Aeroelastic response and limit cycle oscillations for wing-flap-tab section with freeplay in tab

Abstract

A linear and nonlinear theoretical and experimental aeroelastic investigation of a wing-flap-tab typical section model undergoing two-dimensional incompressible airflow is described. The linear flutter velocity (LFV) and frequency are predicted using linear analysis. Then a freeplay structural nonlinearity is considered in the tab. The structural equations of motion have been coupled with Theodorsen aerodynamic theory to produce the theoretical aeroelastic model which is analyzed by a state space method to predict the LFV and flutter frequency. Linear piecewise function has been used to introduce the tab spring stiffness in the freeplay state. The ground vibration test is used to measure the model structural dynamic characteristics. Then the experimental aeroelastic model is placed in a low speed wind tunnel to measure the LFV and the limit cycle oscillation (LCO) of the physical model induced by freeplay. The root main square amplitude value of the pitch, flap pitch, tab pitch and plunge degrees of freedom of the tab nonlinearities are normalized with freeplay gap size to produce a bifurcation diagram with normalized airflow velocity as the bifurcation parameter. The results show that the LCO frequency jumps from low to high frequency at a yet higher flow velocity. At the same flow velocity, the pitch and plunge motion response amplitudes drop while the flap pitch and tab pitch degrees of freedom response amplitude increase. In general the experimental measured LCO is more complicated than the theoretically calculated LCO in terms of the harmonic content of the response. On the other hand there is good agreement between the theoretical and experimental result of the linear system as well the LCO for the tab freeplay nonlinearities.