- Smelova-Reynolds, T. and Dowell, E.H., The role of higher modes in the chaotic motion of the buckled beam. I,
Int. J. Non-Linear Mech. (UK), vol. 31 no. 6
pp. 931 - 9 [S0020-7462(96)00114-X] .
(last updated on 2007/04/10)
The goal of the present work is to combine the study of the chaotic motion of buckled beams with one of the most powerful and widely discussed analytical techniques in non-linear dynamics of the last 10 years. We explore the use of the generalized Melnikov's method for pending the onset of chaos to study the system of modal equations of a buckled beam with an external excitation. It is shown that the critical function of damping, forcing amplitude, and frequency for the first component of the Melnikov vector for the system of higher modal approximations and for a single modal Duffing's equation are related. This relationship, however, is more complex than simply neglecting the higher mode influence as has been suggested in some recent publications