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Indexed by:期刊论文

Date of Publication:2012-12-01

Journal:INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS

Included Journals:SCIE、EI、Scopus

Volume:9

Issue:4

ISSN No.:0219-8762

Key Words:Translating strings; aerodynamic vibration; bifurcation; stability

Abstract:The nonlinear vibration of transverse motion of a translating string excited by steady wind force is investigated in this paper. The stability of the equilibrium configuration is analyzed and the generation of limit cycles via multiple Hopf bifurcations is presented. Single-, double-, and quadruple-Hopf bifurcations are determined in the parametric space. The limit-cycle response is solved through the method of Incremental Harmonic Balance, with its stability determined by Floquet multipliers. For the forced vibration, the coexistence of periodic and quasiperiodic motions is found with varying excitation frequency and amplitude. The Neimark-Sacker (NS) bifurcation and the flip bifurcation are demonstrated in an example. The continuation software MATCONT is adopted to identify the fold and NS bifurcations of periodic motions, as well as other codim-2 bifurcations of NS-NS, the Chenciner and the 1:1, 1:3, and 1:4 resonances. These bifurcations present the complexity of the string dynamics induced by steady wind excitations.