AN EXPLICATION OF AIRFOIL SECTION BENDING-TORSION FLUTTER

This thesis examines the dynamic instability known as flutter using a two-degree-of-freedom airfoil section model in both quasi-steady and unsteady flow. It explains the fundamental forces and moments involved in the bending-torsion flutter of an airfoil section, and demonstrates a solution method for determining the critical flutter frequency and speed for both flow cases. Additionally, through the use of a programmed Mathcad 11 worksheet, it evaluates the flutter characteristics of six example sections, illustrating the effects of the elastic, inertial and aerodynamic properties of an airfoil section. For each section, a parametric study of the effect of the section Center of Gravity position along the section chord is performed. The flutter frequency and speed are calculated using both quasi-steady and unsteady aerodynamic forces and moments, and the results compared. Software used was MathSoft Mathcad 11, Microsoft Word and Intergraph Smart Sketch LE.

Author: Wheeler, Philip Curtis

Source: University of Maryland

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Contents

Chapter 1.0: Introduction
1.1 Motivation for the thesis
1.2 Objectives of the thesis
1.3 Thesis Organization
1.4 Chapter Summary
Chapter 2.0: A Fundamental Description of Flutter
2.1 Types of Aeroelasticity
2.2 Distinctive Characteristics of Classical Airfoil Section Flutter
2.3 Types of Airfoil Section Flutter
2.3.1 Vibratory modes
2.3.2 Examples of Airfoil Section Flutter withIncreasing Numbers of Types of Motion
2.4 Bending-torsion Flutter of an Airfoil Section as Described in this Thesis
2.4.1 Defining the Degrees of Freedom
2.5 Chapter Summary
Chapter 3.0: Solutions for the Flutter Frequency and Speed
3.1 Derivation of the Lagrange Equations of Motion
3.1.1 Strain Energy of Elastic Forces
3.1.2 Kinetic Energy of Inertial Forces
3.1.3 Generalized Forces
3.2 Writing the Lagrange Equations of Motion
3.3 Energy Transfer and Coupling
3.3.1 Energy Transfer from the Airstream
3.3.2 Inertial coupling due to Center of Gravity location
3.3.3 Phasing of the Motions
3.3.4 Aerodynamic Coupling via Phasing
3.4 Frequency Coalescence
3.5 Phasing Diagrams
3.5.1 Stable Condition
3.5.2 Critical Flutter Condition
3.5.3 Full Flutter Condition
3.6 Aerodynamic Forces
3.6.1 Fluid Properties
3.6.2 Basic strip theory
3.6.3 Two Dimensional Airfoil Section Properties
3.6.4 Development of the Quasi-steady Aerodynamic Forces
3.6.4.1 Aerodynamic Moment
3.6.4.2 Forming the Lagrange Equations of Motion using Quasi-steady AerodynamicForces
3.6.5 Development of the Unsteady Aerodynamic Forces
3.6.5.1 Forming the Lagrange Equations
of Motion using Unsteady Aerodynamic Forcesand Moments
3.6.5.1.1 Finding the flutter frequency and speed – Theodorsen’s Method
3.6.5.1.2 Finding the flutter frequency and speed – Materiel Center Method
3.7 Solution of the Double Eigenvalue Problem
3.7.1 Placing the System in Simple Harmonic Motion
3.7.1.1 Flutter Solution in the case of Quasi-steady Aerodynamic Forces
3.7.1.2 Flutter Solution in the Case of Unsteady Aerodynamic Forces and Moments
3.8 Chapter Summary
Chapter 4.0: Calculation of Flutter Properties by Mathcad Worksheet
4.1 Mathcad Worksheet Methodology
4.1.1 Program inputs
4.1.2 Supporting calculations
4.1.2.1 Quasi-steady Case
4.1.2.2 Unsteady Case
4.1.3 Primary calculations
4.1.3.1 Quasi-steady Case
4.1.3.2 Unsteady Case
4.1.4 Program Outputs
4.2 Example Calculations
4.2.1 Example One: Ryan NYP prototype
4.2.1.1 Inputs, Intermediate Calculations and Output
4.2.1.2 Section Characteristics
4.2.1.3. Flutter Calculations for the Quasi-steady Case
4.2.1.4 Flutter Calculations for the Unsteady Case
4.2.1.5 Comparison of Results in the Quasi-steady and Unsteady Cases
4.2.1.6 CG Variation Survey
4.2.2 Example Two: Ryan NYP Final Design
4.2.2.1 Inputs, Intermediate Calculations and Outputs
4.2.2.2 Section Characteristics
4.2.2.3. Flutter Calculations for the Quasi-steady Cas
4.2.2.4 Flutter Calculations for the Unsteady Case
4.2.2.5 Comparison of Results in the Quasi-steady and Unsteady Cases
4.2.2.6 CG Variation Survey
4.2.3 Example Three: MD3-160 Aircraft Section(Usmani, Ho, 2003)
4.2.3.1 Inputs, Intermediate Calculations and Outputs
4.2.3.2 Section Characteristics
4.2.3.3. Flutter Calculations for the Quasi-steady Case
4.2.3.4 Flutter Calculations for the Unsteady Case
4.2.3.5 Comparison of Results in the Quasi-steady and Unsteady Cases
4.2.3.6 Altitude Variation Survey
4.2.2.7 CG Variation Survey
4.2.4 Example Four: Example from NACA TechnicalReport 685, (Theodorsen, Garrick, 1938)
4.2.4.1 Inputs, Intermediate Calculations
and Outputs 4.2.4.2 Section Characteristics
4.2.4.3. Flutter Calculations for the
Quasi-steady Case
4.2.4.4 Flutter Calculations for the
Unsteady Case
4.2.4.5 Comparison of Results in the Quasi-
steady and Unsteady Cases
4.2.4.6 CG Variation Survey
4.2.5 Example Five: Example from USAAF Technical
Report 4798, (Smilg, Wasserman, 1942)
4.2.5.1 Inputs, Intermediate Calculations
and Outputs
4.2.5.2 Section Characteristics
4.2.5.3. Flutter Calculations for the
Quasi-steady Case
4.2.5.4 Flutter Calculations for the
Unsteady Case
4.2.5.5 Comparison of Results in the Quasi-
steady and Unsteady Cases
4.2.5.6 CG Variation Survey
4.2.6 Example Six: Example from Reference 5,
page 203 (Scanlan, Rosenbaum, 1968)
4.2.6.1 Inputs, Intermediate Calculations
and Outputs
4.2.6.2 Section Characteristics
4.2.6.3. Flutter Calculations for the
Quasi-steady Case
4.2.6.4 Flutter Calculations for the
Unsteady Case
4.2.6.5 Comparison of Results in the Quasi-
steady and Unsteady Cases
4.2.6.6 CG Variation Survey
4.3 Chapter Summary
Appendix
References