Transitions from localization to nonlocalization in strongly nonlinear damped oscillators

Chaos, solitons and fractals

Volumn 11, Issue 10, 2000, Pages 1535-1542

  Gendelman, Oleg ^a   Vakakis, Alexander F ^b  

^a SEMENOV INSTITUTE OF CHEMICAL PHYSICS   (Russian Federation)

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

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); DAMPING; DEGREES OF FREEDOM (MECHANICS); INTEGRAL EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS;

LOCALIZED NONLINEAR NORMAL MODE; NONLINEAR OSCILLATOR;

VIBRATIONS (MECHANICAL);

EID: 0033887110     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(99)00076-4     Document Type: Article

References (6)

1. Maree G.J.M. Slow periodic crossing of a pitchfork bifurcation in an oscillating system. Nonlinear Dynamics. 12(1):1997;1-37.
2. Rosenberg R. The Ateb(h)-functions and their properties. Quarter Appl Math. 21(1):1963;37-47.
3. Salenger G, Vakakis AF, Gendelman O, Manevitch L, Andrianov I. Transitions from strongly- to weakly-nonlinear motions of damped nonlinear oscillators. Nonlinear Dynamics, 1998; submitted.
4. Vakakis A.F., Nayfeh T., King M. A multiple-scales analysis of nonlinear, localized modes in a cyclic periodic system. Journal of Applied Mechanics. 60(2):1993;388-397.
5. Vakakis, AF., Manevitch, LI., Mikhlin, YV., Pilipchuk, VN., Zevin, AA. Normal modes and localization in nonlinear systems. New York: Wiley Interscience, 1996.
6. Vakakis AF, Gary Salenger. Generation of localization in a discrete chain with periodic boundary conditions: numerical and analytical results. SIAM J Appl Math, 1998; in press.