ISSN:
1573-269X
Keywords:
Principal resonance
;
nonlinear system
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The principal resonance of a single-degree-of-freedom system with two-frequency parametric and self-excitations is investigated. In particular, the case in which the parametric excitation terms with close frequencies is examined. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. Qualitative analyses are employed to study the behaviour of steady state responses, limit cycle responses and 2-torus responses, including their stability and bifurcation. The effects of damping, detuning, and magnitudes of self-excitation and parametric excitations are analyzed. The theoretical analyses are verified by numerical integration results of the governing equation and the modulation equations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00045437
