- Higuchi, K. and Dowell, E.H., Effect of constant transverse force on chaotic oscillations of sinusoidally excited buckled beam,
Int. J. Non-Linear Mech. (UK), vol. 26 no. 3-4
pp. 419 - 26 [0020-7462(91)90071-Z] .
(last updated on 2007/04/10)
The chaotic oscillation of a buckled beam under sinusoidally varying and static constant transverse external forces is investigated. A harmonic balance method and a direct numerical integration are applied to a Duffings equation model of the buckled beam. For a small transverse constant force, there exists three static equilibrium points, and the near contact between the two orbits of a stable and an unstable limit cycle in the phase plane can predict the onset of chaos. For a large transverse constant force, there exists only one static equilibrium point, but there may exist three different dynamic response amplitudes due to non-linear resonance phenomena. The near contact between two vibration regions of a stable and an unstable limit cycle can predict the onset of chaos