Energy Pumping in Nonlinear Mechanical Oscillators: Part I—Dynamics of the Underlying Hamiltonian Systems

[+] Author and Article Information
O. Gendelman, L. I. Manevitch

Institute of Chemical Physics, Russian Academy of Sciences, Kosygin Str. 4, 117977 Moscow, Russia

A. F. Vakakis

Department of Mechanical and Industrial Engineering, University of Illinois, 1206 W. Green Street, Urbana, IL 61801 e-mail: avakakis@uiuc.edu

R. M’Closkey

Department of Mechanical and Aerospace Engineering, University of California, 38-137N Engineering IV, 405 Hilgard Avenue, Los Angeles, CA 90024-1597 e-mail: obsidian.seas.ucla.edu

J. Appl. Mech 68(1), 34-41 (May 02, 2000) (8 pages) doi:10.1115/1.1345524 History: Received September 29, 1999; Revised May 02, 2000
Copyright © 2001 by ASME
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Grahic Jump Location
Numerical transient responses y1(t) and y2(t) of system (1) for (a) h=0.5, (b) h=0.8, (c) h=1.125; – oscillator 1, [[dashed_line]] oscillator 2
Grahic Jump Location
Numerical transient response of the three-degrees-of-freedom system for (a) ẏ3(0)=2.0, (b) ẏ3(0)=3.0, and (c) ẏ3(0)=4.0; – oscillator 1, [[dotted_line]] oscillator 2, [[dashed_line]] oscillator 3
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Construction of the solution y1 over an entire normalized period (equal to 4) from the half-normalized period solutions (a) eY(τ), and (b) X(τ)
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Leading 2m:1 subharmonic orbits as functions of h: –Y(−1) for m=1, –Y(−1) for m=2, [[dashed_line]]Y(−1) for m=3  
Grahic Jump Location
Leading (2n−1):1 subharmonic orbits as functions of h: –X(−1) for n=1, – −X(−1) for n=2, [[dashed_line]]X(−1) for n=3; ×××× unstable 1:1 subharmonic orbits
Grahic Jump Location
Poincaré maps of the dynamics of the undamped system (1) at varying energy levels for ω22=0.9,C=5.0, ε=0.1: (a) h=0.05, (b) h=0.2, (c) h=0.8, (d) h=2.0
Grahic Jump Location
Phase plots of the system of Eqs. (18) for ω22=0.9,C=5.0, ε=0.1, and varying values of the first integral of motion N: (a) N=0.4, (b) N=0.8, (c) N=1.9




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