Analysis of a nonlinear aeroelastic system with parametric uncertainties under dynamic stall condition

Abstract

In this study, we analyse the response characteristics of a pitch-plunge aeroelastic system subjected to dynamic stall under the influence of system parametric uncertainty. These uncertainties can be caused by a lack of understanding of the system’s parameters, modelling assumptions or system-specific noise. The accuracy and safety of the structure would be enhanced by a systematic assessment of these uncertainties and their impact on the system. In order to account for this, the inflow speed ($U$), plunge to pitch frequency ratio ($\overline{\omega }$), pitch(${\zeta }_{\alpha }$), and plunge (${\zeta }_{\xi }$) damping ratio are all assumed to be uncertain parameters in the present nonlinear aeroelastic system. The uncertain system parameters fluctuations are modelled using a Karhunen–Loeve Expansion formulation and the aerodynamic loads at high angles-of-attacks during stall flutter are calculated using the Leishman–Beddoes (LB) semi-empirical dynamic stall model. Next, the response dynamics of the system under stall flutter conditions, are systematically investigated under isolated cases of deterministic, uncertainties in system parameters and stochastic input flow conditions. First, we investigate the effects of uncertain parameters individually and collectively on system response and then investigate response dynamics due to the effects of uncertain parameters combined with stochastic input flow for different time scales. In order to investigate the effect of system uncertainties on system and stall flutter bifurcation behaviour, stochastic phenomenological bifurcation analysis, is performed by examining the joint probability density function of the response quantities. Shannon entropy measure is used to capture the bifurcation boundary involving a topological change in the j-pdf. It is demonstrated that a phenomenologically rich class of stochastic responses, such as burst type intermittency, on-off intermittency, random oscillations, etc., are observed that give rise to complex cyclic stresses and can be critical to structural health. Importantly, we examine the occurrence of stall flutter events under parametric uncertainty, and fluctuating flow conditions and compare it with deterministic conditions. Finally, the associated fatigue damage is systematically investigated under uncertain parameters and fluctuating oncoming flow conditions.