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Abstract:
The nonlinear dynamic responses of a string-beam coupled system subjected to harmonic external and parametric excitations are studied in this work in the case of 1:2 internal resonance between the modes of the beam and string. First, the nonlinear governing equations of motion for the string-beam coupled system are established. Then, the Galerkin's method is used to simplify the nonlinear governing equations to a set of ordinary differential equations with four-degrees-of-freedom. Utilizing the method of multiple scales, the eight-dimensional averaged equation is obtained. The case of 1: 2 internal resonance between the modes of the beam and string principal parametric resonance-1/2 subharmonic resonance for the beam and primary resonance for the string - is considered. Finally, nonlinear dynamic characteristics of the string-beam coupled system are studied through a numerical method based on the averaged equation. The phase portrait, Poincare map and power spectrum are plotted to demonstrate that the periodic and chaotic motions exist in the string-beam coupled system under certain conditions.
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Source :
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN: 0218-1274
Year: 2009
Issue: 1
Volume: 19
Page: 225-243
2 . 2 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
JCR Journal Grade:2
CAS Journal Grade:1
Cited Count:
WoS CC Cited Count: 4
SCOPUS Cited Count: 5
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 9
Affiliated Colleges: