TY - JOUR
T1 - The chaotic response of the viscoelastic traveling string
T2 - An integral constitutive law
AU - Chen, Li Qun
AU - Wu, Jun
AU - Zu, Jean W.
PY - 2004/7
Y1 - 2004/7
N2 - This paper investigates chaotic behaviors of an axially traveling viscoelastic string with geometric nonlinearity. The stress and the strain of the viscoelastic string obey the Boltzmann superposition principle. The Galerkin method is applied to truncate a nonlinear partial-differential-integral equation governing transverse motion into a set of ordinary differential-integral equations. For the string modeled as a standard linear solid, new auxiliary variables are introduced to transform those equations into ordinary differential equations. By use of the Poincare maps, the chaotic behaviors are presented based on the numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented for varying one of the following parameter: the axial traveling speed, the amplitude of tension fluctuation, the viscoelastic exponent and coefficient of the string, while other parameters are fixed.
AB - This paper investigates chaotic behaviors of an axially traveling viscoelastic string with geometric nonlinearity. The stress and the strain of the viscoelastic string obey the Boltzmann superposition principle. The Galerkin method is applied to truncate a nonlinear partial-differential-integral equation governing transverse motion into a set of ordinary differential-integral equations. For the string modeled as a standard linear solid, new auxiliary variables are introduced to transform those equations into ordinary differential equations. By use of the Poincare maps, the chaotic behaviors are presented based on the numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented for varying one of the following parameter: the axial traveling speed, the amplitude of tension fluctuation, the viscoelastic exponent and coefficient of the string, while other parameters are fixed.
UR - http://www.scopus.com/inward/record.url?scp=1142304474&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=1142304474&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2003.10.037
DO - 10.1016/j.chaos.2003.10.037
M3 - Article
AN - SCOPUS:1142304474
SN - 0960-0779
VL - 21
SP - 349
EP - 357
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
IS - 2
ER -