"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 8, 2017

contents             full textpdf   

The non-stationary delay of magnetoelastic vibrations excitation in regime of frequency multiplication. Part 2. Linear connection
 
A. P. Ivanov1 ,  V. G. Shavrov 2, V. I. Shcheglov 2
1 Syktyvkar State University of Sorokin, Oktyabrskiy prosp. 55, Syktyvkar 167001, Russia

2 Kotel’nikov Institute of Radio Engineering and Electronics, Mokhovaya 11-7, Moscow 125009, Russia

 

The paper is received on July 9, 2017

 

Abstract. It is continued the investigation of task about excitation of forced nonlinear vibrations of magnetization and elastic displacement in normal magnetized ferrite plate having magnetoelastic properties. The investigation is made on basis of two connected oscillators – nonlinear magnetic and linear elastic. Using the quadratic approximation it is written the system of two connected second order differential equations. The connection between these equations is ensured by the formula part of one equation which is proportional to the variable quantity of other equation. For the explanation of the vibrations in this system development it is proposed the model which is consisted of combination of two dynamical potentials. It is investigated the qualitative picture of vibrations development which take place after the excitation is included. It is shown that the combination of synchronization mechanism with first oscillator relaxation process leads to delay of intensive vibrations excitation relatively to the excitation switch moment. It is investigated the process of development vibration in time in the case of symmetrical linear connection between oscillators. It is found four most characteristic regimes corresponding to different levels of linear connection parameter along its increasing: regime ¹1 – two-steps delay; regime ¹2 – smooth saturation; regime ¹3 – intermittent jumps; regime ¹4 – small-amplitude relaxation. In the regime ¹1 the development of vibrations after first delay is occurs by two successive one to other sharp increasing of amplitude. In the regime ¹2 the development of vibrations after first two-steps  delay is occurs by smooth amplitude increasing with going to the permanent level. The regime ¹3 is characterized by two properties: the intermittent jumps amplitude is more then two orders less then amplitude of permanent vibrations in regime ¹2, and after the end of jumps the vibrations continues around the new equilibrium position. The regime ¹4 take place only by very large values of linear connection and characterized by rapid fading of both oscillators vibrations with its own relaxation times. It is made the interpretation of observed properties of these regimes on the basis of two-potential model. It is shown that the non-symmetry of linear connection does not brought to formation of other new vibration regimes except of investigated in the case of symmetrical connection.

Key words: nonlinear vibrations, magnetoelastic interaction, potential.

References

1. Gurevich A.G., Melkov G.A. Magnitnye kolebaniya i volny. [Magnetic oscillations and waves]. Moscow, Fizmatlit Publ. 1994. 464 p. (In Russian).

2. Ferrity v nelineinykh sverkhvysokochastotnykh ustroistvakh. [Ferrites in nonlinear microwave devices]. Edited by Gurevich A.G. Moscow, IL Publ. 1961. 636 p. (In Russian).    

3. Monosov Ya.A.  Nelineinyi ferromagnitnyi rezonans. [Nonlinear ferromagnetic resonance]. Moscow, Nauka Publ. 1971. 376 p. (In Russian). 

4. Lvov V.S. Nelineynye spinovye volny. [Nonlinear spin waves]. Moscow, Nauka Publ. 1987. (In Russian). 

5. LeCraw R.C., Comstock R.L. Magnetoelastic interactions in ferromagnetic dielectrics. In the book: Physical acoustics. Edited by W.P.Mason. V.III. Part B. Lattice Dynamics. New York, London: Academic Press. 1965. P.156-243.  

6. Vlasov V.S., Kotov L.N., Shavrov V.G., Shcheglov V.I. Excitation of connected nonlinear vibrations by nonlinear ferromagnetic resonance. Proceedings of XVI International conference “Radiolocation and radio communication”. Moscow-Firsanovka, MEI Publ. 2008. P.197-205. (In Russian). 

7. Monosov Ya.A., Surin V.V., Shcheglov V.I. The resonance elastic vibrations excitation by nonlinear ferromagnetic resonance. JETP Letters. 1968. V.7. ¹9. P.315-317.

8. Zubkov V.I., Monosov Ya.A., Shcheglov V.I. The Mandelshtam-Brilluen spin-effect. JETP Letters. 1971. V.13. ¹5. P.229-232.

9. Shcheglov V.I. Interaction of elastic vibrations with precession magnetic moment. Journal of Communications Technology and Electronics. 1971. V.16. ¹12. P.2321-2322.  

10. Shcheglov V.I. Double elastic-magnetostatic resonance. Russian JTP Letters. 1980. V.6. ¹15. P.922-924.

11. 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.821-832.   DOI: 10.1134/S1064226909070110

12. Vlasov V.S., Shavrov V.G., Shcheglov V.I.  The Nonlinear Excitation of Hypersound in Bilayer Ferrite Structure. Zhurnal Radio electroniki – Journal of Radio Electronics. 2013. ¹2. Available at: http://jre.cplire.ru/jre/feb13/10/text.pdf (In Russian).

13. Vlasov V.S., Shavrov V.G., Shcheglov V.I. Nonlinear excitation of ultrasound in a two-layer ferrite structure under ferromagnetic resonance conditions. Journal of Communications Technology and Electronics. 2014. V.59. ¹5. P.441-455.   DOI: 10.1134/S1064226914040135

14. Vlasov V.S., Ivanov A.P., Kotov L.N., Shavrov V.G., Shcheglov V.I. The Autovibrations in system of two connected oscillations one of which is gyro-magnetic.  Proceedings of XX International conference “Electromagnetic fields and materials”. Moscow, NIU MEI Publ. 2012. P.248-259. (In Russian). 

15. Kolov L.N., Vlasov V.S., Ivanov A.P., Shcheglov V.I., Shavrov V.G. The investigation of autovibrations of two connected oscillators one of which is nonlinear. Vestnik Chelyabinskogo gosudarstvennogo universiteta - Transactions of Chelyabinsk State University. 2013. ¹25 (316). Physics. ¹18. P.27-30. (In Russian).

16. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The Autovibrations in normal magnetized ferrite plate having the magnetoelastic properties.  Proceedings of XXI International conference “Electromagnetic fields and materials”. Moscow, NIU MEI Publ. 2013. P.188-198. (In Russian). 

17. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The application of connected oscillators model to the analysis of magnetostriction transducer functioning.  Proceedings of XXI International conference “Electromagnetic fields and materials”. Moscow, NIU MEI Publ. 2014. P.176-188. (In Russian). 

20. 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 square approach model.  Proceedings of XXIII International conference “Electromagnetic fields and materials”. Moscow, INFRA-M Publ. 2015. P.202-216. (In Russian). 

21. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. Application of the model of coupled oscillators in the analysis of the nonlinear excitation of hypersound in a ferrite plate under ferromagnetic resonance. Part 1. Basic equations.  Journal of Communications Technology and Electronics. 2015. V.60. ¹1. P.75-86.   DOI: 10.1134/S1064226915010118

22. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I.  Application of the model of coupled oscillators in the analysis of the nonlinear excitation of hypersound in a ferrite plate under ferromagnetic resonance. Part 2. Nonlinear effects.  Journal of Communications Technology and Electronics. 2015. V.60. ¹3. P.280-293.   DOI: 10.1134/S106422691501012X

23. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The analysis of linear hypersoumd vibrations of magnetostriction transducer based on connected oscillators model.  Zhurnal Radio electroniki – Journal of Radio Electronics. 2013. ¹11. Available at: http://jre.cplire.ru/jre/nov13/3/text.pdf (In Russian).  

24. Vlasov V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The analysis of nonlinear hypersound vibrations excitation of magnetostriction transducer based on connected oscillators model in quadratic approximation.  Zhurnal Radio electroniki – Journal of Radio Electronics. 2014. ¹1. Available at: http://jre.cplire.ru/jre/jan14/11/text.pdf (In Russian).

25. Ivanov A.P., Shavrov V.G., Shcheglov V.I.  Analysis of auto-modulation vibrations in magnetoelastic medium on the basis of connected magnetic and elastic oscillators model.  Zhurnal Radio electroniki – Journal of Radio Electronics. 2015. ¹5. Available at: http://jre.cplire.ru/jre/may15/4/text.pdf (In Russian).

26. Ivanov A.P., Shavrov V.G., Shcheglov V.I.  Analysis of auto-modulation phenomena in system of connected magnetic and elastic oscillators on the basis of potential model. Zhurnal Radio electroniki – Journal of Radio Electronics. 2015. ¹6. Available at: http://jre.cplire.ru/jre/jun15/9/text.pdf (In Russian).

27. Vlasov V.S., Shavrov V.G., Shcheglov V.I. Nonlinear hypersound vibrations of magnetostriction transducer on the frequencies, having multiple part of excitation frequency.  Part 1. The division of frequency. .Zhurnal Radio electroniki – Journal of Radio Electronics. 2015. ¹9. Available at: http://jre.cplire.ru/jre/sep15/4/text.pdf (In Russian).

28. Vlasov V.S., Shavrov V.G., Shcheglov V.I. Nonlinear hypersound vibrations of magnetostriction transducer on the frequencies, having multiple part of excitation frequency. Part 2. The multiplication of frequency.  Zhurnal Radio electroniki – Journal of Radio Electronics. 2015. ¹10. Available at: http://jre.cplire.ru/jre/oct15/1/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 Radio electroniki – Journal of Radio Electronics. 2017.  ¹7.   Available at: http://jre.cplire.ru/jre/jul17/6/text.pdf   (In Russian).

30. Strelkov S.P. Vvedenie v teoriyu kolebaniy. [Introduction to theory of vibrations]. Moscow, Nauka Publ. 1964. 440 p. (In Russian).

31. Migulin V.V., Medvedev V.I., Mustel E.R., Parigin V.N. Osnovy teorii kolebaniy. [Basics of the theory of vibrations]. Moscow, Nauka Publ. 1978. 392 p. (In Russian). 

32. Lax B., Button K. Microwave ferrites and ferrimagnetics. New York, McGraw-Hill, 1962. 752 p.  

33. Mandelbrot B.B. The fractal geometry of nature. New Yokk, W. H. Freeman and Company,  1982.

34. Fractals. Encyclopedia of physics. V.5. P.371-372. Moscow, Bol'shaya Sovetskaya Entciklopediya Publ., 1998. 760 p. (In Russian).  

 

For citation:

A.P.Ivanov, V.G.Shavrov, V.I.Shcheglov. The non-stationary delay of magnetoelastic vibrations excitation in regime of frequency multiplication. Part 2. Linear connection. Zhurnal Radioelektroniki - Journal of Radio Electronics, 2017, No. 8. Available at http://jre.cplire.ru/jre/aug17/5/text.pdf. (In Russian)