Experimental and theoretical study of the features of the amplitude-frequency response features of the anharmonic Duffing oscillator
https://doi.org/10.25206/2588-0373-2024-8-3-13-20
EDN: OBKCSQ
Abstract
In this paper, experimental waveforms of the bifurcation phenomena in a Duffing oscillator weakly damped by viscous friction. The bifurcation points are found by solving the numerical solution of a harmonically linearized system with respect to the square of the frequency and the square of the amplitude. Approximate dimensionless expressions for amplitudes and their corresponding frequencies at the bifurcation points are proposed. The comparison of experimental and theoretical amplitude- frequency characteristics and their values at these points is given.
About the Authors
B. A. Kalashnikov
Omsk State Technical University
Russian Federation
Russian Federation
Kalashnikov Boris Aleksandrovich, Doctor of Technical Sciences, Associate Professor, Professor of Aircraft and Rocket Building Department
Omsk, Mira Ave., 11, 644050
AuthorID (SCOPUS): 6701318766,
ResearcherID: M-9643-2014
V. V. Bokhan
Omsk State Technical University;
JSC «Federal Research and Production Center «Progress»
Russian Federation
Russian Federation
Bokhan Vladimir Victorovich, Senior Lecturer of Fundamentals of Mechanics Theory and Automatic Control Department, OmSTU, Omsk; Senior Researcher, JSC «Federal Research and Production Center «Progress
Omsk, Mira Ave., 11, 644050,
Omsk, 5th Kordnaya St., 4, 644018
AuthorID (RSCI): 747705,
ResearcherID: P-3030-2017
V. E. Smolko
Omsk State Technical University
Russian Federation
Russian Federation
Smolko Valeria Evgenyevna, Undergraduate, gr. СМм-241 of Transport, Oil and Gas Faculty
Omsk, Mira Ave., 11, 644050
References
1. Duffing G. Erzwungene Schwingungen bei veranderlicher Eigenfrequenz und ihre technische Bedeutung [Forced Oscillations with Variable Natural Frequency and their Technical Significance]. Vieweg, Braunschweig, 1918. 134 s. DOI: 10.1002/zamm.19210010109. (In Germ.).
2. Nayfeh A. H., Mook D. T. Nonlinear Oscillations. Wiley, New York, 1979, 718 р. (In Engl.).
3. Magnus K. Kolebaniya: Vvedeniye v issledovaniye kolebatel’nykh sistem: per. s nem. [Introduction to the Investigation of oscillatory systems: trans. from Germ.]. Moscow, 1982. 304 p. (In Russ.).
4. Malatkar P., Nayfeh A. H. Calculation of the jump frequencies in the respose of a s.d.o.f. non-linear systems // Journal of Sound and Vibration. 2002. Vol. 254 (5). P. 1005–1011. DOI: 10.1006/jsvi.2001.4104. (In Engl.).
5. Markakis M. P. The jump phenomenon associated with the dynamics of the duffing equation // Physics Open. 2020. Vol. 5. 100042. DOI: 10.1016/j.physo.2020.100042. (In Engl.).
6. Veller V. N. Regulirovaniye i zashchita parovykh turbin [Regulation and protection of steam turbines]. Moscow, 1985. 104 p. (In Russ.).
7. Kirillov I. I. Avtomaticheskoye regulirovaniye parovykh turbin i gazoturbinnykh ustanovok [Automatic control of steam turbines and gas turbine installations]. Leningrad, 1988. 447 p. (In Russ.).
8. Ramlan R., Brennan M. J., Kovacic I. [et al.]. Exploiting knowledge of jump-up and jump-down frequencies to determine the parameters of a Duffing oscillator // Communications in Nonlinear Science and Numerical Simulation. 2016. Vol. 37. P. 282–291. DOI: 10.1016/j.cnsns.2016.01.017. (In Engl.).
9. Jordan D. W., Smith P. Nonlinear ordinary differential equations. 4th ed., Oxford: University Press, 2007. 560 p. ISBN 978-0-19-920824-1; ISBN 978-0-19-920825-8. (In Engl.).
10. Brennan M. J., Kovacic I., Carrella A. [et al.]. On the jump-up and jump-down frequencies of the Duffing oscillator // Journal of Sound and Vibration. 2008. Vol. 318. P. 1250–1261. DOI: 10.1016/j.jsv.2008.04.032. (In Engl.).
11. Chionh E., Goldman R. Elimination and resultants. Part 1: Elimination and bivariate resultants // IEEE Computer Graphics and Applications. 1995. Vol. 15, Issue 1. P. 69–77. DOI: 10.1109/38.364967. (In Engl.).
12. Kalashnikov B. A., Bokhan V. V., Penkov K. V. Eksperimental’noye opredeleniye nelineynoy funktsii dempfirovaniya mekhanicheskikh sistem [Determining the nonlinear damping function using experiments] // Omskiy nauchnyy vestnik. Omsk Scientific Bulletin. 2024. No. 3 (191). P. 5–13. DOI: 10.25206/1813-8225-2024-191-5-13. EDN: GRFNGU. (In Russ.).
13. Kalashnikov B. A. Prikladnyye metody teorii kolebaniy v raschetakh mekhanicheskikh sistem i konstruktsiy [Applied methods of vibration theory in calculations of mechanical systems and structures]. Omsk: OmSTU Publ., 2022. 238 p. ISBN 978-5- 8149-3570-0. EDN: HAJSQP. (In Russ.).
Review
For citations:
Kalashnikov B.A., Bokhan V.V., Smolko V.E. Experimental and theoretical study of the features of the amplitude-frequency response features of the anharmonic Duffing oscillator. Omsk Scientific Bulletin. Series Aviation-Rocket and Power Engineering. 2024;8(3):13-20. (In Russ.) https://doi.org/10.25206/2588-0373-2024-8-3-13-20. EDN: OBKCSQ
Views:
20
JATS XML
Email this article 