Multi-fractality in aeroelastic response as a precursor to flutter

Abstract Wind tunnel tests on a NACA 0012 airfoil have been carried out to study the transition in aeroelastic response from an initial state characterised by low-amplitude aperiodic fluctuations to aeroelastic flutter when the system exhibits limit cycle oscillations. An analysis of the aeroelastic measurements reveals multi-fractal characteristics in the pre-flutter regime. This has not been studied in the literature. As the flow velocity approaches the flutter velocity from below, a gradual loss in multi-fractality is observed. Measures based on the generalised Hurst exponents are developed and are shown to have the potential to warn against impending aeroelastic flutter. The results of this study could be useful for health monitoring of aeroelastic structures.

[1]  H. G. E. Hentschel,et al.  Fractal nature of turbulence as manifested in turbulent diffusion , 1983 .

[2]  Thomas Andrianne,et al.  Experimental Analysis of the Bifurcation Behaviour of a Bridge Deck Undergoing Across-Wind Galloping , 2011 .

[3]  Kurt Wiesenfeld,et al.  Noisy precursors of nonlinear instabilities , 1985 .

[4]  Marty Brenner,et al.  Flutterometer: An On-Line Tool to Predict Robust Flutter Margins , 2000 .

[5]  Charles Meneveau,et al.  The fractal facets of turbulence , 1986, Journal of Fluid Mechanics.

[6]  Michael W. Kehoe,et al.  A historical overview of flight flutter testing , 1995 .

[7]  F. C. Gouldin,et al.  Chemical Closure Model for Fractal Flamelets , 1989 .

[8]  Yuan-Cheng Fung,et al.  An introduction to the theory of aeroelasticity , 1955 .

[9]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Takashi Hikihara,et al.  Bifurcation and multifractal vibration in dynamics of a high-Tc superconducting levitation system , 1997 .

[11]  E. Montroll,et al.  On 1/f noise and other distributions with long tails. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Dominique Poirel,et al.  Self-sustained aeroelastic oscillations of a NACA0012 airfoil at low-to-moderate Reynolds numbers , 2008 .

[13]  Bruce J. West,et al.  Multifractality of cerebral blood flow , 2003 .

[14]  Thomas W. Strganac,et al.  Wind Tunnel Testing of the NASA-DFRC Flutterometer using a Two DOF Wing Section , 2001 .

[15]  Elena Surovyatkina.  Prebifurcation noise amplification and noise-dependent hysteresis as indicators of bifurcations in nonlinear geophysical systems , 2005 .

[16]  F. C. Gouldin,et al.  Experimental evaluation of the fractal geometry of flamelets , 1989 .

[17]  Stuart J. Price,et al.  NON-LINEAR DYNAMICS OF AN AIR FOIL FORCED TO OSCILLATE IN DYNAMIC STALL , 1996 .

[18]  Lei-Yong Jiang,et al.  FLUTTER OF AN AIRFOIL WITH A CUBIC RESTORING FORCE , 1999 .

[19]  Vikram Pakrashi,et al.  Hurst exponent footprints from activities on a large structural system , 2013 .

[20]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[21]  Thomas Andrianne,et al.  Subcritical, nontypical and period-doubling bifurcations of a delta wing in a low speed wind tunnel , 2011 .

[22]  R. I. Sujith,et al.  Multifractality in combustion noise: predicting an impending combustion instability , 2014, Journal of Fluid Mechanics.

[23]  K. Sreenivasan,et al.  Singularities of the equations of fluid motion. , 1988, Physical review. A, General physics.

[24]  Sunetra Sarkar,et al.  Precursors to flutter instability by an intermittency route: A model free approach , 2016 .

[25]  S. J. Price,et al.  Evaluation and Extension of the Flutter-Margin Method for Flight Flutter Prediction , 1993 .

[26]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[27]  Thomas W. Strganac,et al.  Aeroelastic Response of a Rigid Wing Supported by Nonlinear Springs , 1998 .

[28]  M. Shlesinger,et al.  Fractal Time and 1/f Noise in Complex Systems , 1987 .

[29]  Walter Eversman,et al.  Chaotic and nonlinear dynamic response of aerosurfaces with structural nonlinearities , 1992 .

[30]  Andrew J. Kurdila,et al.  An Investigation of Internal Resonance in Aeroelastic Systems , 2003 .

[31]  Chunbo Xiu,et al.  Short-term prediction method of wind speed series based on fractal interpolation , 2014 .

[32]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[33]  Sunetra Sarkar,et al.  Analysis of a Nonlinear Aeroelastic System with Parametric Uncertainties Using Polynomial Chaos Expansion , 2010 .

[34]  C. Meneveau,et al.  The multifractal nature of turbulent energy dissipation , 1991, Journal of Fluid Mechanics.

[35]  B. West.  Physiology in Fractal Dimensions , 1990 .

[36]  S. J. Price,et al.  NONLINEAR AEROELASTIC ANALYSIS OF AIRFOILS : BIFURCATION AND CHAOS , 1999 .

[37]  Muhammad R. Hajj,et al.  Modeling and identification of freeplay nonlinearity , 2012 .

[38]  Stuart J. Price,et al.  The post-Hopf-bifurcation response of an airfoil in incompressible two-dimensional flow , 1996 .

[39]  H. Daniels.  Saddlepoint Approximations in Statistics , 1954 .

[40]  F. Gouldin.  An application of fractals to modeling premixed turbulent flames , 1987 .

[41]  Wenliao Du,et al.  Wavelet leaders multifractal features based fault diagnosis of rotating mechanism , 2014 .

[42]  N. H. Zimmerman,et al.  Prediction of flutter onset speed based on flight testing at subcritical speeds , 1963 .

[43]  K. Sreenivasan.  FRACTALS AND MULTIFRACTALS IN FLUID TURBULENCE , 1991 .

[44]  Stuart J. Price,et al.  Transient and Limit Cycle Simulation of a Nonlinear Aeroelastic System , 2007 .

[45]  Mihai Mihaescu,et al.  Analysis of the Turbocharger Compressor Surge Margin Using a Hurst-Exponent-based Criterion , 2016 .

[46]  Frederic M. Hoblit,et al.  Gust Loads on Aircraft: Concepts and Applications , 1988 .

[47]  Pascal Hémon,et al.  By-pass transition to airfoil flutter by transient growth due to gust impulse , 2009 .

[48]  Dewey H. Hodges,et al.  Introduction to Structural Dynamics and Aeroelasticity , 2002 .

[49]  Bruce J. West,et al.  Fractal physiology , 1994, IEEE Engineering in Medicine and Biology Magazine.

[50]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[51]  Robert H. Scanlan,et al.  A Modern Course in Aeroelasticity , 1981, Solid Mechanics and Its Applications.

[52]  W. Kinsner,et al.  Characterization and feature extraction of transient signals using multifractal measures , 1999, Engineering Solutions for the Next Millennium. 1999 IEEE Canadian Conference on Electrical and Computer Engineering (Cat. No.99TH8411).

[53]  S. Havlin,et al.  Detecting long-range correlations with detrended fluctuation analysis , 2001, cond-mat/0102214.

[54]  Satya N. Atluri,et al.  Chaos and chaotic transients in an aeroelastic system , 2014 .

[55]  Yau Shu Wong,et al.  An expert system for predicting nonlinear aeroelastic behavior of an airfoil , 2009 .

[56]  Jianmin Gao,et al.  Condition prediction of chemical complex systems based on Multifractal and Mahalanobis-Taguchi system , 2011, 2011 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering.