Chaotic Dynamics of a Quasi-Periodically Forced Beam
Keyword(s):
A straight beam with fixed ends, forced with two frequencies is considered. By using Galerkin’s method, the equation of motion of the beam is reduced to a finite degree-of-freedom system. The resulting equation is transformed into a multi-frequency system and the averaging method is applied. It is shown, by using Melnikov’s method, that there exist transverse homoclinic orbits in the averaged system associated with the first-mode equation. This implies that chaotic motions may occur in the single-mode equation. Furthermore, the effect of higher modes and the implications of this result for the full beam motions are described.
2017 ◽
Vol 09
(04)
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pp. 1750060
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2009 ◽
Vol 19
(11)
◽
pp. 3753-3776
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2020 ◽
Vol 30
(07)
◽
pp. 2050106
Keyword(s):