Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators

Abstract

The vibrating system of a class of linkage-slider structure is considered, and its initial-sensitive dynamical behaviors such as safe jump, locking instability, and chaos are studied. First, static bifurcation of the dynamical system is discussed. Then, via analyzing the effect of the external excitation on the periodic solutions under primary resonance, it is found that the change of the excitation frequency may lead to bistability and safe jump. Furthermore, it follows from the investigation of the heteroclinic bifurcation that the increase of the external excitation amplitude may lead to locking instability, chaos, and static locking. The results have some potential values in the design of geometrically nonlinear oscillators.