ORIGINAL PAPER Stability analysis of whirl flutter in rotor-nacelle systems with freeplay nonlinearity Christopher Mair . Branislav Titurus . Djamel Rezgui Received: 16 July 2020 / Accepted: 29 January 2021 / Published online: 27 February 2021 Ó The Author(s) 2021 Abstract Tiltrotor aircraft are growing in preva- lence due to the usefulness of their unique flight envelope. However, aeroelastic stability—particularly whirl flutter stability—is a major design influence that demands accurate prediction. Several nonlinearities that may be present in tiltrotor systems, such as freeplay, are often neglected for simplicity, either in the modelling or the stability analysis. However, the effects of such nonlinearities can be significant, sometimes even invalidating the stability predictions from linear analysis methods. Freeplay is a nonlinear- ity that may arise in tiltrotor nacelle rotation actuators due to the tension–compression loading cycles they undergo. This paper investigates the effect of a freeplay structural nonlinearity in the nacelle pitch degree of freedom. Two rotor-nacelle models of contrasting complexity are studied: one represents classical whirl flutter (propellers) and the other captures the main effects of tiltrotor aeroelasticity (proprotors). The manifestation of the freeplay in the systems’ dynamical behaviour is mapped out using Continuation and Bifurcation Methods, and consequently the change in the stability boundary is quantified. Furthermore, the effects on freeplay behaviour of (a) model complexity and (b) deadband edge sharpness are studied. Ultimately, the freeplay nonlinearity is shown to have a complex effect on the dynamics of both systems, even creating the possibil- ity of whirl flutter in parameter ranges that linear analysis methods predict to be stable. While the size of this additional whirl flutter region is finite and bounded for the basic model, it is unbounded for the higher complexity model. Keywords Whirl flutter  Continuation and bifurcation methods  Nonlinear aeroelasticity Abbreviations VTOL Vertical Take-Off and Landing V/STOL Vertical and/or Short Take-Off and Landing CBM Continuation and Bifurcation Methods LCO Limit Cycle Oscillation DoF Degree of Freedom 1 Introduction Tiltrotor aircraft such as the XV-15 shown in Fig. 1 aim to combine the speed and range of turboprop aircraft with the VTOL capabilities of helicopters. C. Mair (&)  B. Titurus  D. Rezgui Department of Aerospace Engineering, University of Bristol, Queens Building, Bristol, UK e-mail: chris.mair@bristol.ac.uk B. Titurus e-mail: brano.titurus@bristolac.uk D. Rezgui e-mail: djamel.rezgui@bristol.ac.uk 123 Nonlinear Dyn (2021) 104:65–89 https://doi.org/10.1007/s11071-021-06271-z