INTRODUCTION AEROELASTICITY: Interaction between aerodynamic forces and structural motion. FLUTTER INSTABILITY:

1. Case Case DOF Combination Flutter-Derivatives Extracted Noise-to-Signal Ratio Diagonal Stiffness Terms Non-Diagonal Stiffness Terms Diagonal Damping Terms Non-Diagonal Damping Terms 1-DOF (ILS) 1 1-DOF Vertical (V) H1*, H4* 20% 0.02 - 1.67 - 2 2-DOF (MITD) 1-DOF Torsional (T) A2*, A3* 5% 0.19 2.22 0.81 2.02 2-DOF (MITD) 3 1-DOF Lateral (L) P1*, P4* 10% 0.37 4.47 1.60 2.92 2-DOF (ILS) 4 2-DOF Vertical+Torsional (V&T) H1*, H2*, H3*, H4*, A1*, A2*, A3*, A4* 10% 0.06 0.82 0.56 1.41 5 2-DOF (ILS) 2-DOF Vertical+Lateral (V&L) H1*, H4*, H5*, H6*, P1*, P4*, P5*, P6* 20% 0.13 0.96 2.01 5.04 6 3-DOF (ILS) 2-DOF Lateral+Torsional (L&T) P1*, P4*, P2*, P3*, A2*, A3*, A5*, A6* 5% 0.44 1.51 2.55 5.99 7 3-DOF (ILS) 3-DOF All the 18 flutter derivatives 10% 0.89 2.34 4.83 8.43 U , M h, L OBTAIN NOISY DISPLACEMENT TIME HISTORIES [SIZE n x (2N+2)] p, D BUILD LOW PASS ‘BUTTERWORTH’ FILTER PERFORM ZERO-PHASE DIGITAL FILTERING OF DISPLACEMENTS OBTAIN VELOCITY AND ACCELERATION TIME HISTORIES BY FINITE DIFFERENCE FORMULATION (EACH HAVING SIZE n x 2N ) PERFORM ‘WINDOWING’ TO OBTAIN NEW SETS OF DISPLACEMENT, VELOCITY, ACCELERATION TIME HISTORIES (EACH HAVING SIZE n x N) CONSTRUCT (EACH HAVING SIZE 2n x N) GENERATE A MATRIX BY LEAST SQUARES (SIZE 2n x 2n) USING INITIAL CONDITIONS SIMULATE, UPDATE A MATRIX BY LEAST SQUARES (SIZE 2n x 2n): Vertical & Horizontal Force Transducers ITERATE TILL THE CONVERGENCE OF A MATRIX CALCULATE FLUTTER DERIVATIVES FROM ELEMENTS OF A MATRIX EXTRACTED AT ZERO AND VARIOUS NON-ZERO WIND SPEEDS Identification of Eighteen Flutter DerivativesArindam Gan Chowdhury a and Partha P. Sarkar ba Graduate Research Assistant, Department of Aerospace Engineering, Iowa State University, Ames, Iowa, USAb Associate Professor/Wilson Chair, Departments of Aerospace Engineering and Civil, Construction and Environmental Engrg., Iowa State University, Ames, Iowa, USA • INTRODUCTION • AEROELASTICITY: • Interaction between aerodynamic forces and structural motion. • FLUTTER INSTABILITY: • Self-excited oscillation of a structural system (e.g., flutter-induced failure of the Tacoma Narrows Bridge in 1940). • FLUTTER ANALYSIS: • Flutter speed is calculated using frequency-dependant Flutter Derivatives that are experimentally obtainedfrom wind • tunnel testing of section models. EXPERIMENTAL SETUP (WiST Laboratory, ISU) • ALGORITHM FOR ILS METHOD: FLUTTER DERIVATIVE FORMULATION • SECTION MODEL FOR WIND TUNNEL TESTING: Three-DOF Elastic Suspension System • AEROELASTIC FORCE VECTOR: Torsional DOF Assembly & Torque Sensor RESULTS DOF Combinations and Corresponding Flutter Derivatives Obtained where,  is air density; U is the mean wind velocity; B is the width of section model; K = B /U is the reduced frequency Non-dimensional aerodynamic coefficients Hi, Aiand Pi, i = 1-6, are called the Flutter Derivatives. Flutter Derivatives evolve as functions of reduced velocity, U / n B = 2/K (n is frequency;  is circular frequency). • AEROELASTICALLY MODIFIED EQUATIONS OF MOTION: • STATE-SPACE FORMULATION: Average Percentage Errors for Numerical Simulations Ceff and Keff are the aeroelastically modified effective damping and stiffness matrices. Flutter Derivatives are extracted by identifying elements of effective damping & stiffness matrices at zero & various non-zero wind speeds. REFERENCES: • Sarkar, P.P., Jones, N.P., Scanlan, R.H. (1994). “Identification of Aeroelastic Parameters of Flexible Bridges”. J. of Engineering Mechanics, ASCE 1994, 120 (8), pp. 1718-1742. • Gan Chowdhury, A., Sarkar, P.P. (2003). “A New Technique for Identification of Eighteen Flutter Derivatives using Three-Degrees-of-Freedom Section Model”. Accepted 21 July 2003, Engineering Structures. • Sarkar, P.P., Gan Chowdhury, A., Gardner, T. B. (2003). “A Novel Elastic Suspension System for Wind Tunnel Section Model Studies”. Accepted 12 September 2003, J. of Wind Engineering and Industrial Aerodynamics. • Gan Chowdhury, A., Sarkar, P.P. (2003). “Identification of Eighteen Flutter Derivatives”. Proceedings of the 11th International Conference on Wind Engineering , Lubbock, Texas, USA, pp. 365-372. NEW SYSTEM IDENTIFICATION (SID) TECHNIQUE • MOTIVATION: Extraction of all eighteen flutter derivatives required development of a robust SID technique that will efficiently work with noisy signal outputs from a three-degree-of-freedom dynamic system. • ITERATIVE LEAST SQUARE METHOD (ILS METHOD): A new SID technique was developed for the extraction of flutter derivatives from free vibration displacement time histories obtained from a section model testing. • SAMPLE DISPLACEMENT TIME HISTORY WITH NOISE/SIGNAL RATIO OF 20% OBTAINED NUMERICALLY TO TEST THE NEW SID TECHNIQUE: (Note: Modified Ibrahim Time Domain (MITD) method was developed by Sarkar, Jones, and Scanlan in1994) • EIGHTEEN FLUTTER DERIVATIVES OF NACA 0020 AIRFOIL: • DISPLACEMENT TIME HISTORY AS ABOVE WITHOUT NOISE MATCHES WELL WITH THE FILTERED ONE (SEE ALGORITHM):