Super and sub-harmonic synchronization in generalized van der Pol oscillator. (November 2019) - Náprstek, Jiří; Fischer, Cyril
Highlights: Complex behavior of resonance of a generalized van der Pol system is described. The sub- and superharmonic effects in the nonlinear system are tracked. Such effects appear in aeroelasticity of large slender engineering structures, etc. Abstract: Effects of quasiperiodic beatings and sub- and super-harmonic synchronization reveal in plasma physics, optics, acoustics, neurophysiology, etc., but also very often in aero-elasticity of large slender engineering structures, e.g., bridge decks, towers, masts, high rise buildings, ropes, where these phenomena emerge in relation with vortex shedding effects. This applies mainly to quasiperiodic beatings that can be encountered especially in the lock-in regimes, when the vortex frequency becomes close to the structure eigenfrequency ω 0 with a small positive or negative detuning. This phenomenon has been thoroughly investigated for the van der Pol system in the previous study by the authors of this paper. However, experimental testing in a wind tunnel showed also other phenomena that can occur in the system resonance zone due to excitations with a multiple or rational fraction frequency leading to sub- or super-harmonic synchronization. All these effects are very dangerous from the viewpoint of reliability and safety of respective systems and hence, a robust theoretical background for design of adequate countermeasures are worthwhile to be developed. In this subsequent study the original sub- and super-synchronization effects are identified and quantified including assessment of their dynamic stability.