Introduction to nonlinear aeroelasticity / Dr. Grigorios Dimitriadis.

Format:

Book

Author/Creator:

Dimitriadis, Grigorios, 1972- author.

Series:

Aerospace series (Chichester, England)

Aerospace Series

Language:

English

Subjects (All):

Aeroelasticity.

Nonlinear theories.

Physical Description:

1 online resource (592 pages) : illustrations (some color).

Edition:

1 edition.

Place of Publication:

Hoboken, New Jersey ; Chichester, England : Wiley, 2017.

Summary:

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.

Contents:

Intro

Title Page

Copyright Page

Contents

Preface

Dimitriadis: Nonlinear Aeroelasticity - Series Preface Oct 2016

About the Companion Website

Chapter 1 Introduction

1.1 Sources of Nonlinearity

1.2 Origins of Nonlinear Aeroelasticity

References

Chapter 2 Nonlinear Dynamics

2.1 Introduction

2.2 Ordinary Differential Equations

2.3 Linear Systems

2.3.1 Stable Oscillatory Response

2.3.2 Neutral Oscillatory Response

2.3.3 Unstable Oscillatory Response

2.3.4 Stable Non-oscillatory Response

2.3.5 Unstable Non-oscillatory Response

2.3.6 Fixed Point Summary

2.4 Nonlinear Systems

2.4.1 Linearisation Around Fixed Points

2.4.2 The Pitching Wing Section with Cubic Stiffness

2.4.3 The Pitchfork Bifurcation

2.5 Stability in the Lyapunov Sense

2.6 Asymmetric Systems

2.6.1 The Fold Bifurcation

2.6.2 The Transcritical Bifurcation

2.7 Existence of Periodic Solutions

2.7.1 Nonlinear Aeroelastic Galloping

2.8 Estimating Periodic Solutions

2.8.1 Periodic Solutions of the Nonlinear Galloping Oscillator

2.8.2 The Hopf Bifurcation

2.9 Stability of Periodic Solutions

2.9.1 Stability of Galloping Oscillations

2.9.3 The Fold Bifurcation of Cycles

2.10 Concluding Remarks

Chapter 3 Time Integration

3.1 Introduction

3.2 Euler Method

3.2.1 Linear Systems

3.2.2 Nonlinear Systems

3.3 Central Difference Method

3.3.1 Explicit Solution of Nonlinear Systems

3.3.2 Implicit Solution of Nonlinear Systems

3.4 Runge-Kutta Method

3.5 Time-Varying Linear Approximation

3.6 Integrating Backwards in Time

3.7 Time Integration of Systems with Multiple Degrees of Freedom

3.8 Forced Response

3.9 Harmonic Balance

3.9.1 Newton-Raphson

3.9.2 Discrete Fourier Transform Techniques

3.10 Concluding Remarks

References.

Chapter 4 Determining the Vibration Parameters

4.1 Introduction

4.2 Amplitude and Frequency Determination

4.2.1 Event Detection

4.3 Equivalent Linearisation

4.4 Hilbert Transform

4.5 Time-Varying Linear Approximation

4.6 Short Time Fourier Transform

4.7 Pinpointing Bifurcations

4.7.1 Newton-Raphson

4.7.2 Successive Bisection

4.8 Limit Cycle Study

4.9 Poincaré Sections

4.10 Stability of Periodic Solutions

4.10.1 Floquet Analysis

4.11 Concluding Remarks

Chapter 5 Bifurcations of FundamentalAeroelastic Systems

5.1 Introduction

5.2 Two-Dimensional Unsteady Pitch-Plunge-ControlWing

5.3 Linear Aeroelastic Analysis

5.4 Hardening Stiffness

5.4.1 Supercritical Hopf Bifurcation

5.4.2 Subcritical Hopf Bifurcation

5.4.3 Fold Bifurcation of Cycles

5.4.4 Flutter of Nonlinear Systems

5.4.5 Period-Doubling Bifurcation

5.4.6 Torus Bifurcation

5.5 Softening Stiffness

5.6 Damping Nonlinearity

5.6.1 Subcritical Hopf Bifurcation

5.6.2 Static Divergence of Cycles

5.6.3 Pitchfork Bifurcation of Cycles

5.7 Two-Parameter Bifurcations

5.7.1 Generalised Hopf Bifurcation

5.7.2 Pitchfork-Hopf Bifurcation

5.7.3 Hopf-Hopf Bifurcation

5.8 Asymmetric Nonlinear Aeroelastic Systems

5.8.1 Fold Bifurcation of Fixed Points and Cycles

5.8.2 Transcritical Bifurcation of Fixed Points and Cycles

5.8.3 Fold-Hopf Bifurcation

5.9 Concluding Remarks

Chapter 6 Discontinuous Nonlinearities

6.1 Introduction

6.2 Piecewise Linear Stiffness

6.2.1 Underlying and Overlying Linear Systems

6.2.2 Fixed Points and Boundary Equilibrium Bifurcations

6.2.3 Equivalent Linearisation of Piecewise Linear Stiffness

6.2.4 Three-Domain Limit Cycles

6.2.5 Two-Domain Limit Cycles

6.2.6 Time Domain Solutions.

6.3 Discontinuity-Induced Bifurcations

6.3.1 The Boundary Equilibrium Bifurcation

6.3.2 The Grazing Bifurcation

6.4 Freeplay and Friction

6.5 Concluding Remarks

Chapter 7 Numerical Continuation

7.1 Introduction

7.2 Algebraic Problems

7.2.1 Prediction Correction

7.2.2 Arclength Continuation

7.2.3 Pseudo-Arclength Continuation

7.3 Direct Location of Folds

7.4 Fixed Point Solutions of Dynamic Systems

7.4.1 Branch Points

7.4.2 Arclength Step Control

7.5 Periodic Solutions of Dynamic Systems

7.5.1 Starting the Continuation Scheme

7.5.2 Folds and Branch Points

7.5.3 Branch Switching

7.6 Stability of Periodic Solutions Calculated from Numerical Continuation

7.7 Shooting

7.7.1 Starting the Continuation Scheme

7.7.2 Arclength Continuation

7.7.3 Stability Analysis

7.7.4 Branch Point Location and Branch Switching

7.7.5 Grazing

7.8 Harmonic Balance

7.9 Concluding Remarks

Chapter 8 Low-Speed AerodynamicNonlinearities

8.1 Introduction

8.2 Vortex-Induced Vibrations

8.3 Galloping

8.4 Stall Flutter

8.4.1 Dynamic Stall

8.4.2 Leishman-Beddoes Model

8.4.3 ONERA Model

8.4.4 Aeroelastic Simulations using Dynamic Stall Models

8.5 Concluding Remarks

Chapter 9 High-Speed AeroelasticNonlinearities

9.1 Introduction

9.2 Piston Theory

9.3 Panel Flutter

9.3.1 Buckling

9.3.2 Limit Cycle Oscillations

9.4 Concluding Remarks

Chapter 10 Finite Wings

10.1 Introduction

10.2 Cantilever Plate in Supersonic Flow

10.3 Three-Dimensional Aerodynamic Modelling by the Vortex Lattice Method

10.3.1 Aeroelastic Coupling

10.3.2 Transforming to the Time Domain

10.3.3 Nonlinear Response

10.4 Concluding Remarks

Appendix A Aeroelastic Models

A.1 Galloping Oscillator.

A.2 Two-Dimensional Pitch-Plunge-Control Wing Section with Unsteady Aerodynamics

A.3 Two-Dimensional Pitch-Plunge-Control Wing Section with Quasi-Steady Aerodynamics

A.4 Two-Dimensional Pitch-Plunge Wing Section with Quasi-Steady Aerodynamics

A.5 Two-Dimensional Pitching Wing Section with Quasi-Steady Aerodynamics

A.6 Two-Dimensional Pitch-Plunge Wing with Leishman-Beddoes Aerodynamic Mode

A.7 Two-Dimensional Pitch-Plunge Wing with ONERA Aerodynamic Model

A.8 Two-Dimensional Pitch-Plunge-Control Wing Section with Supersonic Aerodynamics

A.9 Two-Dimensional Pitch-Plunge Wing Section with Supersonic Aerodynamics

Index.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-118-75646-0

1-118-75647-9

OCLC:

967457042