TY - JOUR
T1 - Analysis of internal resonance in a two-degree-of-freedom nonlinear dynamical system
AU - Dai, Honghua
AU - Wang, Xuechuan
AU - Schnoor, Matt
AU - Atluri, Satya N.
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - This study is devoted to the analysis of the three-to-one internal resonance in a two degree-of-freedom system with cubic nonlinearity. Quasi-periodic motion is found to appear in the present system with internal resonance, while it does not show up in the case without internal resonance. Both the time domain collocation method and the harmonic balance method are applied to obtain the periodic solutions, and are compared with the benchmark solution of the numerical integration method. In contrast, the quasi-periodic solutions can only be captured via the numerical integration method. A combination of the phase plane portrait, Poincare map, and the frequency spectrum are employed to identify the quasi-periodic motions. A peculiar bifurcation-of-attraction-basin phenomenon is found and demonstrated. Moreover, for strongly nonlinear system subject to high external force, a long-lived chaotic transient is observed.
AB - This study is devoted to the analysis of the three-to-one internal resonance in a two degree-of-freedom system with cubic nonlinearity. Quasi-periodic motion is found to appear in the present system with internal resonance, while it does not show up in the case without internal resonance. Both the time domain collocation method and the harmonic balance method are applied to obtain the periodic solutions, and are compared with the benchmark solution of the numerical integration method. In contrast, the quasi-periodic solutions can only be captured via the numerical integration method. A combination of the phase plane portrait, Poincare map, and the frequency spectrum are employed to identify the quasi-periodic motions. A peculiar bifurcation-of-attraction-basin phenomenon is found and demonstrated. Moreover, for strongly nonlinear system subject to high external force, a long-lived chaotic transient is observed.
KW - Bifurcation of attraction basin
KW - Chaotic transient
KW - Internal resonance
KW - Time domain collocation method
UR - http://www.scopus.com/inward/record.url?scp=85013231226&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2017.01.023
DO - 10.1016/j.cnsns.2017.01.023
M3 - Article
AN - SCOPUS:85013231226
VL - 49
SP - 176
EP - 191
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
ER -