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Introduction to Aircraft Aeroelasticity and Loads, Second Edition is an updated new edition offering comprehensive coverage of the main principles of aircraft aeroelasticity and loads. For ease of reference, the book is divided into three parts and begins by reviewing the underlying disciplines of vibrations, aerodynamics, loads and control, and then goes on to describe simplified models to illustrate aeroelastic behaviour and aircraft response and loads for the flexible aircraft before introducing some more advanced methodologies. Finally, it explains how industrial certification requirements for aeroelasticity and loads may be met and relates these to the earlier theoretical approaches used.
Key features of this new edition include:
Introduction to Aircraft Aeroelasticity and Loads, Second Edition is a must-have reference for researchers and practitioners working in the aeroelasticity and loads fields, and is also an excellent textbook for senior undergraduate and graduate students in aerospace engineering.
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Second Edition
Jan R. Wright
University of Manchester andJ2W Consulting, UK
Jonathan E. Cooper
University of Bristol, UK
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Library of Congress Cataloging-in-Publication Data
Wright, Jan R.Introduction to aircraft aeroelasticity and loads / Jan R. Wright, Jonathan E. Cooper. – Second edition. pages cm Includes bibliographical references and index.
ISBN 978-1-118-48801-0 (cloth)1. Aeroelasticity. I. Cooper, Jonathan E. II. Title. TL574.A37W75 2014 629.132'362--dc23
2014027710
A catalogue record for this book is available from the British Library
To our children and grandchildren
Jodi, Peter, Laura, Rhys & Erin
&
William, Rory, Tyler & Ella
The field of aerospace is multi-disciplinary and wide-ranging, covering a large variety of products, disciplines and domains, not merely in engineering but in many related supporting activities. These combine to enable the aerospace industry to produce exciting and technologically advanced vehicles. The wealth of knowledge and experience that has been gained by expert practitioners in the various aerospace fields needs to be passed on to others working in the industry, including those just entering from University.
The Aerospace Series aims to be a practical, topical and relevant series of books aimed at people working in the aerospace industry, including engineering professionals and operators, allied professions such as commercial and legal executives, and also engineers in academia. The range of topics is intended to be wide-ranging, covering the design and development, manufacture, operation and support of aircraft, as well as topics such as infrastructure operations and developments in research and technology.
Aeroelasticity and loads are important interdisciplinary topics, involving the interaction of aerodynamic, elastic and inertia forces, which have a significant effect on aircraft designs and flight performance. Important phenomena include those that are critical for structural stability e.g. flutter, divergence and shimmy, the shape of aircraft wings in-flight, and the critical design loads due to the aircraft response to turbulence and flight / ground manoeuvres that have a significant influence on aircraft structural designs.
This book, Introduction to Aircraft Aeroelasticity and Loads, provides a welcome update to the first edition. Containing a range of revised material, the same approach is used as before, employing simple mathematical models to guide the reader towards an understanding of key underlying concepts relating to both aeroelasticity and loads. Of particular note is the frequent reference to the airworthiness certification procedures for civil aircraft, with the final section providing an introduction to current industrial practice. The companion website provides a number of computer codes that can be used to gain further understanding of the mathematical models that are discussed within the book.
Peter Belobaba, Jonathan Cooper and Alan Seabridge
Following publication of the first edition of Introduction to Aircraft Aeroelasticity and Loads, the authors have run a series of in-house short courses, based upon the book, for several companies within the world-wide aerospace industry. These lectures enabled the material to be tested on engineers from industry in a classroom situation; this, combined with both authors also using some of the content to teach undergraduate modules at the Universities of Sheffield and Bristol, resulted in a number of changes being made to the course content. These changes have resulted in this second edition and are aimed at improving the presentation and content throughout the book, while maintaining the philosophy of illustrating the underlying concepts of aeroelasticity and loads using as simple mathematical models as possible.
The most significant changes are:
Use of the same binary wing model for the static and dynamic aeroelasticity chapters, based on an unswept, untapered cantilever with one bending and one torsion assumed shape, rather than the previous use of a pitching and flapping wing – this has meant that the models used for aeroelastics and loads are now more closely related.
Revised treatment of swept wing divergence.
Major revision of the flutter and aeroservoelasticity chapters.
Changing the chapter order so that the chapters involving a discrete treatment of structures and aerodynamics all sit together.
Inclusion of more elements relevant to modelling of aircraft structures.
Inclusion of simpler examples relating to potential flow aerodynamics.
Revision to multiple degree of freedom damped free vibration.
Revision to the Ground Maneouvres chapter to include redundancy in gear attachments, Craig-Bampton modes and bookcase landing examples.
Combining the two chapters in the first edition on the Flight Mechanics Model and Dynamic Manoeuvres, and revising the lateral bookcase modelling material.
Introduce unsteady aerodynamics effects into the examples in the Gust and Turbulence Encounters chapter.
Revision of the introduction to the Flight Control System (FCS).
Update of the certification requirements.
The authors would like to thank a number of their colleagues for their valued comments on the content of the industrial short courses, and this second edition. Particular mention needs to be made of Mark Hockenhull, Tom Wilson, Gido Brendes, Tobias Mauermann and Hans-Gerd Giesseler (all Airbus), Raj Nangia (Nangia Associates), George Constandinidis (Messier-Bugatti-Dowty), Dorian Jones, Arthur Richards, Olivia Stodieck and Luke Lambert (all University of Bristol).
Aeroelasticity is the study of the interaction of aerodynamic, elastic and inertia forces. For fixed wing aircraft there are two key areas: (a) static aeroelasticity, where the deformation of the aircraft influences the lift distribution can lead to the statically unstable condition of divergence and will normally reduce the control surface effectiveness, and (b) dynamic aeroelasticity, which includes the critical area of flutter where the aircraft can become dynamically unstable in a condition where the structure extracts energy from the air stream.
Aircraft are also subject to a range of static and dynamic loads resulting from flight manoeuvres (equilibrium/steady and dynamic), ground manoeuvres and gust/turbulence encounters. These load cases are responsible for the critical design loads over the aircraft structure and hence influence the structural design. Determination of such loads involves consideration of aerodynamic, elastic and inertia effects and requires the solution of the dynamic responses; consequently there is a strong link between aeroelasticity and loads.
The aircraft vibration characteristics and response are a result of the flexible modes combining with the rigid body dynamics, with the inclusion of the Flight Control System (FCS) if it is present. In this latter case, the aircraft will be a closed loop system and the FCS affects both the aeroelasticity and loads behaviour. The interaction between the FCS and the aeroelastic system is often called aeroservoelasticity.
This book aims to embrace the range of basic aeroelastic and loads topics that might be encountered in an aircraft design office and to provide an understanding of the main principles involved. Colleagues in industry have often remarked that it is not appropriate to give some of the classical books on aeroelasticity to new graduate engineers as many of the books are too theoretical for a novice aeroelastician. Indeed, the authors have found much of the material in them to be too advanced to be used in the undergraduate level courses that they have taught. Also, the topics of aeroelasticity and loads have tended to be treated separately in textbooks, whereas in industry the fields have become much more integrated. This book is seen as providing some grounding in the basic analysis techniques required which, having been mastered, can then be supplemented via more advanced texts, technical papers and industry reports.
Some of the material covered in this book developed from undergraduate courses given at Queen Mary College, University of London and at the University of Manchester. In the UK, many entrants into the aerospace industry do not have an aerospace background, and almost certainly will have little knowledge of aeroelasticity or loads. To begin to meet this need, during the early 1990s the authors presented several short courses on Aeroelasticity and Structural Dynamics to young engineers in the British aerospace industry, and this has influenced the content and approach of this book. A further major influence was the work by Hancock, Simpson and Wright (1985) on the teaching of flutter, making use of a simplified flapping and pitching wing model with strip theory aerodynamics (including a simplified unsteady aerodynamics model) to illustrate the fundamental principles of flutter. This philosophy has been employed here for the treatment of static aeroelasticity and flutter, and has been extended into the area of loads by focusing on a simplified flexible whole aircraft model in order to highlight key features of modelling and analysis.
The intention of the book is to provide the reader with the technical background to understand the underlying concepts and application of aircraft aeroelasticity and loads. As far as possible, simplified mathematical models for the flexible aircraft are used to illustrate the phenomena and also to demonstrate the link between these models, industrial practice and the certification process. Thus, fairly simple continuum models based upon a small number of assumed modes (so avoiding partial differential equations) have been used. Consequently, much of the book is based upon strip theory aerodynamics and the Rayleigh–Ritz assumed modes method. By using this approach, it has been possible to illustrate most concepts using a maximum of three degrees of freedom. Following on from these continuum models, basic discretized structural and aerodynamic models are introduced in order to demonstrate some underlying approaches in current industrial practice. The book aims to be suitable for final year undergraduate or Masters level students, or engineers in industry who are new to the subject. For example, it could provide the basis of two taught modules in aeroelasticity and loads. It is hoped that the book will fill a gap in providing a broad and relatively basic introductory treatment of aeroelastics and loads.
A significant number of different topics are covered in order to achieve the goals of this book, namely structural dynamics, steady and unsteady aerodynamics, loads, control, static aeroelastic effects, flutter, flight manoeuvres (both steady/equilibrium and dynamic), ground manoeuvres (e.g. landing, taxiing), gust and turbulence encounters, calculation of loads and, finally, Finite Element and three-dimensional panel methods. In addition, a relatively brief explanation is given as to how these topics might typically be approached in industry when seeking to meet the certification requirements. Most of the focus is on commercial and not military aircraft, though of course all of the underlying principles, and much of the implementation, are common between the two.
The notation employed has not been straightforward to define, as many of these disciplines have tended to use the same symbols for different variables and so inevitably this exercise has been a compromise. A further complication is the tendency for aeroelasticity textbooks from the USA to use the reduced frequency k for unsteady aerodynamics, as opposed to the frequency parameter ν that is often used elsewhere. The reduced frequency has been used throughout this textbook to correspond with the classical textbooks of aeroelasticity.
The book is split into three parts. After a brief introduction to aeroelasticity and loads, Part A provides some essential background material on the fundamentals of single and multiple degree of freedom (DoF) vibrations for discrete parameter systems and continuous systems (Rayleigh–Ritz and Finite Element), steady aerodynamics, loads and control. The presentation is not very detailed, assuming that a reader having a degree in engineering will have some background in most of these topics and can reference more comprehensive material if desired.
Part B is the main part of the book, covering the basic principles and concepts required to provide a bridge to begin to understand current industry practice. The chapters on aeroelasticity include static aeroelasticity (lift distribution, divergence and control effectiveness), unsteady aerodynamics, dynamic aeroelasticity (i.e. flutter) and aeroservoelasticity; the treatment is based mostly on a simple two-DoF flapping/pitching wing model, sometimes attached to a rigid fuselage free to heave and pitch. The chapters on loads include equilibrium and dynamic flight manoeuvres, gusts and turbulence encounters, ground manoeuvres and internal loads. The
