The interaction of an elastic structure such as an airfoil and fluid flow can give rise to nonlinear phenomenon such as limit cycle oscillations, period doubling or chaos. These phenomena are indicated by a change in the stability behaviour of the dynamical known as bifurcations. Presence of viscous effects in the fluid flow can give rise to flow separation which causes a stability change in the system that is identified to happen via a Hopf bifurcation. In such cases, the airfoil exhibits limit cycle oscillations which are torsionally dominant, known as stall flutter. Despite identifying the route to stall flutter under uniform flow conditions, investigating a stall problem under stochastic wind has received minimal attention. The ability of fluctuating flows to change the stability boundaries and disrupt the route to flutter, compels the need to carry out a stochastic analysis of stalling airfoils. Study of stall flutter in such systems under the influence of a time varying sinusoidal gust is undertaken and the route to flutter is identified by carrying out a stochastic bifurcation analysis. © The Authors, published by EDP Sciences, 2018.

J Venkatramani

Mechanical Engineering

(SoE) School of Engineering

Bethi R.V.

Gali S.V.R.

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Aeroelastic systems with hardening nonlinearity exhibit supercritical Hopf bifurcation when the flow velocity exceeds a critical velocity leading to self-sustaining large amplitude limit cycle oscillations known as flutter. This study investigates the effects of irregular fluctuations in the flow on the dynamical stability characteristics of a two-degree-of-freedom pitch-plunge aeroelastic system with hardening nonlinearity. Dynamical or D-bifurcations are investigated through the computation of the largest Lyapunov exponent, while phenomenological or P-bifurcation analysis is carried out by examining the structure of the joint probability density function of the response quantities and their instantaneous time derivatives. The qualitative nature of P-bifurcation analysis makes it difficult to pinpoint the regimes of different response dynamics. In the light of this difficulty, a quantitative analysis using the Shannon entropy measure has been undertaken to quantify the P-bifurcation regime. This regime is shown to be coincident with the intermittency regime observed in the response time histories prior to flutter oscillations in fluctuating flows. © 2018, Springer Science+Business Media B.V., part of Springer Nature.

Nonlinear Dynamics

Intermittency in pitch-plunge aeroelastic systems explained through stochastic bifurcations

Introduction to Nonlinear Aeroelasticity

Intermittency has been observed in the response of aeroelastic systems in the presence of flow fluctuations. This study focuses on developing an understanding of the physical mechanisms that lead to intermittency in such systems. Specifically, the role of time scales of the input flow fluctuations is investigated. Numerical investigations reveal that flow fluctuations with predominantly long time scales in the pre-flutter regime lead to “on–off” type intermittency. On the other hand, rapid fluctuations constituting of small time scales lead to another qualitatively different intermittency, which is referred to in this paper as “burst” type intermittency. It is further shown that the unsteady wake effects play a crucial role in the burst type intermittency. Measures derived from time series analysis of the aeroelastic response are proposed to identify the different dynamical states quantitatively. © 2017 Elsevier Ltd

Journal of Fluids and Structures

Physical mechanism of intermittency route to aeroelastic flutter

Stall induced oscillations are likely instabilities in modern wind engineering systems. For their robust design, it is crucial to take parametric and load uncertainties into consideration. Presently, study of a stall flutter system under the influence of random gust is undertaken using the probability density evolution method, and qualitative changes in the response output are presented. This probability based approach when compared with a spectral tool called polynomial chaos expansion, shows better accuracy for the same level of discretisation. © 2015 Elsevier Ltd.