Nonlinear system vibration---The appearance of chaos

Conference · Mon Jan 01 00:00:00 EST 1990

OSTI ID:6996362

Hunter, Jr, N F

This paper begins with an examination of the differential equation for a single degree of freedom force excited oscillator and considers the state space behavior of linear, nonlinear, and chaotic single degree of freedom systems. The fundamental characteristics of classical chaos are reviewed: sensitivity to initial conditions, positive Lyapunov exponents, complex Poincare maps, fractal properties of motion in the state space, and broadening of the power spectrum of the system response. Illustrated examples of chaotic behavior include motion in a two well potential -- the chaos beam described in Moon and a hardening base excited Duffing system. Chaos-like phenomenon which occur with nonperiodic forcing are examined in the context of the two well potential and hardening Duffing systems. The paper concludes with some suggestions for detecting and modelling nonlinear or chaotic behavior. 19 refs., 19 figs.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: DOE/MA
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6996362
• Report Number(s): LA-UR-90-356; CONF-900479-6; ON: DE90007546
• Resource Relation: Conference: 36. Institute of Environmental Science annual technology meeting, New Orleans, LA (USA), 23-27 Apr 1990
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
LORENTZ TRANSFORMATIONS
MECHANICAL VIBRATIONS
NONLINEAR PROBLEMS
POINCARE GROUPS
ACCELERATION
BEAMS
DATA COVARIANCES
DIFFERENTIAL EQUATIONS
DYNAMIC FUNCTION STUDIES
FLUID FLOW
FREQUENCY ANALYSIS
HISTORICAL ASPECTS
OSCILLATIONS
PERTURBATION THEORY
RANDOMNESS
SENSITIVITY
STABILITY
STRUCTURAL MODELS
TECHNOLOGY ASSESSMENT
THREE-DIMENSIONAL CALCULATIONS
TRAJECTORIES
TRANSIENTS
EQUATIONS
LIE GROUPS
SYMMETRY GROUPS
TRANSFORMATIONS
990200* - Mathematics & Computers