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Introduction to Nonlinear Aeroelasticity

Book Description

Introduces the latest developments and technologies in the area of nonlinear aeroelasticity

Nonlinear aeroelasticity has become an increasingly popular research area in recent years. There have been many driving forces behind this development, increasingly flexible structures, nonlinear control laws, materials with nonlinear characteristics, etc. Introduction to Nonlinear Aeroelasticity covers the theoretical basics in nonlinear aeroelasticity and applies the theory to practical problems.

As nonlinear aeroelasticity is a combined topic, necessitating expertise from different areas, the book introduces methodologies from a variety of disciplines such as nonlinear dynamics, bifurcation analysis, unsteady aerodynamics, non-smooth systems and others. The emphasis throughout is on the practical application of the theories and methods, so as to enable the reader to apply their newly acquired knowledge.

Key features:

  • Covers the major topics in nonlinear aeroelasticity, from the galloping of cables to supersonic panel flutter.
  • Discusses nonlinear dynamics, bifurcation analysis, numerical continuation, unsteady aerodynamics and non-smooth systems.
  • Considers the practical application of the theories and methods.
  • Covers nonlinear dynamics, bifurcation analysis and numerical methods.
  • Accompanied by a website hosting Matlab code.

Introduction to Nonlinear Aeroelasticity is a comprehensive reference for researchers and workers in industry and is also a useful introduction to the subject for graduate and undergraduate students across engineering disciplines.

Table of Contents

  1. Cover
  2. Title Page
  3. Preface
  4. Dimitriadis: Nonlinear Aeroelasticity – Series Preface Oct 2016
  5. About the Companion Website
  6. 1 Introduction
    1. 1.1 Sources of Nonlinearity
    2. 1.2 Origins of Nonlinear Aeroelasticity
    3. References
  7. 2 Nonlinear Dynamics
    1. 2.1 Introduction
    2. 2.2 Ordinary Differential Equations
    3. 2.3 Linear Systems
    4. 2.4 Nonlinear Systems
    5. 2.5 Stability in the Lyapunov Sense
    6. 2.6 Asymmetric Systems
    7. 2.7 Existence of Periodic Solutions
    8. 2.8 Estimating Periodic Solutions
    9. 2.9 Stability of Periodic Solutions
    10. 2.10 Concluding Remarks
    11. References
  8. 3 Time Integration
    1. 3.1 Introduction
    2. 3.2 Euler Method
    3. 3.3 Central Difference Method
    4. 3.4 Runge–Kutta Method
    5. 3.5 Time‐Varying Linear Approximation
    6. 3.6 Integrating Backwards in Time
    7. 3.7 Time Integration of Systems with Multiple Degrees of Freedom
    8. 3.8 Forced Response
    9. 3.9 Harmonic Balance
    10. 3.10 Concluding Remarks
    11. References
  9. 4 Determining the Vibration Parameters
    1. 4.1 Introduction
    2. 4.2 Amplitude and Frequency Determination
    3. 4.3 Equivalent Linearisation
    4. 4.4 Hilbert Transform
    5. 4.5 Time‐Varying Linear Approximation
    6. 4.6 Short Time Fourier Transform
    7. 4.7 Pinpointing Bifurcations
    8. 4.8 Limit Cycle Study
    9. 4.9 Poincaré Sections
    10. 4.10 Stability of Periodic Solutions
    11. 4.11 Concluding Remarks
    12. References
  10. 5 Bifurcations of Fundamental Aeroelastic Systems
    1. 5.1 Introduction
    2. 5.2 Two‐Dimensional Unsteady Pitch‐Plunge‐Control Wing
    3. 5.3 Linear Aeroelastic Analysis
    4. 5.4 Hardening Stiffness
    5. 5.5 Softening Stiffness
    6. 5.6 Damping Nonlinearity
    7. 5.7 Two‐Parameter Bifurcations
    8. 5.8 Asymmetric Nonlinear Aeroelastic Systems
    9. 5.9 Concluding Remarks
    10. References
  11. 6 Discontinuous Nonlinearities
    1. 6.1 Introduction
    2. 6.2 Piecewise Linear Stiffness
    3. 6.3 Discontinuity‐Induced Bifurcations
    4. 6.4 Freeplay and Friction
    5. 6.5 Concluding Remarks
    6. References
  12. 7 Numerical Continuation
    1. 7.1 Introduction
    2. 7.2 Algebraic Problems
    3. 7.3 Direct Location of Folds
    4. 7.4 Fixed Point Solutions of Dynamic Systems
    5. 7.5 Periodic Solutions of Dynamic Systems
    6. 7.6 Stability of Periodic Solutions Calculated from Numerical Continuation
    7. 7.7 Shooting
    8. 7.8 Harmonic Balance
    9. 7.9 Concluding Remarks
    10. References
  13. 8 Low‐Speed Aerodynamic Nonlinearities
    1. 8.1 Introduction
    2. 8.2 Vortex‐Induced Vibrations
    3. 8.3 Galloping
    4. 8.4 Stall Flutter
    5. 8.5 Concluding Remarks
    6. References
  14. 9 High‐Speed Aeroelastic Nonlinearities
    1. 9.1 Introduction
    2. 9.2 Piston Theory
    3. 9.3 Panel Flutter
    4. 9.4 Concluding Remarks
    5. References
  15. 10 Finite Wings
    1. 10.1 Introduction
    2. 10.2 Cantilever Plate in Supersonic Flow
    3. 10.3 Three‐Dimensional Aerodynamic Modelling by the Vortex Lattice Method
    4. 10.4 Concluding Remarks
    5. References
  16. Appendix A: Aeroelastic Models
    1. A.1 Galloping Oscillator
    2. A.2 Two‐Dimensional Pitch‐Plunge‐Control Wing Section with Unsteady Aerodynamics
    3. A.3 Two‐Dimensional Pitch‐Plunge‐Control Wing Section with Quasi‐Steady Aerodynamics
    4. A.4 Two‐Dimensional Pitch‐Plunge Wing Section with Quasi‐Steady Aerodynamics
    5. A.5 Two‐Dimensional Pitching Wing Section with Quasi‐Steady Aerodynamics
    6. A.6 Two‐Dimensional Pitch‐Plunge Wing with Leishman–Beddoes Aerodynamic Model
    7. A.7 Two‐Dimensional Pitch‐Plunge Wing with ONERA Aerodynamic Model
    8. A.8 Two‐Dimensional Pitch‐Plunge‐Control Wing Section with Supersonic Aerodynamics
    9. A.9 Two‐Dimensional Pitch‐Plunge Wing Section with Supersonic Aerodynamics
    10. References
  17. Index
  18. End User License Agreement