Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities

International Journal of Non-Linear Mechanics

Volumn 39, Issue 7, 2004, Pages 1079-1091

  Vakakis, Alexander F ^a,b   Rand, Richard H ^c  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b University of Illinois at Urbana Champaign   (United States)

^c Department of Obstetrics Gynecology   (United States)

Author keywords

Capture; Coupled oscillators; Non linear; Resonance

Indexed keywords

DAMPING; DEGREES OF FREEDOM (MECHANICS); ENERGY TRANSFER; NONLINEAR SYSTEMS; OSCILLATIONS; VIBRATIONS (MECHANICAL);

ENERGY PUMPING;

OSCILLATORS (MECHANICAL);

EID: 0344308470     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(03)00098-2     Document Type: Article

References (16)

1. Nayfeh A.H., Mook D. Nonlinear Oscillations. 1985;Wiley Interscience, New York.
2. Rand R.H., Armbruster D. Perturbation Methods, Bifurcation Theory and Computer Algebra. 1987;Springer, New York.
3. Luongo A., Di Egidio A., Paolone A. On the proper form of the amplitude modulation equations for resonant systems. Nonlinear Dyn. 27:2002;237-254.
4. A. Luongo, A. Paolone, A. Di Egidio, Quantitative analysis of classes of motion for multiresonant systems I. An algebraic method, Nonlinear Dyn., submitted for publication.
5. Quinn D. Resonance capture in a three degree of freedom mechanical system. Nonlinear Dyn. 14:1997;309-333.
6. D. Quinn, Resonant dynamics in strongly nonlinear systems, Nonlinear Dyn., submitted for publication.
7. Vakakis A.F., Gendelman O. Energy pumping in nonlinear mechanical oscillators. part II - resonance capture J. Appl. Mech. 68:2001;42-48.
8. Vakakis A.F. Inducing passive nonlinear energy sinks in linear vibrating systems. J. Vibr. Acoust. 123:2001;324-332.
9. Barkham P.G.D., Soudack A.C. An extension of the method of Kryloff and Bogoliuboff. Int. J. Control. 10:1969;377-392.
10. Barkham P.G.D., Soudack A.C. Approximate solutions of nonlinear nonautonomous second-order differential equations. Int. J. Control. 11:1970;101-114.
11. Barkham P.G.D., Soudack A.C. New results on the elliptic function method. Int. J. Control. 26:1977;341-358.
12. Coppola V.T., Rand R.H. Averaging using elliptic functions. approximation of limit cycles Acta Mechanica. 81:1990;125-142.
13. Byrd P., Friedman M. Handbook of Elliptic Integrals for Engineers and Physicists. 1954;Springer, Berlin.
14. Chirikov B.V. A universal instability of many-dimensional oscillator systems. Phys. Rep. 52:1979;265-376.
15. R.H. Rand, Lecture Notes on Nonlinear Vibrations, http://www.tam.cornell.edu/randdocs/ , version 45, 2003.
16. Gendelman O., Manevitch L.I., Vakakis A.F., M'Closkey R. Energy pumping in nonlinear mechanical oscillators. part I - dynamics of the underlying Hamiltonian systems J. Appl. Mech. 68:2001;34-41.