Short Course on Aeroelasticity; Theory and Practice Presented at SFTE 2017 International Symposium The Henderson Beach Resort Destin, Florida 30 October 2017 Vin Sharma, PhD. Material presented here is extracted from the Aeroelasticity course offered at the University of Florida Inertial Forces Static: Deformation, Divergence, & Control Reversal Dynamic Instability: Flutter Dynamic Response: Gust, Buffet; Aeroservoelasticity with Flight Control System
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Short Course on
Aeroelasticity; Theory and PracticePresented at SFTE 2017 International SymposiumThe Henderson Beach ResortDestin, Florida30 October 2017
Vin Sharma, PhD.
Material presented here is extracted from the Aeroelasticity course offered at the University of Florida Inertial Forces
Divergence is an instability issue; The wing generates more lift due to elastic twist than the structure canresist; For a small input to 𝛼𝛼0, divergence leads to a large angle of twist.
Aileron effectiveness is where the control surface fails to develop the desired increment in lift; above the reversal speed, a control input 𝛿𝛿𝑎𝑎produces lift or moment opposite to that intended.
Elastic wing twist in response to increased pitching moment
TE down aileron deflection increases the camber Increased lift Increased pitching down moment (negative) Supposed to generate the desired rolling moment about x-axis
At critical dynamic pressure, loss of lift due to wing twist counters any lift required due to aileron deflection
Vortex Shedding & DownwashDelay in build of full strength of the bound vortex leading to lift deficiencyTheodorsen’s function accounts for this lift deficiency
�𝛼𝛼 𝑅𝑅 = 𝐶𝐶 𝑘𝑘 α0 + 𝐴𝐴𝑘𝑘𝑏𝑏𝑧𝑧0 + 𝐴𝐴
𝑘𝑘2α0 𝑒𝑒𝑜𝑜𝜔𝜔𝑒𝑒
𝐶𝐶 𝑘𝑘 = 𝐺𝐺 𝑘𝑘 + 𝐴𝐴𝐺𝐺 𝑘𝑘 =𝐾𝐾1 𝐴𝐴𝑘𝑘
𝐾𝐾0 𝐴𝐴𝑘𝑘 + 𝐾𝐾1 𝐴𝐴𝑘𝑘Modified Bessel Functions of the second kind
Unsteady aero force vector provides the forcing function o An airfoil of flat plate typeo Strip theory; each strip independent of the others (aerodynamically)o Simple harmonic motiono Two degrees of freedom model; plunge and pitcho Origin at mid-chord
Dynamic equations of motion in generalized modal coordinate systemGeneralize the forcing function Formulate a new eigenvalue problem with complex coefficients Solve for complex eigenvalues and eigenvectorsObtain the frequencies and associated damping ratios as a function of velocityDetermine the flutter instability by observing damping going from negative to
positive at the flutter speedCompute the complex flutter mode shape
Big Picture of Flutter AnalysisDynamic Aeroelasticity
M= 4.0/386 lb-sec^2/in of unit spanIcg = 0.3454 lb-sec^2-in about cg, per unit spanc_bar = 20 inches chordc = -0.35, fraction of semi-chord b; elastic axis locatione = -0.35, fraction of semi-chord; cg of the sectionKz=2.0 lbf/in; vertical spring rateKrot= 300.0 in-lb/rad; rotation spring raterho_SL = 1.146E-7 lbs-sec^2/in^4, Air mass density at sea level
‘Introduction to Aircraft Aeroelasticity and Loads’, Jan Wright and Jonathan Cooper, John Wiley & Sons
‘Introduction to Structural Dynamics and Aeroelasticity’, Hodges & Pierce; Cambridge University Press
‘An Introduction to the Theory of Aeroelasticity’, YC Fung; Dover Publications ‘Aeroelasticity’, Bisplinghoff, Ashley, & Halfman; Addison Wesley Publishing Company ‘Introduction to the study of Aircraft Vibration and Flutter’, Scanlan and Rosenbaum; The
McMillan Company ‘Theoretical and Computational Aeroelasticity’, Rodden ‘Fundamentals of Structural Dynamics’, Roy Craig, Andrew Kurdila; John Wiley & Sons Prof. Weisshaar’s Aeroelasticity class notes