Abstract A theoretical study of periodic solutions, their local stability and period doubling bifurcations in a non-linear oscillator made by the aid of approximate analytical methods is completed by a computer simulation analysis to verify theoretical results and observe chaotic behaviour. Thus the chaotic motion is observed against a background of the classical resonance curves, stability limits and jump phenomena. It has been shown that the chaotic motion appears in the neighbourhood of the stability limit of the 1 2 subharmonic resonance and forms a transition zone between the subharmonic and principal resonance solution. Because the averaged power spectrum in this case shows only one narrow continuous segment, an essence of an irregularity of the motion has been roughly interpreted as random-like fluctuation of the amplitude and frequency of the 1 2 subharmonic component.
[1]
P. Holmes,et al.
A periodically forced piecewise linear oscillator
,
1983
.
[2]
Hiroyuki Kumano,et al.
Forced Vibrations in an Unsymmetric Piecewise-Linear System Excited by General Periodic Force Functions
,
1979
.
[3]
Y. Ueda.
EXPLOSION OF STRANGE ATTRACTORS EXHIBITED BY DUFFING'S EQUATION
,
1979
.
[4]
On the 1/2-th Subharmonic Vibrations of a Non-linear Vibrating System with a Hard Duffing Type Restoring Characteristic
,
1984
.
[5]
P. Holmes,et al.
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
,
1983,
Applied Mathematical Sciences.
[6]
Y. Ueda.
Randomly transitional phenomena in the system governed by Duffing's equation
,
1978
.
[7]
F. Moon.
Experiments on Chaotic Motions of a Forced Nonlinear Oscillator: Strange Attractors
,
1980
.