Nonlinear system vibration---The appearance of chaos
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 Lab., NM (USA)
- 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
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
990200* -- Mathematics & Computers
ACCELERATION
BEAMS
DATA COVARIANCES
DIFFERENTIAL EQUATIONS
DYNAMIC FUNCTION STUDIES
EQUATIONS
FLUID FLOW
FREQUENCY ANALYSIS
HISTORICAL ASPECTS
LIE GROUPS
LORENTZ TRANSFORMATIONS
MECHANICAL VIBRATIONS
NONLINEAR PROBLEMS
OSCILLATIONS
PERTURBATION THEORY
POINCARE GROUPS
RANDOMNESS
SENSITIVITY
STABILITY
STRUCTURAL MODELS
SYMMETRY GROUPS
TECHNOLOGY ASSESSMENT
THREE-DIMENSIONAL CALCULATIONS
TRAJECTORIES
TRANSFORMATIONS
TRANSIENTS