# Two-domain and three-domain limit cycles in a typical aeroelastic system with freeplay in pitch

## TL;DR

This paper investigates the existence and characteristics of two-domain and three-domain limit cycle oscillations in a typical aeroelastic system with freeplay in pitch, combining theoretical analysis and wind tunnel experiments.

## Contribution

It demonstrates the existence of two- and three-domain limit cycles in aeroelastic systems with freeplay through theoretical derivation and experimental validation.

## Key findings

- Two-domain limit cycles can result from grazing bifurcation.
- Limit cycle amplitudes and frequencies can be predicted by equivalent linearization.
- Experimental results agree with theoretical predictions.

## Abstract

Freeplay is a significant source of nonlinearity in aeroelastic systems and is strictly regulated by airworthiness authorities. It splits the phase plane of such systems into three piecewise linear subdomains. Depending on the location of the freeplay, limit cycle oscillations can result that span either two or three of these subdomains. The purpose of this work is to demonstrate the existence of two-domain cycles both theoretically and experimentally. A simple aeroelastic system with pitch, plunge and control deflection degrees of freedom is investigated in the presence of freeplay in pitch. It is shown that two-domain and three-domain cycles can result from a grazing bifurcation and propagate in the decreasing airspeed direction. Close to the bifurcation, the two limit cycle branches interact with each other and aperiodic oscillations ensue. Equivalent linearization is used to derive the conditions of existence of each type of limit cycle and to predict their amplitudes and frequencies. Comparisons with measurements from wind tunnel experiments demonstrate that the theory describes these phenomena with accuracy.