| | Mechanics of Solids A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544 Online ISSN 1934-7936 |
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<< Previous article | Volume 39, Issue 3 / 2004 | Next article >> |
K. V. Avramov, "The analysis of period-doubling bifurcations of the impact oscillator by means of the amplitude surface method," Mech. Solids. 39 (3), 20-26 (2004) |
Year |
2004 |
Volume |
39 |
Number |
3 |
Pages |
20-26 |
Title |
The analysis of period-doubling bifurcations of the impact oscillator by means of the amplitude surface method |
Author(s) |
K. V. Avramov (Kharkov) |
Abstract |
Impact-oscillation systems have been considered by many authors in various aspects. This is accounted for by the importance of such systems for engineering. The theory of impact-oscillation systems is considered in [1, 2] and the review of the results in this field is given in [3]. Experimental studies of impact oscillators are presented in [4, 5]. The limit cycles and their bifurcations are analyzed in [6]. The families of subharmonic modes and their bifurcations are considered in [9, 10]. The papers [11, 12] are devoted to the utilization of impact-oscillation systems for modeling the dynamics of force transmissions. Although the theory of bifurcations of periodic motions is a fairly well developed area of applied mathematics [13, 14], the bifurcations of periodic motions in impact-oscillation systems in the case where two parameters change virtually have not been analyzed. The dynamics of an impact-oscillation system with two changing parameters was studied in [7, 8]. However, various oscillation modes and their bifurcations have not been considered in these papers. Apparently, this issue is considered in the present paper for the first time.
We propose a method for the analysis of bifurcations in the impact oscillator under the change of two parameters. This method is based on the construction of the amplitude surface that graphically represents bifurcations in the case of two variable parameters. This method allowed us to identify a number of bifurcation points of co-dimension 2. Publications in which the amplitude surfaces are utilized for the analysis of impact-oscillation systems have not been known to the author. Note that bifurcation points of co-dimension 2 have not been investigated previously for such systems. |
References |
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3. | S. R. Bishop, "Impact oscillator," Phil. Trans. Roy. Soc. London, Ser. A, Vol. 347, No. 1683, pp. 347-351, 1994. |
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|
Received |
13 December 2001 |
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