Analysis of a piecewise linear aeroelastic system with and without tuned vibration absorber

Abstract

The dynamics of a two-degrees-of-freedom (pitch–plunge) aeroelastic system is investigated. The aerodynamic force is modeled as a piecewise linear function of the effective angle of attack. Conditions for admissible (existing) and virtual equilibria are determined. The stability and bifurcations of equilibria are analyzed. We find saddle-node, border collision and rapid bifurcations. The analysis shows that the pitch–plunge model with a simple piecewise linear approximation of the aerodynamic force can reproduce the transition from divergence to the complex aeroelastic phenomenon of stall flutter. A linear tuned vibration absorber is applied to increase stall flutter wind speed and eliminate limit cycle oscillations. The effect of the absorber parameters on the stability of equilibria is investigated using the Liénard–Chipart criterion. We find that with the vibration absorber the onset of the rapid bifurcation can be shifted to higher wind speed or the oscillations can be eliminated altogether.

Analysis of a Mass-Spring-Relay System With Periodic Forcing

“…By varying the forcing frequency ω three types of bifurcations occur: saddle-center, supercritical pitchfork bifurcation (two centers and a saddle point) and discontinuity induced bifurcation. At the discontinuity induced bifurcation two fixed points disappear, similarly as in [38].…”

Analysis of a mass-spring-relay system with periodic forcing

“…By varying the forcing frequency ω three types of bifurcations occur: saddle-center, supercritical pitchfork bifurcation (two centers and a saddle point) and discontinuity induced bifurcation. At the discontinuity induced bifurcation two fixed points disappear, similarly as in [44].…”

Analytical Study of Series Solutions for the ‘Nonlinear Mechanical System’ with Stability Analysis

“…However, any normal nonlinear system can be realized using some piecewise linear model which is discovered at least 70 years back. Lelkes, J. et al [29] explained the entire operation of a typical nonlinearly coupled system using the concept of piece linear model. This paper basically tells that, whatever nay be the complexity of a system, if we blindly apply the rule of piecewise linear model, we can get the approximated result of a nonlinear system.…”