Characterization of a 3DOF aeroelastic system with freeplay and aerodynamic nonlinearities – Part II: Hilbert–Huang transform Michael Candon a,⇑ , Robert Carrese a , Hideaki Ogawa a , Pier Marzocca a , Carl Mouser b , Oleg Levinski b a School of Engineering (Aerospace and Aviation), RMIT University, Melbourne, Victoria, Australia b Defence Science and Technology Group, Fishermans Bend, Victoria, Australia article info Article history: Received 18 October 2017 Received in revised form 12 April 2018 Accepted 22 April 2018 Keywords: Nonlinear aeroelasticity System identification Hilbert–Huang Transform Structural freeplay Transonic flow Nonstationary response Time–frequency analysis abstract The Hilbert–Huang Transform is used to analyze the nonlinear aeroelastic response of a 2D 3DOF aeroelastic airfoil system with control surface freeplay under transonic flow condi- tions. Both static and dynamic aerodynamic conditions, i:e:, for accelerating freestream speed, are considered using a linearized aerodynamic model. The main aim of this paper is to provide an in-depth physical understanding of the observed transition between peri- odic and aperiodic behavior, and the presence of a stable periodic region well below the domain characterized by stable limit cycles. Physical insights towards the forward and backward abrupt transition between aperiodic/chaotic and periodic behavior types appear to be the result of an internal resonance (IR) phenomenon between linear modes followed by a lock-in between linear and nonlinear modes. More specifically, initially a 2:1 IR between linear modes leads to a shift in the frequency composition and dynamic behavior of the system. A secondary effect of the IR can be observed immediately after the exact point of 2:1 IR such that a nonlinear mode locks into a subharmonic of the linear mode which in-turn drives a finite stable periodic region. Crown Copyright Ó 2018 Published by Elsevier Ltd. All rights reserved. 1. Introduction Structural and aerodynamic nonlinearities in transonic aeroelastic systems can introduce a range of nonlinear phenom- ena which cause the behavior of the aeroelastic system to vary significantly from that of a linear system. More specifically, the phenomena observed may include bifurcations, chaotic/quasi-period response, limit cycle oscillation (LCO) and reduced flutter instability boundary. All of these phenomena induce cyclic loading on the airframe which can lead to fatigue and hence reduce the operational lifetime of aircraft. Furthermore, in extreme cases these phenomena (LCO in particular) can cause fatigue or catastrophic failure. Airframe vibration can also interfere with the with avionic systems. This can be prob- lematic for smart ordnance and scientific payloads which may contain onboard guidance systems and/or advanced imaging/ sensory technology. Finally, intense vibration can lead to poor handling qualities and difficulty for the pilot in reading flight instrumentation, which is more pertinent to defense based fighter aircraft in atypical maneuvers. Expanding on the nonlinear phenomena mentioned above, internal resonance (IR) is one of which has been studied exten- sively for nonlinear mechanical systems in general, however, has seen limited attention for nonlinear aeroelastic systems, https://doi.org/10.1016/j.ymssp.2018.04.039 0888-3270/Crown Copyright Ó 2018 Published by Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: candon.michael@rmit.edu.au (M. Candon), robert.carrese@rmit.edu.au (R. Carrese), hideaki.ogawa@rmit.edu.au (H. Ogawa), pier. marzocca@rmit.edu.au (P. Marzocca), Carl.Mouser@dsto.defence.gov.au (C. Mouser), Oleg.Levinski@dsto.defence.gov.au (O. Levinski). Mechanical Systems and Signal Processing 114 (2019) 628–643 Contents lists available at ScienceDirect Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp