Energy pumping in nonlinear mechanical oscillators: Part II—resonance capture

Journal of Applied Mechanics, Transactions ASME

Volumn 68, Issue 1, 2001, Pages 42-48

  Vakakis, A F ^a   Gendelman, O ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b SEMENOV INSTITUTE OF CHEMICAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002298634     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.1345525     Document Type: Article

References (18)

1. Gendelman, O., Manevitch, L. I., Vakakis, A. F., and M’Closkey, R., 2001, “Energy ‘Pumping’ in Coupled Mechanical Oscillators I: Dynamics of the Underlying Hamiltonian Systems,” ASME J. Appl. Mech., Vol. 68, pp. 3441.
2. Arnold, V. I., ed., 1988, Dynamical Systems III (Encyclopaedia of Mathematical Sciences), Vol. 3, Springer-Verlag, Berlin.
3. Lochak, P., and Meunier, C., 1988, Multiphase Averaging for Classical Systems (Series on Applied Mathematical Sciences), Vol. 72, Springer-Verlag, Berlin.
4. Morozov, A. D., 1998, Quasi-conservative Systems, Cycles, Resonances and Chaos (Series on Nonlinear Science, Series A), Vol. 30, World Scientific, Singapore.
5. Neishtadt, A. I., 1975, “Passage Through a Resonance in the Two-Frequency Problem,” Dokl. Akad. Nauk, 221, pp. 301-304.
6. Neishtadt, A. I., 1976, “Averaging in Multifrequency Systems II,” Dokl. Akad. Nauk SSSR, 226, pp. 1295-1298.
7. Neishtadt, A. I., 1975, “Passage Through a Separatrix in a Resonance Problem With a Slowly-Varying Parameter,” Prikl. Mat. Meck. (PMM), 39, No. 4, pp. 621-632.
8. Haberman, P., 1983, “Energy Bounds for the Slow Capture by a Center in Sustained Resonance,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 43, No. 2, pp. 244-256.
9. Morozov, A. D., and Shil’nikov, L. P., 1984, “On Nonconservative Periodic Systems Close to Two-Dimensional Hamiltonian,” Prikl. Mat. Meck. (PMM), 47, No. 3, pp. 327-334.
10. Lewin, L., and Kevorkian, J., 1978, “On the Problem of Sustained Resonance,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 35, No. 4, pp. 738-754.
11. Kath, W. L., 1983, “Necessary Conditions for Sustained Reentry Roll Resonance,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 43, No. 2, pp. 314-324.
12. Kath, W. L., 1983, “Conditions for Sustained Resonance II,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 43, No. 3, pp. 579-583.
13. Quinn, D., and Rand, R., 1995, “The Dynamics of Resonance Capture,” Nonlinear Dyn., 8, pp. 1-20.
14. Rand, R., and Quinn, D., 1995, “Resonant Capture in a System of Two Coupled Homoclinic Oscillators,” J. Vib. Control, 1, pp. 41-56.
15. Bosley, D. L., and Kevorkian, J., 1995, “On the Asymptotic Solution of Non-Hamiltonian Systems Exhibiting Sustained Resonance,” Stud. Appl. Math., 94, pp. 83-130.
16. Bosley, D. L., 1996, “An Improved Matching Procedure for Transient Resonance Layers in Weakly Nonlinear Oscillatory Systems,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 56, No. 2, pp. 420-445.
17. Percival, I., and Richards, D., 1982, Introduction to Dynamics, Cambridge University Press, Cambridge, UK.
18. Vakakis, A. F., 1994, “Exponentially Small Splittings of Manifolds in a Rapidly Forced Duffing System,” J. Sound Vib., 170, No. 1, pp. 119-129.