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E-raamat: Introduction to Nonlinear Aeroelasticity

Series edited by (University of Liverpool, UK), Series edited by (MIT), Series edited by (BAE Systems, UK), (University of Liege, Belgium)
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  • Sari: Aerospace Series
  • Ilmumisaeg: 10-Mar-2017
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118756461
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Introduction to Nonlinear AeroelasticitySuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Aerospace Series
  • Ilmumisaeg: 10-Mar-2017
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118756461
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Introduction to Nonlinear Aeroelasticity

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 and so on. 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.
Preface xi
Dimitriadis: Nonlinear Aeroelasticity -- Series Preface Oct 2016 xiii
About the Companion Website xv
1 Introduction
1(8)
1.1 Sources of Nonlinearity
3(2)
1.2 Origins of Nonlinear Aeroelasticity
5(4)
References
6(3)
2 Nonlinear Dynamics
9(54)
2.1 Introduction
9(1)
2.2 Ordinary Differential Equations
9(2)
2.3 Linear Systems
11(13)
2.3.1 Stable Oscillatory Response
13(2)
2.3.2 Neutral Oscillatory Response
15(2)
2.3.3 Unstable Oscillatory Response
17(2)
2.3.4 Stable Non-oscillatory Response
19(2)
2.3.5 Unstable Non-oscillatory Response
21(2)
2.3.6 Fixed Point Summary
23(1)
2.4 Nonlinear Systems
24(10)
2.4.7 Linearisation Around Fixed Points
25(3)
2.4.2 The Pitching Wing Section with Cubic Stiffness
28(2)
2.4.3 The Pitchfork Bifurcation
30(4)
2.5 Stability in the Lyapunov Sense
34(3)
2.6 Asymmetric Systems
37(8)
2.6.1 The Fold Bifurcation
38(3)
2.6.2 The Transcritical Bifurcation
41(4)
2.7 Existence of Periodic Solutions
45(4)
2.7.7 Nonlinear Aeroelastic Galloping
47(2)
2.8 Estimating Periodic Solutions
49(4)
2.8.1 Periodic Solutions of the Nonlinear Galloping Oscillator
50(2)
2.8.2 The Hopf Bifurcation
52(1)
2.9 Stability of Periodic Solutions
53(8)
2.9.7 Stability of Galloping Oscillations
55(1)
2.9.2 Supercritical and Subcritical Hopf Bifurcations
56(1)
2.9.3 The Fold Bifurcation of Cycles
56(5)
2.10 Concluding Remarks
61(2)
References
61(2)
3 Time Integration
63(50)
3.1 Introduction
63(1)
3.2 Euler Method
64(4)
3.2.1 Linear Systems
65(1)
3.2.2 Nonlinear Systems
66(2)
3.3 Central Difference Method
68(6)
3.3.1 Explicit Solution of Nonlinear Systems
69(3)
3.3.2 Implicit Solution of Nonlinear Systems
72(2)
3.4 Runge--Kutta Method
74(6)
3.5 Time-Varying Linear Approximation
80(6)
3.6 Integrating Backwards in Time
86(2)
3.7 Time Integration of Systems with Multiple Degrees of Freedom
88(4)
3.8 Forced Response
92(7)
3.9 Harmonic Balance
99(11)
3.9.1 Newton--Raphson
103(3)
3.9.2 Discrete Fourier Transform Techniques
106(4)
3.10 Concluding Remarks
110(3)
References
111(2)
4 Determining the Vibration Parameters
113(46)
4.1 Introduction
113(1)
4.2 Amplitude and Frequency Determination
113(7)
4.2.1 Event Detection
117(3)
4.3 Equivalent Linearisation
120(5)
4.4 Hilbert Transform
125(4)
4.5 Time-Varying Linear Approximation
129(2)
4.6 Short Time Fourier Transform
131(6)
4.7 Pinpointing Bifurcations
137(6)
4.7.1 Newton--Raphson
141(1)
4.7.2 Successive Bisection
142(1)
4.8 Limit Cycle Study
143(3)
4.9 Poincare Sections
146(3)
4.10 Stability of Periodic Solutions
149(7)
4.10.1 Floquet Analysis
152(4)
4.11 Concluding Remarks
156(3)
References
156(3)
5 Bifurcations of Fundamental Aeroelastic Systems
159(102)
5.1 Introduction
159(1)
5.2 Two-Dimensional Unsteady Pitch-Plunge-Control Wing
160(1)
5.3 Linear Aeroelastic Analysis
161(9)
5.4 Hardening Stiffness
170(39)
5.4.1 Supercritical Hopf Bifurcation
170(10)
5.4.2 Subcritical Hopf Bifurcation
180(3)
5.4.3 Fold Bifurcation of Cycles
183(6)
5.4.4 Flutter of Nonlinear Systems
189(4)
5.4.5 Period-Doubling Bifurcation
193(8)
5.4.6 Torus Bifurcation
201(8)
5.5 Softening Stiffness
209(5)
5.6 Damping Nonlinearity
214(19)
5.6.7 Subcritical Hopf Bifurcation
216(4)
5.6.2 Static Divergence of Cycles
220(4)
5.6.3 Pitchfork Bifurcation of Cycles
224(9)
5.7 Two-Parameter Bifurcations
233(9)
5.7.7 Generalised Hopf Bifurcation
233(4)
5.7.2 Pitchfork--Hopf Bifurcation
237(3)
5.7.3 Hopf-Hopf Bifurcation
240(2)
5.8 Asymmetric Nonlinear Aeroelastic Systems
242(15)
5.8.1 Fold Bifurcation of Fixed Points and Cycles
243(8)
5.8.2 Transcritical Bifurcation of Fixed Points and Cycles
251(5)
5.8.3 Fold-Hopf Bifurcation
256(1)
5.9 Concluding Remarks
257(4)
References
259(2)
6 Discontinuous Nonlinearities
261(52)
6.1 Introduction
261(1)
6.2 Piecewise Linear Stiffness
262(35)
6.2.7 Underlying and Overlying Linear Systems
264(5)
6.2.2 Fixed Points and Boundary Equilibrium Bifurcations
269(3)
6.2.3 Equivalent Linearisation of Piecewise Linear Stiffness
272(6)
6.2.4 Three-Domain Limit Cycles
278(7)
6.2.5 Two-Domain Limit Cycles
285(4)
6.2.6 Time Domain Solutions
289(8)
6.3 Discontinuity-Induced Bifurcations
297(12)
6.3.1 The Boundary Equilibrium Bifurcation
297(5)
6.3.2 The Grazing Bifurcation
302(7)
6.4 Freeplay and Friction
309(1)
6.5 Concluding Remarks
310(3)
References
310(3)
7 Numerical Continuation
313(76)
7.1 Introduction
313(1)
7.2 Algebraic Problems
314(14)
7.2.7 Prediction Correction
316(5)
7.2.2 Arclength Continuation
321(6)
7.2.3 Pseudo-Arclength Continuation
327(1)
7.3 Direct Location of Folds
328(4)
7.4 Fixed Point Solutions of Dynamic Systems
332(10)
7.4.1 Branchpoints
332(5)
7.4.2 Arclength Step Control
337(5)
7.5 Periodic Solutions of Dynamic Systems
342(16)
7.5.7 Starting the Continuation Scheme
348(3)
7.5.2 Folds and Branch Points
351(4)
7.5.3 Branch Switching
355(3)
7.6 Stability of Periodic Solutions Calculated from Numerical Continuation
358(6)
7.7 Shooting
364(15)
7.7.7 Starting the Continuation Scheme
367(1)
7.7.2 Arclength Continuation
368(2)
7.7.3 Stability Analysis
370(2)
7.7.4 Branch Point Location and Branch Switching
372(3)
7.7.5 Grazing
375(4)
7.8 Harmonic Balance
379(8)
7.9 Concluding Remarks
387(2)
References
387(2)
8 Low-Speed Aerodynamic Nonlinearities
389(64)
8.1 Introduction
389(4)
8.2 Vortex-Induced Vibrations
393(9)
8.3 Galloping
402(9)
8.4 Stall Flutter
411(38)
8.4.1 Dynamic Stall
413(4)
8.4.2 Leishman--Beddoes Model
417(17)
8.4.3 ONERA Model
434(8)
8.4.4 Aeroelastic Simulations using Dynamic Stall Models
442(7)
8.5 Concluding Remarks
449(4)
References
449(4)
9 High-Speed Aeroelastic Nonlinearities
453(50)
9.1 Introduction
453(1)
9.2 Piston Theory
453(15)
9.3 Panel Flutter
468(33)
9.3.1 Buckling
470(14)
9.3.2 Limit Cycle Oscillations
484(17)
9.4 Concluding Remarks
501(2)
References
501(2)
10 Finite Wings
503(52)
10.1 Introduction
503(1)
10.2 Cantilever Plate in Supersonic Flow
504(15)
10.3 Three-Dimensional Aerodynamic Modelling by the Vortex Lattice Method
519(33)
10.3.1 Aeroelastic Coupling
528(8)
10.3.2 Transforming to the Time Domain
536(6)
10.3.3 Nonlinear Response
542(10)
10.4 Concluding Remarks
552(3)
References
552(3)
Appendix A Aeroelastic Models 555(16)
Index 571
Grigorios Dimitriadis, University of Liège, Belgium
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