In dependence from the excitation level it is found five basal regimes of vibrations: ¹1 – synchronize, ¹2 – three-multiplication of frequency, ¹3 – chaos, ¹4 – gigantic oscillations, ¹5 – delayed stabilization. In these regimes the time-evolvent of vibrations and its parametric portraits in coordinates displacement – derivative from displacement and also frequency spectra of forced vibrations are investigated. The regimes ¹1á ¹2 are stable. The vibrations in this regimes are harmonic and complete determined. The regimes ¹3-¹5 are non-stable. The vibrations in this regimes has chaotic or near to chaotic character. On the level of excitation the stable regimes are separated from non-stable by sharp threshold. By the overcoming of which the vibration amplitude increases by sharp jump over two-three orders. By the excitation on non-stable regimes it is established the application on the main vibrations the attendant vibrations. The frequency of attendant vibrations is higher than excitation frequency on two-three orders. The amplitude of attendant vibrations is smaller than the main vibrations amplitude more then two orders. It is proposed the model of attendant vibrations excitations. On the basis of this model the quantity appreciation of vibrations character in non-stable regimes. The recommendations for future development of investigations are proposed.

Key words:nonlinear vibrations, connected oscillators, cubic nonlinearity.

Financing:The work was carried out as part of the state task of the V.A. Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences.

Corresponding author:Shcheglov Vladimir Ignatyevich, vshcheg@cplire.ru1. Karlov N.V. Kirichenko N.A.

Kolebaniya, volny, struktury[Vibrations, waves, structures]. Moscow, Fizmatlit. 2003. 496 p. (In Russian)2. Zaslavzky G.M., Sagdeev R.Z.

Vvedenie v nelineinuyu fiziku[Introguction to nonlinear physics]. Moscow, Nauka. 1988. 379 p. (In Russian)3. Riskin N.M., Trubetskov D.I.

Nelineinye volny[Nonlinear waves].Moscow, Nauka-Fizmatlit. 2000. 272 p. (In Russian)4. Kuznetsov S.P.

Dinamicheskii khaos (kurs lektsii)[Dynamical chaos (course of lectures)]. Moscow, Fizmatlit. 2001. 296 p. (In Russian)5. Dmitriev A.S., Panas A.I.

Dinamicheskii khaos: novye nositeli informatsii dlya sistem svyazi[Dynamical chaos: new carriers of information for communication systems]. Moscow, Fizmatlit. 2002. 251 p. (In Russian)6. Gurevich A.G.

Ferrity na sverkhvysokikh chastotakh[Ferrites on microwave frequencies].Moscow, Gos. Izd. fiz. mat. lit. 1960. 409 p. (In Russian)7. Gurevich A.G.

Magnitnyi rezonans v ferritakh i antiferromagnetikakh[Magnetic resonance in ferrites and antiferromagnetics]. Moscow, Nauka. 1973. 588 p. (In Russian)8. Gurevich A., Melkov G.

Magnitnye kolebaniya i volny[Magnetic oscillations and waves]. Moscow, Nauka-Fizmatlit. 1994. 464 p. (In Russian)9. Monosov Ya.A.

Nelineyny ferromagnitniy rezonans[Nonlinear ferromagnetic resonance]. Moscow, Nauka. 1971. 376 p. (In Russian)10. LeCraw R.C., Comstock R.L. Magnetoelastic interactions in ferromagnetic dielectrics.

In book: Physical Acoustics. V.3. Part.B. Lattice dynamics. New York and London, Academic Press. 1965. P.156.11. Monosov Ya.A., Surin V.V., Shcheglov V.I. Excitation of resonance elastic vibrations by nonlinear ferromagnetic resonance.

Experimental and Theoretic Physics Letters. 1968. V.7. ¹9. P.315.12. Zubkov V.I., Monosov Ya.A., Shcheglov V.I. Spin-effect of Mandelshtamm-Brilluen.

Experimental and Theoretic Physics Letters. 1971. V.13. ¹5. P.161-163.13. Vlasov V.S., Kotov L.N., Shavrov V.G., Shcheglov V.I. Nonlinear excitation of hypersound in a ferrite plate under the ferromagnetic-resonance conditions.

Journal of Communications Technology and Electronics. 2009. V.54. ¹7. P.821.14. Vlasov V.S., Shavrov V.G., Shcheglov V.I. The nonlinear excitation of hypersound in bilayer ferrite structure.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online]. 2013. ¹2. http://jre.cplire.ru/jre/feb13/10/text.pdf (In Russian)15. Vlasov V.S., Shavrov V.G., Shcheglov V.I. Nonlinear excitation of hypersound in bilayer ferrite structure by ferromagnetic resonance.

Journal of Communications Technology and Electronics.2014. V.59. ¹5. P.441.16. Weiss M. T. The microwave and low frequency vibrations which is determined by unstable of resonance in ferrites.

Phys. Rev. Lett.1958. V.1. ¹7. P.239.17. Shcheglov V.I., Shavrov V.G., Zubkov V.I., Vlasov V.S., Kotov L.N. Auto-modulation regime of nonlinear forced vibrations of magnetization of ferrite in resonator.

Sbornik trudov XII Mezhdunarodnoi konferentsii «Magnetizm, dal'nee i blizhnee spin-spinovoe vzaimodeistvie»[Book of papers XII International conference «Magnetism, distant and near spin-spin interaction»]. Moscow-Firsanovka, Publ.MEI. 2009. P.100. (In Russian)18. Ivanov A.P., Shavrov V.G., Shcheglov V.I. Forced vibrations in the system of two connected oscillators in conditions of cubic nonlinearity and quadratic connection.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online]. 2020. ¹8. https://doi.org/10.30898/1684-1719.2020.8.7 (In Russian)19. Vlasov V.S., Ivanov A.P., Kotov L.N., Shavrov V.G., Shcheglov V.I. Autovibrations in the system of two connected oscillators when one of its is gyromagnetic.

Sbornik trudov XX Mezhdunarodnoi konferentsii «Ehlektromagnitnoe pole i materialy»[Book of papers XXI International conference «Electromagnetic field and materials»].Moscow, NIU MEI. 2012. P.248. (In Russian)20. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The analysis of linear excitation of hypersound vibrations of magnetostriction transducer on the basis of connected oscillators model.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online].2014. ¹10. http://jre.cplire.ru/jre/nov13/3/text.pdf (In Russian)21. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. Autovibrations in the normal biased ferrite plate having magnetoelastic properties.

Sbornik trudov XXI Mezhdunarodnoi konferentsii «Ehlektromagnitnoe pole i materialy»[Book of papers XXI International conference «Electromagnetic field and materials»]. Moscow, NIU MEI. 2012. P.188. (In Russian)22. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The application of connected oscillators model for the analysis of working of magnetostriction transducer.

Sbornik trudov XXI Mezhdunarodnoi konferentsii «Ehlektromagnitnoe pole i materialy»[Book of papers XXI International conference «Electromagnetic field and materials»]. Moscow, NIU MEI. 2012. P.199. (In Russian)23. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The analysis of nonlinear excitation of hypersound vibrations on the basis of connected oscillators model in quadratic approximation.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online].2014. ¹1. http://jre.cplire.ru/jre/jan14/11/text.pdf (In Russian)24. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The analysis of vibrations in ferrite plate having magnetoelastic properties on the basis of quadratic approximation model.

Materialy XXIII Vserossiiskoi konferentsii «Ehlektromagnitnoe pole i materialy»[Book of papers XXIII All-Russian conference «Electromagnetic field and materials»]. Moscow, INFRA-M. 2015. P.202. (In Russian)25. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. Application of connected oscillators model for the analysis of nonlinear excitation of hypersound in ferrite plate by ferromagnetic resonance. Part 1. Basis equations.

Journal of Communications Technology and Electronics.2015. V.60. ¹1. P.79.26. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. Application of connected oscillators model for the analysis of nonlinear excitation of hypersound in ferrite plate by ferromagnetic resonance. Part 2. Some nonlinear phenomenon.

Journal of Communications Technology and Electronics.2015. V.60. ¹3. P.297.27. Ivanov A.P., Shavrov V.G., Shcheglov V.I. The analysis of auto-modulation vibrations in magnetoelastic medium on the basis of connected magnetic and elastic oscillators.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online]. 2015. ¹5. http://jre.cplire.ru/jre/may15/4/text.pdf (In Russian)28. Ivanov A.P., Shavrov V.G., Shcheglov V.I. The analysis of auto-modulation phenomena in the system of connected magnetic and elastic oscillators on the basis of potential model .

Zhurnal radioelektroniki[Journal of Radio Electronics] [online]. 2015. ¹6. http://jre.cplire.ru/jre/jun15/9/text.pdf (In Russian)29. Ivanov A.P., Shavrov V.G., Shcheglov V.I. The non-stationary delay of magnetoelastic vibrations excitation in regime of frequency multiplication. Part 1. Dynamical potential.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online]. 2017. ¹7. http://jre.cplire.ru/jre/jul17/6/text.pdf (In Russian)30. Ivanov A.P., Shavrov V.G., Shcheglov V.I. The non-stationary delay of magnetoelastic vibrations excitation in regime of frequency multiplication. Part 2. Linear connection.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online]. 2017. ¹8. http://jre.cplire.ru/jre/aug17/5/text.pdf (In Russian)31. Ivanov A.P., Shavrov V.G., Shcheglov V.I. The non-stationary delay of magnetoelastic vibrations excitation in regime of frequency multiplication. Part 3. Nonlinear connection.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online].2017. ¹8. http://jre.cplire.ru/jre/aug17/6/text.pdf (In Russian)32. Shavrov V.G., Shcheglov V.I., Ivanov A.P.

Nelineinye kolebaniya v zadache vozbuzhdeniya giperzvuka[Nonlinear vibrations in the task about hypersound excitation]. Syktivkar, OOO “Komi republican printing-house”. 2021. 192 p. (In Russian)33. Sivukhin D.V.

Obshchii kurs fiziki. T.3. Ehlektrichestvo[General course of physics. V.3. Electricity]. Moscow, Nauka. 1977. 704 p. (In Russian)34. Ivanov A.P., Shavrov V.G., Shcheglov V.I. The non-stationary delay of vibrations development magnetostriction transducer in regime of frequency multiplication.

Journal of Communications Technology and Electronics.2023. V.68. ¹5.35. Mandelbrot B.B.

The fractal geometry of nature.San Francisco, W.H. Freeman. 1982. 469 p.

For citation:Ivanov A.P. Shavrov V.G., Shcheglov V.I. Non-stationary vibrations in the system of two connected oscillators in conditions of cubic nonlinearity and cubic connection. Part 1. Multi-regime character of vibrations.

Zhurnal radioelektroniki[Journal of Radio Electronics] [online]. 2023. ¹5. https://doi.org/10.30898/1684-1719.2023.5.6 (In Russian)