Analysis of Nonlinear Oscilators with Finite Degrees of Freedom

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PUŠENJAK, Rudi .
Analysis of Nonlinear Oscilators with Finite Degrees of Freedom. 
Strojniški vestnik - Journal of Mechanical Engineering, [S.l.], v. 43, n.5-6, p. 219-230, november 2017. 
ISSN 0039-2480.
Available at: <https://www.sv-jme.eu/article/analysis-of-nonlinear-oscilators-with-finite-degrees-of-freedom/>. Date accessed: 12 jul. 2024. 
doi:http://dx.doi.org/.
Pušenjak, R.
(1997).
Analysis of Nonlinear Oscilators with Finite Degrees of Freedom.
Strojniški vestnik - Journal of Mechanical Engineering, 43(5-6), 219-230.
doi:http://dx.doi.org/
@article{.,
	author = {Rudi  Pušenjak},
	title = {Analysis of Nonlinear Oscilators with Finite Degrees of Freedom},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {43},
	number = {5-6},
	year = {1997},
	keywords = {nonlinear oscillators; incremental harmonic balance method; subharmonic resonance; superharmonic resonance; primary resonance; },
	abstract = {This paper presents the analysis of nonlinear oscillators with finite degrees of freedom exhibiting self-sustained oscillations (autonomous systems) or performing oscillations under periodic excitation. The incremental harmonic balance method is used for calculation of the steady time response, limit cycles, stable and unstable branches of the resonance curves and for construction of solution diagrams in dependence of system parameters. The stability of the calculated solutions is proved by Floquet theory. In the paper construction of primary, superharmonic and subharmonic resonances of higher order of the Duffing oscillator is made by the use of IHB method. Autonomous systems are studied on the examples of the Van der Poloscillator and coupled nonlinear oscillator with two degrees of freedom, where the solution diagram is shown. Additionally, the resonance curves for the same nonlinear oscillator under excitation with variable frequency are calculated and plotted.},
	issn = {0039-2480},	pages = {219-230},	doi = {},
	url = {https://www.sv-jme.eu/article/analysis-of-nonlinear-oscilators-with-finite-degrees-of-freedom/}
}
Pušenjak, R.
1997 November 43. Analysis of Nonlinear Oscilators with Finite Degrees of Freedom. Strojniški vestnik - Journal of Mechanical Engineering. [Online] 43:5-6
%A Pušenjak, Rudi 
%D 1997
%T Analysis of Nonlinear Oscilators with Finite Degrees of Freedom
%B 1997
%9 nonlinear oscillators; incremental harmonic balance method; subharmonic resonance; superharmonic resonance; primary resonance; 
%! Analysis of Nonlinear Oscilators with Finite Degrees of Freedom
%K nonlinear oscillators; incremental harmonic balance method; subharmonic resonance; superharmonic resonance; primary resonance; 
%X This paper presents the analysis of nonlinear oscillators with finite degrees of freedom exhibiting self-sustained oscillations (autonomous systems) or performing oscillations under periodic excitation. The incremental harmonic balance method is used for calculation of the steady time response, limit cycles, stable and unstable branches of the resonance curves and for construction of solution diagrams in dependence of system parameters. The stability of the calculated solutions is proved by Floquet theory. In the paper construction of primary, superharmonic and subharmonic resonances of higher order of the Duffing oscillator is made by the use of IHB method. Autonomous systems are studied on the examples of the Van der Poloscillator and coupled nonlinear oscillator with two degrees of freedom, where the solution diagram is shown. Additionally, the resonance curves for the same nonlinear oscillator under excitation with variable frequency are calculated and plotted.
%U https://www.sv-jme.eu/article/analysis-of-nonlinear-oscilators-with-finite-degrees-of-freedom/
%0 Journal Article
%R 
%& 219
%P 12
%J Strojniški vestnik - Journal of Mechanical Engineering
%V 43
%N 5-6
%@ 0039-2480
%8 2017-11-11
%7 2017-11-11
Pušenjak, Rudi.
"Analysis of Nonlinear Oscilators with Finite Degrees of Freedom." Strojniški vestnik - Journal of Mechanical Engineering [Online], 43.5-6 (1997): 219-230. Web.  12 Jul. 2024
TY  - JOUR
AU  - Pušenjak, Rudi 
PY  - 1997
TI  - Analysis of Nonlinear Oscilators with Finite Degrees of Freedom
JF  - Strojniški vestnik - Journal of Mechanical Engineering
DO  - 
KW  - nonlinear oscillators; incremental harmonic balance method; subharmonic resonance; superharmonic resonance; primary resonance; 
N2  - This paper presents the analysis of nonlinear oscillators with finite degrees of freedom exhibiting self-sustained oscillations (autonomous systems) or performing oscillations under periodic excitation. The incremental harmonic balance method is used for calculation of the steady time response, limit cycles, stable and unstable branches of the resonance curves and for construction of solution diagrams in dependence of system parameters. The stability of the calculated solutions is proved by Floquet theory. In the paper construction of primary, superharmonic and subharmonic resonances of higher order of the Duffing oscillator is made by the use of IHB method. Autonomous systems are studied on the examples of the Van der Poloscillator and coupled nonlinear oscillator with two degrees of freedom, where the solution diagram is shown. Additionally, the resonance curves for the same nonlinear oscillator under excitation with variable frequency are calculated and plotted.
UR  - https://www.sv-jme.eu/article/analysis-of-nonlinear-oscilators-with-finite-degrees-of-freedom/
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	author = {Pušenjak, R.},
	title = {Analysis of Nonlinear Oscilators with Finite Degrees of Freedom},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
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	number = {5-6},
	year = {1997},
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TY  - JOUR
AU  - Pušenjak, Rudi 
PY  - 2017/11/11
TI  - Analysis of Nonlinear Oscilators with Finite Degrees of Freedom
JF  - Strojniški vestnik - Journal of Mechanical Engineering; Vol 43, No 5-6 (1997): Strojniški vestnik - Journal of Mechanical Engineering
DO  - 
KW  - nonlinear oscillators, incremental harmonic balance method, subharmonic resonance, superharmonic resonance, primary resonance, 
N2  - This paper presents the analysis of nonlinear oscillators with finite degrees of freedom exhibiting self-sustained oscillations (autonomous systems) or performing oscillations under periodic excitation. The incremental harmonic balance method is used for calculation of the steady time response, limit cycles, stable and unstable branches of the resonance curves and for construction of solution diagrams in dependence of system parameters. The stability of the calculated solutions is proved by Floquet theory. In the paper construction of primary, superharmonic and subharmonic resonances of higher order of the Duffing oscillator is made by the use of IHB method. Autonomous systems are studied on the examples of the Van der Poloscillator and coupled nonlinear oscillator with two degrees of freedom, where the solution diagram is shown. Additionally, the resonance curves for the same nonlinear oscillator under excitation with variable frequency are calculated and plotted.
UR  - https://www.sv-jme.eu/article/analysis-of-nonlinear-oscilators-with-finite-degrees-of-freedom/
Pušenjak, Rudi"Analysis of Nonlinear Oscilators with Finite Degrees of Freedom" Strojniški vestnik - Journal of Mechanical Engineering [Online], Volume 43 Number 5-6 (11 November 2017)

Authors

Affiliations

  • University of Maribor, Faculty of Mechanical Engineering, Slovenia

Paper's information

Strojniški vestnik - Journal of Mechanical Engineering 43(1997)5-6, 219-230
© The Authors, CC-BY 4.0 Int. Change in copyright policy from 2022, Jan 1st.

This paper presents the analysis of nonlinear oscillators with finite degrees of freedom exhibiting self-sustained oscillations (autonomous systems) or performing oscillations under periodic excitation. The incremental harmonic balance method is used for calculation of the steady time response, limit cycles, stable and unstable branches of the resonance curves and for construction of solution diagrams in dependence of system parameters. The stability of the calculated solutions is proved by Floquet theory. In the paper construction of primary, superharmonic and subharmonic resonances of higher order of the Duffing oscillator is made by the use of IHB method. Autonomous systems are studied on the examples of the Van der Poloscillator and coupled nonlinear oscillator with two degrees of freedom, where the solution diagram is shown. Additionally, the resonance curves for the same nonlinear oscillator under excitation with variable frequency are calculated and plotted.

nonlinear oscillators; incremental harmonic balance method; subharmonic resonance; superharmonic resonance; primary resonance;