- Smelova-Reynolds, T. and Dowell, E.H., The role of higher modes in the chaotic motion of the buckled beam. II,
Int. J. Non-Linear Mech. (UK), vol. 31 no. 6
pp. 941 - 50 [S0020-7462(96)00115-1] .
(last updated on 2007/04/10)
Part II of this work completes the analysis of the necessary conditions for the chaos in the system of modal equations of motion of the buckled beam, i.e. a system of coupled Duffing equations. The direct calculation of the stable and unstable perturbed manifolds is used to establish the necessary condition for chaotic motion. It is shown that the higher components of the modified Melnikov vector do not change the critical condition obtained from consideration of only the first component. Analysis of the Lyapunov exponents of the system demonstrates the difference between necessary and sufficient conditions for steady-state chaos. Finally, the additional consideration of the non-hyperbolic modes shows that they can be neglected while developing the condition for the intersection of the stable and unstable manifolds