Abstract. The excitation of
nonlinear forced vibrations of magnetization and elastic displacement in normal
magnetized ferrite plate having magnetoelastic properties is investigated. This
investigation is made on the basis of simplified system consist of two
connected oscillators one of its having gyromagnetic properties. It is derived
the system containing two second order differential equations which gives the
connection between oscillators. It is drawn the significant role of nonlinear
component which having the multiplication of magnetic oscillator vibration amplitude
in square on the first degree of elastic oscillator vibration amplitude. For
the typical parameters of the task about microwave hypersound vibrations
excitation in the film of yttrium iron garnet it is made the numerical
appreciation of nonlinear coefficient item. On the basis of obtained equation
system for the case when resonance frequencies both oscillators are differed in
multiple relation it is made the investigation of forced vibrations development
in time. It is shown that in conditions of multiplication of second oscillator
frequency in comparison to the first oscillator frequency by defined values of
parameters the excitation of vibrations take place with non-stationary delay in
time. After the end of this delay the jumping increasing of vibrations
amplitude on one-two orders in value take place. It is shown that the
significant condition of delay is the large distinctions between the relaxation
time of both oscillators. It is found the threshold character of delay
realization over the excitation amplitude and critical character over the cubic
nonlinearity of first oscillator parameter. For the interpretation of delay
effect is proposed the hypothesis about the existence of the additional minimum
of system potential separated from the main minimum by potential barrier. It is
created the model on dynamical potential which defined the first oscillator
vibrations character in connection with the second oscillator amplitude as a
task parameter. It is shown that the main reason of minimum appearance is
nonlinear connection which is proportional to multiplication of magnetic oscillator
vibration amplitude in square on the first degree of elastic oscillator
vibration amplitude. The proposed model allows to describing the threshold
character of delay realization and the necessity of frequency multiplication of
second oscillator in comparison of first oscillator frequency. It is
investigated the delay character in wide interval of excitation amplitude
variation. It is found the critical value of amplitude which exceeding is the
necessary condition of delay. It is shown that after the critical value
exceeding the delay time is decreased in the law which is near to opposite
proportionality. It is investigated the dependence of delay and excited vibrations
character from the cubic nonlinearity parameter of first oscillator. It is
found the lower critical level of cubic nonlinearity parameter which is
necessary to the vibrations amplitude limitation. It is found the upper
critical level of cubic nonlinearity parameter above which the delay is suppressed.
The observed lower and upper critical levels of cubic nonlinearity parameter
are explained on the basis of dynamical potential model.
Key words: nonlinear vibrations,
magnetoelastic interaction, potential.
References
1. Andronov
A.A., Witt A.A., Haikin S.E. Teoriya kolebaniy. [Theory of vibrations]. Moscow, Nauka
Publ. 1981. 568 p. (In
Russian).
2. Zaslavsky
G.M., Sagdeev R.Z. Vvedenie v nelineynuyu fiziku. [Introduction to nonlinear physics]. Moscow, Nauka
Publ. 1988. 368 p.
(In Russian).
3. Monosov
Ya.A. Nelineinyi ferromagnitnyi rezonzans. [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. Seavey
M.H., Tannenwald P.E. Direct observation of spin-wave resonance. Phys. Rev. Lett. 1958. V.1. ¹5. P.168-169.
6. Kittel C.
Excitation of spin waves in a ferromagnet by a uniform rf field. Phys. Rev.
1958. V.110. ¹6. P.1295-1297.
7. Weiss M.T.
Microwave and low-frequency oscillations due to resonance instabilities in
ferrites. J. Appl. Phys. 1958. V.30. ¹4. P.146S-147S.
8. 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. Moscow,
NIU
MEI Publ. 2008. P.197-205. (In Russian).
9. 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.
10. Zubkov
V.I., Monosov Ya.A., Shcheglov V.I. The Mandelshtam-Brilluen spin-effect.
JETP
Letters. 1971. V.13. ¹5. P.229-232.
11. 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).
12. Kotov
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 - Proceedings of Chelyabinsk State
University. 2013. ¹25 (316). Physics. ¹18.
P.27-30. (In Russian).
13. 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”. NIU
MEI Publ.. 2013. P.188-198. (In Russian).
14. 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”. NIU
MEI Publ. 2013. P.199-215. (In Russian).
15. Vlasov
V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The application of connected
oscillators model to the analysis of auto-modulation regime of hypersound
excitation by magnetostriction transducer. Proceedings of XXII International
conference “Electromagnetic fields and materials”. NIU
MEI Publ.. 2014.
P.161-175. (In Russian).
16. Vlasov
V.S., Ivanov A.P., Shavrov V.G., Shcheglov V.I. The dynamics of forced
magnetization vibrations in ferrite plate having magnetoelastic properties in
conditions of orientational transition. Proceedings of XXII International
conference “Electromagnetic fields and materials”. NIU
MEI Publ.. 2014.
P.176-188. (In Russian).
17. 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).
18. 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
19. 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
20. 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).
21.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).
22. 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).
23. 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).
24. 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).
25. 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).
26. Gurevich
A.G., Melkov G.A. Magnitnye kolebaniya i volny. [Magnetic oscillations and waves]. Moscow, Fizmatlit
Publ. 1994. 464 p.
(In Russian).
27. 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
28. Korn G.,
Korn T. Spravochnik po matamatike dlya nauchnykh sotrudnikov i inzhenerov.
[Handbook on mathematics for scientists and engineers]. Moscow, Nauka Publ. 1973.
832 p. (In Russian).