TY - JOUR
T1 - Normal modes and global dynamics of a two-degree-of-freedom non-linear system-I. Low energies
AU - Vakakis, A. F.
AU - Rand, R. H.
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1992/9
Y1 - 1992/9
N2 - The global dynamics of an undamped, strongly non-linear, two-degree-of-freedom system are analyzed by means of Poincaré maps. The oscillator under consideration contains "similar" non-linear normal modes and at certain values of its structural parameters a mode bifurcation is possible. The effect of this bifurcation on the global dynamics is investigated by numerical and analytical techniques. For low energies, a homoclinic orbit exists in the Poincaré map, and is approximately analyzed by the two-variable expansion method. This homoclinic orbit is exclusively caused by the similar mode bifurcation, and as shown in a companion paper [A.K. Vakakis and R.H. Rand, Int. J. Non-Linear Mech. 27, 875-888 (1992)] it gives rise to large-scale chaotic motions when the energy is increased.
AB - The global dynamics of an undamped, strongly non-linear, two-degree-of-freedom system are analyzed by means of Poincaré maps. The oscillator under consideration contains "similar" non-linear normal modes and at certain values of its structural parameters a mode bifurcation is possible. The effect of this bifurcation on the global dynamics is investigated by numerical and analytical techniques. For low energies, a homoclinic orbit exists in the Poincaré map, and is approximately analyzed by the two-variable expansion method. This homoclinic orbit is exclusively caused by the similar mode bifurcation, and as shown in a companion paper [A.K. Vakakis and R.H. Rand, Int. J. Non-Linear Mech. 27, 875-888 (1992)] it gives rise to large-scale chaotic motions when the energy is increased.
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U2 - 10.1016/0020-7462(92)90040-E
DO - 10.1016/0020-7462(92)90040-E
M3 - Article
AN - SCOPUS:0026923335
SN - 0020-7462
VL - 27
SP - 861
EP - 874
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
IS - 5
ER -