The phenomenon of multiplicative noise induced intermittency (mNII) observed due to random temporal fluctuations in the system parameters of nonlinear dynamical systems is investigated using maps. Generic conditions for the onset and disappearance of mNII are derived. The role of correlation in the noise is investigated. The phenomenon of mNII is interpreted in terms of stochastic bifurcations as well. The developments are verified through numerical results for a set of simple1-d maps. Further, through a numerical example involving an aeroelastic system, it is shown that the proposed results are applicable for analysis of complicated engineering systems by considering Poincáre maps from the times histories of the response. © 2019 Elsevier Ltd

Sunetra Sarkar

Department of Aerospace Engineering

Sayan Gupta

Department of Applied Mechanics

Santosh Krishna Kumar

Bifurcation (mathematics)

Dynamical systems

Nonlinear dynamical systems

Numerical methods

Stochastic systems

AEROELASTIC SYSTEM

Engineering systems

Intermittency

multiplicative noise

Numerical results

STOCHASTIC BIFURCATION

TEMPORAL FLUCTUATION

Phase noise

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IIT Madras

International Journal of Non-Linear Mechanics

Fluid–elastic systems nearing dynamic instabilities are known to be sensitive to fluctuations in fluid flow. A cantilever plate in axial flow with random temporal fluctuations, is examined numerically for its dynamical behaviour. The numerical model comprises of a nonlinear structural model for the flexible plate, coupled with unsteady lumped vortex model for the fluid forces. As the mean flow velocity is increased, the system transitions to limit cycle oscillations from a state of rest, through a regime of intermittent oscillations. The conditions for onset and disappearance of intermittency are discussed and are interpreted using stochastic bifurcation theories. While the onset of intermittency is found to be unaffected by the time scales of the flow fluctuations, they are observed to affect the length of the intermittency regime. The effect of plate flexibility on intermittency is also discussed. © 2019 Elsevier Ltd

Journal of Fluids and Structures

Intermittency in a cantilever plate in a randomly fluctuating fluid flow

Coupling nonlinear dynamical systems can lead to a host of phenomena, one of which leads to the complete cessation of their oscillations. This phenomenon is referred to as amplitude death (AD) in the dynamical systems literature. Recently, there is a growing interest to mitigate oscillatory or dynamic instabilities in a variety of engineering systems using AD. Deriving impetus from the same, we investigate the possibility of cessation of oscillatory instabilities in aeroelastic systems using the concept of AD. In specific, the suppression of flutter instability that arises in aeroelastic systems due to highly nonlinear fluid–structure interactions is investigated from the purview of AD. To that end, we consider two identical airfoils that are exposed to input fluid forces along the axial directions. The airfoils, via translational and rotational springs, are allowed to oscillate in plunge and pitch degrees of freedom. To augment the findings to in-field scenarios, we consider the individual cases of the input flow to be either uniform (deterministic) or possess randomly time varying components, respectively. To promote coupled interactions, the airfoils are coupled using a linear torsional spring. The coupled interaction of the airfoils at the flutter regime are then studied by obtaining the pitch and plunge responses. Further, the strength of the coupling and the time delay between the airfoils are systematically varied to investigate its effect on the regime of AD. The ability of AD to suppress flutter instability and thereby serve as a possible flutter suppression mechanism in both deterministic and stochastic input flow cases is then demonstrated. Finally, the phase delay values between the airfoils is computed to heuristically present a relationship between the coupling parameters and the post coupling signatures. © 2020 Elsevier Ltd

Investigating amplitude death in a coupled nonlinear aeroelastic system

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

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

Physical mechanism of intermittency route to aeroelastic flutter

This study carried out investigations on the bifurcation characteristics of a Duffing-Van der Pol (DVDP) oscillator subjected to white noise excitations. Dynamical (or D-) bifurcations are characterised by dramatic changes in the dynamical behaviour leading to topological changes in the phase portrait. An additional mode of bifurcation - phenomenological (or P-) bifurcation, is observed in stochastically excited systems when the stationary joint probability density function of the state variables undergo topological changes in the probability space. While D-bifurcation analysis is quantified in terms of the sign changes in the largest Lyapunov exponent, P-bifurcation analysis is usually qualitative and through visual inspection. In this study, a new quantitative measure for P-bifurcations based on the Shannon entropy is proposed. A comparison of the parameter regimes of the noisy DVDP oscillator identified by the three bifurcation methodologies have been presented. © 2016 Elsevier Ltd. All rights reserved.

Probabilistic Engineering Mechanics

Investigations on the bifurcation of a noisy Duffing-Van der Pol oscillator

The aeroelastic response of a NACA 0012 airfoil in the flow regimes prior to flutter is investigated in a wind tunnel. We observe intermittent bursts of periodic oscillations in the pitch and plunge response, that appear in an irregular manner from a background of relatively lower amplitude aperiodic fluctuations. As the flow speed is increased, the intermittent bursts last longer in time until eventually transitioning to a fully developed periodic response, indicating the onset of flutter. The repeating patterns in the measured response are visualized using recurrence plots. We show that statistics of the recurrence states extracted from these plots can be used to develop model-free precursors that forewarn an impending transition to flutter, well before its onset. © 2015 Elsevier Ltd.

Fulltext

Precursors to flutter instability by an intermittency route: A model free approach

Advances in Space Research

On–off intermittency and spatiotemporal chaos in three-dimensional Rayleigh–Bénard convection

Multiplicative noise induced intermittency in maps

Journal	Data powered by TypesetInternational Journal of Non-Linear Mechanics
Publisher	Data powered by TypesetElsevier Ltd
ISSN	00207462
Open Access	No