**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).