Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator

Eugeny V. Mamontov; Alexander I. Ulitenko; Michael Y. Sudakov; Alexander A. Dyagilev; Olga V. Melnik; Galina I. Melnik

doi:10.1109/MECO.2018.8406092

Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator

Eugeny V. Mamontov, Alexander I. Ulitenko, Michael Y. Sudakov, Alexander A. Dyagilev, Olga V. Melnik, Galina I. Melnik

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Analytic and computer models of a harmonic oscillator with slowly varying natural frequency of oscillations are considered. The representation of Green's function in the form of harmonic oscillation with an envelope and a phase depending on the natural frequency is used. The excitation function is used to describe forced oscillations induced by an external harmonic influence. The case of a harmonic oscillator with linearly varying natural frequency of oscillations is considered. Analytic expressions for free and forced oscillations are obtained; the relationship between natural frequency scanning parameters and excitation function parameters is established. The results of numerical simulation of charged particle oscillations in a quadruple radio frequency electric field with a linearly varying amplitude with a uniform excitation field superimposed on it confirm correctness of the analytical calculations obtained.

Original language	English
Title of host publication	2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings
Editors	Lech Jozwiak, Budimir Lutovac, Drazen Jurisic, Radovan Stojanovic
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1-4
Number of pages	4
ISBN (Electronic)	9781538656822
DOIs	https://doi.org/10.1109/MECO.2018.8406092
State	Published - Jul 6 2018
Externally published	Yes
Event	7th Mediterranean Conference on Embedded Computing, MECO 2018 - Budva, Montenegro Duration: Jun 10 2018 → Jun 14 2018

Publication series

Name	2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings

Conference

Conference	7th Mediterranean Conference on Embedded Computing, MECO 2018
Country/Territory	Montenegro
City	Budva
Period	06/10/18 → 06/14/18

Funding

The reported study was funded by RFBR according to the research project № 18-07-00429 and by Ministry of Education and Science of Russia grant 8.8760.2017/8.9.

Keywords

excitation function of a nonstationary oscillator
free oscillations of a parametric oscillator
nonstationary harmonic oscillator
resonant excitation

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10.1109/MECO.2018.8406092

Cite this

Mamontov, E. V., Ulitenko, A. I., Sudakov, M. Y., Dyagilev, A. A., Melnik, O. V., & Melnik, G. I. (2018). Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator. In L. Jozwiak, B. Lutovac, D. Jurisic, & R. Stojanovic (Eds.), 2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings (pp. 1-4). (2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/MECO.2018.8406092

Mamontov, Eugeny V. ; Ulitenko, Alexander I. ; Sudakov, Michael Y. et al. / Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator. 2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings. editor / Lech Jozwiak ; Budimir Lutovac ; Drazen Jurisic ; Radovan Stojanovic. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 1-4 (2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings).

@inproceedings{4b6f361dc1d94f9d9dda097df4ce7720,

title = "Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator",

abstract = "Analytic and computer models of a harmonic oscillator with slowly varying natural frequency of oscillations are considered. The representation of Green's function in the form of harmonic oscillation with an envelope and a phase depending on the natural frequency is used. The excitation function is used to describe forced oscillations induced by an external harmonic influence. The case of a harmonic oscillator with linearly varying natural frequency of oscillations is considered. Analytic expressions for free and forced oscillations are obtained; the relationship between natural frequency scanning parameters and excitation function parameters is established. The results of numerical simulation of charged particle oscillations in a quadruple radio frequency electric field with a linearly varying amplitude with a uniform excitation field superimposed on it confirm correctness of the analytical calculations obtained.",

keywords = "excitation function of a nonstationary oscillator, free oscillations of a parametric oscillator, nonstationary harmonic oscillator, resonant excitation",

author = "Mamontov, {Eugeny V.} and Ulitenko, {Alexander I.} and Sudakov, {Michael Y.} and Dyagilev, {Alexander A.} and Melnik, {Olga V.} and Melnik, {Galina I.}",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 7th Mediterranean Conference on Embedded Computing, MECO 2018 ; Conference date: 10-06-2018 Through 14-06-2018",

year = "2018",

month = jul,

day = "6",

doi = "10.1109/MECO.2018.8406092",

language = "English",

series = "2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "1--4",

editor = "Lech Jozwiak and Budimir Lutovac and Drazen Jurisic and Radovan Stojanovic",

booktitle = "2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings",

}

Mamontov, EV, Ulitenko, AI, Sudakov, MY, Dyagilev, AA, Melnik, OV & Melnik, GI 2018, Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator. in L Jozwiak, B Lutovac, D Jurisic & R Stojanovic (eds), 2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings. 2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 1-4, 7th Mediterranean Conference on Embedded Computing, MECO 2018, Budva, Montenegro, 06/10/18. https://doi.org/10.1109/MECO.2018.8406092

Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator. / Mamontov, Eugeny V.; Ulitenko, Alexander I.; Sudakov, Michael Y. et al.
2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings. ed. / Lech Jozwiak; Budimir Lutovac; Drazen Jurisic; Radovan Stojanovic. Institute of Electrical and Electronics Engineers Inc., 2018. p. 1-4 (2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator

AU - Mamontov, Eugeny V.

AU - Ulitenko, Alexander I.

AU - Sudakov, Michael Y.

AU - Dyagilev, Alexander A.

AU - Melnik, Olga V.

AU - Melnik, Galina I.

PY - 2018/7/6

Y1 - 2018/7/6

N2 - Analytic and computer models of a harmonic oscillator with slowly varying natural frequency of oscillations are considered. The representation of Green's function in the form of harmonic oscillation with an envelope and a phase depending on the natural frequency is used. The excitation function is used to describe forced oscillations induced by an external harmonic influence. The case of a harmonic oscillator with linearly varying natural frequency of oscillations is considered. Analytic expressions for free and forced oscillations are obtained; the relationship between natural frequency scanning parameters and excitation function parameters is established. The results of numerical simulation of charged particle oscillations in a quadruple radio frequency electric field with a linearly varying amplitude with a uniform excitation field superimposed on it confirm correctness of the analytical calculations obtained.

AB - Analytic and computer models of a harmonic oscillator with slowly varying natural frequency of oscillations are considered. The representation of Green's function in the form of harmonic oscillation with an envelope and a phase depending on the natural frequency is used. The excitation function is used to describe forced oscillations induced by an external harmonic influence. The case of a harmonic oscillator with linearly varying natural frequency of oscillations is considered. Analytic expressions for free and forced oscillations are obtained; the relationship between natural frequency scanning parameters and excitation function parameters is established. The results of numerical simulation of charged particle oscillations in a quadruple radio frequency electric field with a linearly varying amplitude with a uniform excitation field superimposed on it confirm correctness of the analytical calculations obtained.

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KW - free oscillations of a parametric oscillator

KW - nonstationary harmonic oscillator

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M3 - Conference contribution

AN - SCOPUS:85050688684

T3 - 2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings

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BT - 2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings

A2 - Jozwiak, Lech

A2 - Lutovac, Budimir

A2 - Jurisic, Drazen

A2 - Stojanovic, Radovan

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 7th Mediterranean Conference on Embedded Computing, MECO 2018

Y2 - 10 June 2018 through 14 June 2018

ER -

Mamontov EV, Ulitenko AI, Sudakov MY, Dyagilev AA, Melnik OV, Melnik GI. Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator. In Jozwiak L, Lutovac B, Jurisic D, Stojanovic R, editors, 2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings. Institute of Electrical and Electronics Engineers Inc. 2018. p. 1-4. (2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings). doi: 10.1109/MECO.2018.8406092

Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator

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