Nonlinear combination parametric resonance of axially accelerating viscoelastic strings constituted by the standard linear solid model

Nonlinear combination parametric resonance is investigated for an axially accelerating viscoelastic string. The governing equation of in-planar motion of the string is established by introducing a coordinate transform in the Eulerian equation of a string with moving boundaries. The string under investigation is constituted by the standard linear solid model in which the material, not partial, time derivative was used. The governing equation leads to the Mote model for transverse vibration by omitting the lo...     

Global view of Hopf bifurcations of a van der Pol oscillator with delayed state feedback

This paper presents both analytical and numerical studies on the global view of Hopf bifurcations of a van der Pol oscillator with delayed state feedback. Based on a detailed analysis of the stability switches of the trivial equilibrium of the system, the stability charts are given in a parameter space consisting of the time delay and the feedback gains. The center manifold reduction and the normal form method are used to study Hopf bifurcations with respect to the time delay. To gain an insight into the pe...