TY - JOUR
T1 - Power spectra of chaotic vibrations of a buckled beam
AU - Brunsden, V.
AU - Cortell, J.
AU - Holmes, P. J.
N1 - Funding Information:
This research was partially supported by NSF under MSM 84-02069 and DMS 87-03656 and ONR under SRO IV, NOOO14-85-k-0172.T he authors wish to thank F. C. Moon, who kindly made his laboratory available for the experimental work, and W. T. Holmes, who provided technical assistance and advice.
PY - 1989/4/8
Y1 - 1989/4/8
N2 - Many of the strange attractors associated with low dimensional differential equations are known to contain transverse homoclinic orbits. In particular, the Duffing equation with negative linear stiffness, which models the behavior of a buckled beam subject to transverse excitation, possesses such orbits. On the assumption that the chaotic time history of a single variable in such an equation can be represented by the random superposition of deterministic structures, each being a single excursion around a homoclinic orbit, the power spectrum of the variable in question is predicted. Good agreement is demonstrated among our predictions, numerical simulations of Duffing's equation and experimental spectra obtained from a cantilever beam buckled by magnetic forces.
AB - Many of the strange attractors associated with low dimensional differential equations are known to contain transverse homoclinic orbits. In particular, the Duffing equation with negative linear stiffness, which models the behavior of a buckled beam subject to transverse excitation, possesses such orbits. On the assumption that the chaotic time history of a single variable in such an equation can be represented by the random superposition of deterministic structures, each being a single excursion around a homoclinic orbit, the power spectrum of the variable in question is predicted. Good agreement is demonstrated among our predictions, numerical simulations of Duffing's equation and experimental spectra obtained from a cantilever beam buckled by magnetic forces.
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U2 - 10.1016/0022-460X(89)90516-6
DO - 10.1016/0022-460X(89)90516-6
M3 - Article
AN - SCOPUS:0024964427
SN - 0022-460X
VL - 130
SP - 1
EP - 25
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 1
ER -