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E-raamat: Active Control of Noise and Vibration

(Charles Darwin University, Australia), (University of Adelaide, Australia), (Nanjing University, China), (University of Adelaide, Australia), (University of Adelaide, Australia)
  • Formaat: 1554 pages
  • Ilmumisaeg: 02-Nov-2012
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781040074107
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Active Control of Noise and VibrationSuurem pilt
  • Formaat: 1554 pages
  • Ilmumisaeg: 02-Nov-2012
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781040074107
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Since the publication of the first edition, considerable progress has been made in the development and application of active noise control (ANC) systems, particularly in the propeller aircraft and automotive industries. Treating the active control of both sound and vibration in a unified way, this second edition of Active Control of Noise and Vibration continues to combine coverage of fundamental principles with the most recent theoretical and practical developments.

Whats New in This Edition





Revised, expanded, and updated information in every chapter Advances in feedforward control algorithms, DSP hardware, and applications Practical application examples of active control of noise propagating in ducts The use of a sound intensity cost function, model reference control, sensing radiation modes, modal filtering, and a comparison of the effectiveness of various sensing strategies New material on feedback control of sound transmission into enclosed spaces New material on model uncertainty, experimental determination of the system model, optimization of the truncated model, collocated actuators and sensors, biologically inspired control, and a discussion of centralised versus de-centralised control A completely revised chapter on control system implementation New material on parametric array loudspeakers, turbulence filtering, and virtual sensing More material on smart structures, electrorheological fluids, and magnetorheological fluids

Integrating the related disciplines of active noise control and active vibration control, this comprehensive two-volume set explains how to design and implement successful active control systems in practice. It also details the pitfalls one must avoid to ensure a reliable and stable system.

Arvustused

"The fact is that there is not one work that is as comprehensive and detailed as this one in the realm of ANVC. Anyone considering fundamental or applied research work in this field must take the plunge and buy this outstanding reference." Dominique J. Chéenne in Noise Control Engineering Journal

Praise for the Previous Edition

"... the treatment is attractive and meticulous and accurate ... appears to be a good buy." Bulletin of the Institute of Acoustics

"... a very good and complete reference on the subject." The Structural Engineer

Preface To First Edition xvii
Preface To Second Edition xix
Author Biographies xxi
Acknowledgements xxv
Chapter 1 Background
1(14)
1.1 Introduction And Potential Applications
1(7)
1.2 Overview Of Active Control Systems
8(7)
References
13(2)
Chapter 2 Foundations Of Acoustics And Vibration
15(174)
2.1 Acoustic Wave Equation
15(14)
2.1.1 Conservation Of Mass
16(1)
2.1.2 Euler's Equation Of Motion
17(1)
2.1.3 Equation Of State
18(1)
2.1.4 Wave Equation (Linearised)
19(2)
2.1.5 Velocity Potential
21(1)
2.1.6 Inhomogeneous Wave Equation
22(1)
2.1.7 Wave Equation For One-Dimensional Mean Flow
22(2)
2.1.8 Wave Equation In Cartesian, Cylindrical And Spherical Coordinates
24(1)
2.1.8.1 Cartesian Coordinates
24(1)
2.1.8.2 Cylindrical Coordinates
24(1)
2.1.8.3 Spherical Coordinates
25(1)
2.1.9 Speed Of Sound, Wave Number, Frequency And Period
25(2)
2.1.10 Speed Of Sound In Gases, Liquids And Solids
27(2)
2.1.11 Sound Propagation In Porous Media
29(1)
2.2 Structural Mechanics Fundamentals
29(14)
2.2.1 Summary Of Newtonian Mechanics
29(1)
2.2.1.1 Systems Of Particles
30(1)
2.2.2 Summary Of Analytical Mechanics
31(1)
2.2.2.1 Generalised Coordinates
31(1)
2.2.2.2 Principle Of Virtual Work
32(2)
2.2.2.3 D'Alembert's Principle
34(1)
2.2.2.4 Hamilton's Principle
34(3)
2.2.2.5 Lagrange's Equations Of Motion
37(5)
2.2.3 Influence Coefficients
42(1)
2.3 Vibration Of Continuous Systems
43(50)
2.3.1 Nomenclature And Sign Conventions
44(2)
2.3.2 Damping
46(1)
2.3.3 Waves In Beams
46(1)
2.3.3.1 Longitudinal Waves
47(3)
2.3.3.2 Torsional Waves (Transverse Shear Waves)
50(1)
2.3.3.3 Flexural Waves
51(8)
2.3.4 Waves In Thin Plates
59(2)
2.3.4.1 Longitudinal Waves
61(1)
2.3.4.2 Transverse Shear Waves
62(2)
2.3.4.3 Flexural Waves
64(3)
2.3.4.3.1 Effects Of Shear Deformation And Rotary Inertia
67(6)
2.3.5 Waves In Thin Circular Cylinders
73(8)
2.3.5.1 Boundary Conditions
81(6)
2.3.5.2 Cylinder Equations Of Motion: Alternative Derivation
87(2)
2.3.5.3 Solution Of The Equations Of Motion
89(1)
2.3.5.4 Effect Of Longitudinal And Circumferential Stiffeners
90(2)
2.3.5.5 Other Complicating Effects
92(1)
2.4 Structural Sound Radiation, Sound Propagation And Green's Functions
93(23)
2.4.1 Acoustic Green's Function: Unbounded Medium
95(2)
2.4.2 Reciprocity Of Green's Functions
97(1)
2.4.3 Acoustic Green's Function For A Three-Dimensional Bounded Fluid
98(4)
2.4.4 Acoustical Green's Function For A Source In A Two-Dimensional Duct Of Infinite Length
102(3)
2.4.5 Green's Function For A Vibrating Surface
105(2)
2.4.6 General Application Of Green's Functions
107(1)
2.4.6.1 Excitation Of A Structure By Point Forces
107(1)
2.4.6.2 Excitation Of A Structure By A Distributed Force
107(1)
2.4.6.3 Excitation Of An Acoustic Medium By A Number Of Point Acoustic Sources
108(1)
2.4.6.4 Excitation Of An Acoustic Medium By A Vibrating Structure
108(2)
2.4.7 Structural Sound Radiation And Wavenumber Transforms
110(5)
2.4.8 Effect Of Fluid Loading On Structural Sound Radiation
115(1)
2.5 Impedance And Intensity
116(73)
2.5.1 Acoustic Impedances
116(1)
2.5.1.1 Specific Acoustic Impedance, Zs
116(1)
2.5.1.2 Acoustic Impedance, Za
116(1)
2.5.1.3 Mechanical Impedance, Zm
117(1)
2.5.1.4 Radiation Impedance And Radiation Efficiency
117(9)
2.5.2 Structural Input Impedance
126(2)
2.5.2.1 Force Impedance Of An Infinite Beam (Flexural Waves)
128(3)
2.5.2.2 Summary Of Impedance Formulae For Infinite And Semi-Infinite Isotropic Beams And Plates
131(2)
2.5.2.3 Point Force Impedance Of Finite Systems
133(1)
2.5.2.4 Point Force Impedance Of Cylinders
134(1)
2.5.2.4.1 Infinite Cylinder
134(2)
2.5.2.4.2 Finite Cylinder --- Shear Diaphragm Ends
136(1)
2.5.2.5 Wave Impedance Of Finite Structures
137(1)
2.5.3 Sound Intensity And Sound Power
138(4)
2.5.3.1 Measurement Of Acoustic Intensity
142(1)
2.5.3.1.1 Sound Intensity Measurement By The P-U Method
142(1)
2.5.3.1.2 Accuracy Of The P-U Method
143(1)
2.5.3.1.3 Sound Intensity Measurement By The P-P Method
144(3)
2.5.3.1.4 Accuracy Of The P-P Method
147(2)
2.5.3.1.5 Frequency Decomposition Of The Intensity
149(1)
2.5.3.1.6 Direct Frequency Decomposition
149(1)
2.5.3.1.7 Indirect Frequency Decomposition
149(1)
2.5.4 Structural Intensity And Structural Power Transmission
150(7)
2.5.4.1 Intensity And Power Transmission Measurement In Beams
157(1)
2.5.4.1.1 Longitudinal Waves
157(5)
2.5.4.1.2 Torsional Waves
162(1)
2.5.4.1.3 Flexural Waves
162(7)
2.5.4.1.4 Total Power Transmission
169(1)
2.5.4.1.5 Measurement Of Beam Accelerations
170(4)
2.5.4.1.6 Effect Of Transverse Sensitivity Of Accelerometers
174(1)
2.5.4.2 Structural Power Transmission Measurement In Plates
175(1)
2.5.4.2.1 Longitudinal Waves
175(1)
2.5.4.2.2 Transverse Shear Waves
176(1)
2.5.4.2.3 Flexural Waves
177(2)
2.5.4.2.4 Intensity Measurement In Circular Cylinders
179(1)
2.5.4.2.5 Sources Of Error In The Measurement Of Structural Intensity
179(2)
2.5.5 Power Transmission Through Vibration Isolators Into Machine Support Structures, And Power Transmission Into Structures From An Excitation Source
181(4)
References
185(4)
Chapter 3 Spectral Analysis
189(24)
3.1 Digital Filtering
189(3)
3.2 Discrete Fourier Analysis
192(11)
3.2.1 Power Spectrum
196(3)
3.2.2 Uncertainty Principle
199(1)
3.2.3 Sampling Frequency And Aliasing
199(1)
3.2.4 Weighting Functions
200(3)
3.3 Signal Types
203(2)
3.3.1 Stationary Deterministic Signals
203(1)
3.3.2 Stationary Random Signals
204(1)
3.3.3 Pseudo-Random Signals
204(1)
3.4 Convolution
205(3)
3.4.1 Convolution With A Delta Function
207(1)
3.4.2 Convolution Theorem
208(1)
3.5 Important Frequency Domain Functions
208(5)
3.5.1 Cross-Spectrum
208(1)
3.5.2 Coherence
209(1)
3.5.3 Frequency-Response (Or Transfer) Functions
210(1)
3.5.4 Correlation Functions
211(1)
References
211(2)
Chapter 4 Modal Analysis
213(44)
4.1 Introduction
213(1)
4.2 Modal Analysis: Analytical
214(15)
4.2.1 Single-Degree-Of-Freedom System
214(3)
4.2.2 Measures Of Damping
217(1)
4.2.3 Multi-Degree-Of-Freedom Systems
218(3)
4.2.3.1 Forced Response Of Undamped Systems
221(2)
4.2.3.2 Damped Mdof Systems: Proportional Damping
223(1)
4.2.3.2.1 Forced Response Analysis
224(1)
4.2.3.3 Damped Mdof Systems: General Structural Damping
225(1)
4.2.3.3.1 Forced Response Analysis
226(1)
4.2.3.4 Damped Mdof Systems: General Viscous Damping
227(1)
4.2.3.4.1 Forced Response Analysis
227(2)
4.2.4 Summary
229(1)
4.3 Modal Analysis: Experimental
229(21)
4.3.1 Transfer Function Method: Traditional Experimental Modal Analysis
230(1)
4.3.1.1 Test Procedure
231(1)
4.3.1.1.1 Test Set-Up
231(1)
4.3.1.1.2 Excitation By Step Relaxation
232(1)
4.3.1.1.3 Excitation By Electrodynamic Shaker
232(1)
4.3.1.1.4 Excitation By Impact Hammer
233(2)
4.3.1.1.5 Response Transducers
235(1)
4.3.1.1.6 Frf Measurement Points
235(1)
4.3.1.2 Transfer Function (Or Frequency-Response) Measurements
236(4)
4.3.1.3 Modal Parameter Identification
240(1)
4.3.1.3.1 Mode Shapes
241(1)
4.3.1.3.2 Single-Degree-Of-Freedom Curve Fitting Of Frf Data
241(3)
4.3.1.3.3 Circle Fit Analysis Procedure
244(2)
4.3.1.3.4 Residuals
246(1)
4.3.1.3.5 Multi-Degree-Of-Freedom Curve Fitting Frf Data
247(1)
4.3.1.3.6 Computational Mode Elimination
247(1)
4.3.1.3.7 Global Fitting Frf Data
248(1)
4.3.1.4 Response Models
248(1)
4.3.1.5 Structural Response Prediction
249(1)
4.4 Modal Amplitude Determination From System Response Measurements
250(7)
References
256(1)
Chapter 5 Modern Control Review
257(112)
5.1 Introduction
257(1)
5.2 System Arrangements
258(5)
5.2.1 General System Outlines
258(3)
5.2.2 Additions For Digital Implementation
261(2)
5.3 State-Space System Models For Feedback Control
263(13)
5.3.1 Development Of State Equations
264(6)
5.3.2 Solution Of The State Equation
270(6)
5.4 Discrete Time System Models For Feedback Control
276(25)
5.4.1 Development Of Difference Equations
276(2)
5.4.2 State-Space Equations For Discrete Time Systems
278(1)
5.4.3 Discrete Transfer Functions
279(3)
5.4.4 Transfer Function Realisation In A Digital Filter
282(3)
5.4.5 System Identification Using Digital Filters
285(1)
5.4.5.1 Least-Squares Prediction
286(4)
5.4.5.2 Application To State-Space Modelling
290(2)
5.4.5.3 Problems With Least-Squares Prediction
292(1)
5.4.5.4 Generalised Least-Squares Estimation
292(1)
5.4.5.5 Recursive Least-Squares Estimation
293(3)
5.4.5.6 Inclusion Of A Forgetting Factor
296(1)
5.4.5.7 Extended Least-Squares Algorithm
296(1)
5.4.5.8 Stochastic Gradient Algorithm
297(2)
5.4.5.9 Projection Algorithm
299(2)
5.4.5.10 Note On Model Order Selection
301(1)
5.5 Frequency Domain Analysis Of Poles, Zeroes And System Response
301(14)
5.5.1 Introduction
301(2)
5.5.2 Block Diagram Manipulation
303(1)
5.5.3 Control Gain Trade-Offs
304(2)
5.5.4 Poles And Zeroes
306(7)
5.5.5 Stability
313(1)
5.5.5.1 Bibo Stability
313(1)
5.5.5.2 Routh-Hurwitz Stability
314(1)
5.6 Controllability And Observability
315(12)
5.6.1 Introduction
315(1)
5.6.2 Controllability
316(3)
5.6.3 Observability
319(2)
5.6.4 Brief Comment On Joint Relationships Between Controllability And Observability
321(1)
5.6.5 Lyapunov Stability
322(5)
5.7 Control Law Design Via Pole Placement
327(6)
5.7.1 Transformation Into Controller Canonical Form
328(4)
5.7.2 Ackermann's Formula
332(1)
5.7.3 Note On Gains For Mimo Systems
333(1)
5.8 Optimal Control
333(10)
5.8.1 Introduction
333(1)
5.8.2 Problem Formulation
334(2)
5.8.3 Preview: Evaluation Of A Performance Index Using Lyapunov's Second Method
336(1)
5.8.4 Solution To The Quadratic Optimal Control Problem
337(1)
5.8.5 Robustness Characteristics
338(4)
5.8.6 Frequency Weighting
342(1)
5.9 Observer Design
343(5)
5.9.1 Full Order Observer Design
343(3)
5.9.2 Reduced Order Observers
346(2)
5.10 Random Processes Revisited
348(9)
5.10.1 Models And Characteristics
349(2)
5.10.2 White Noise
351(3)
5.10.3 State-Space Models
354(3)
5.11 Optimal Observers: Kalman Filter
357(4)
5.11.1 Problem Formulation
358(3)
5.12 Combined Control Law/Observer: Compensator Design
361(4)
5.12.1 Steady-State Relationships
361(2)
5.12.2 Robustness
363(2)
5.13 Adaptive Feedback Control
365(4)
References
365(4)
Chapter 6 Feedforward Control System Design
369(328)
6.1 Introduction
369(2)
6.2 What Does Feedforward Control Do?
371(3)
6.3 Fixed Characteristic Feedforward Control Systems
374(10)
6.4 Waveform Synthesis
384(11)
6.4.1 Chaplin's Waveform Synthesis
385(2)
6.4.2 Direct Digital Synthesis
387(2)
6.4.3 Multi-Channel Implementation
389(6)
6.5 Non-Recursive (Fir) Deterministic Gradient Descent Algorithm
395(14)
6.5.1 Fir Filter
395(1)
6.5.2 Development Of The Error Criterion
396(2)
6.5.3 Characterisation Of The Error Criterion
398(5)
6.5.4 Development And Characteristics Of The Deterministic Gradient Descent Algorithm
403(6)
6.6 Lms Algorithm
409(10)
6.6.1 Development Of The Lms Algorithm
409(3)
6.6.2 Practical Improvements To The Lms Algorithm
412(1)
6.6.2.1 Introduction Of Tap Leakage
412(3)
6.6.2.2 Selection Of A Convergence Coefficient Based On System Error
415(2)
6.6.2.3 Normalised Lms Algorithm
417(2)
6.6.2.4 Final Note On Convergence Coefficients
419(1)
6.7 Single-Channel Filtered-X Lms Algorithm
419(39)
6.7.1 Derivation Of The Siso Filtered-X Lms Algorithm
420(5)
6.7.1.1 Practical Implementation Of The Filtered-X Lms Algorithm
425(1)
6.7.2 Solution For The Optimum Weight Coefficients And Examination Of The Error Surface
425(6)
6.7.3 Stability Analysis Of The Exact Algorithm
431(2)
6.7.4 Effect Of Continuously Updating The Weight Coefficients
433(3)
6.7.5 Effect Of Cancellation Path Transfer Function Estimation Errors: Frequency Domain Algorithm, Sine Wave Input
436(4)
6.7.6 Effect Of Transfer Function Estimation Errors: Time Domain Algorithm, Sine Wave Input
440(6)
6.7.7 Equivalent Cancellation Path Transfer Function Representation
446(4)
6.7.8 Note On Implementing Adaptive Feedforward Control Systems With Other Control Systems
450(8)
6.8 The Multiple Input, Multiple Output Filtered-X Lms Algorithm
458(19)
6.8.1 Algorithm Derivation
458(3)
6.8.2 Solution For The Optimum Set Of Weight Coefficient Vectors
461(2)
6.8.3 Solution For A Single Optimum Weight Coefficient Vector
463(1)
6.8.4 Stability And Convergence Of The Mimo Filtered-X Lms Algorithm
464(8)
6.8.5 Effect Of Transfer Function Estimation Errors Upon Algorithm Stability
472(2)
6.8.6 Convergence Properties Of The Control System
474(3)
6.9 Other Useful Algorithms Based On The Lms Algorithm
477(54)
6.9.1 Filtered-E Lms Algorithm
479(1)
6.9.1.1 Derivation Of The Single-Channel Filtered-E Lms Algorithm
479(3)
6.9.1.2 Multi-Channel Filtered-E Lms Algorithm
482(2)
6.9.2 Modified Filtered-X Lms Algorithm
484(3)
6.9.3 Douglas Fxlms Algorithm
487(1)
6.9.3.1 Derivation Of The Single-Channel Douglas Fxlms Algorithm
487(3)
6.9.3.2 Derivation Of The Multi-Channel Douglas Fxlms Algorithm
490(2)
6.9.4 Pre-Conditioned Lms Algorithm
492(6)
6.9.5 Block Processing Algorithms
498(1)
6.9.5.1 Common Block Processing Filtered-X Lms Algorithm
498(1)
6.9.5.2 Exact Block Processing Filtered-X Lms Algorithm
499(1)
6.9.5.2.1 Fast Fir Filtering
500(2)
6.9.5.2.2 Fast Fir Filter Adaptation
502(1)
6.9.6 Sparse Adaptation Algorithms
502(1)
6.9.6.1 Periodic And Sequential Update Filtered-X Lms Algorithm
503(3)
6.9.6.2 Scanning Error And Minimax Filtered-X Lms Algorithms
506(2)
6.9.6.3 Periodic Block Filtered-X Lms Algorithm
508(1)
6.9.7 Sub-Band Algorithms
509(2)
6.9.7.1 Single-Channel Delayless Sub-Band Filtered-X Lms Algorithm
511(1)
6.9.7.1.1 Sub-Band Signal Generation
511(2)
6.9.7.1.2 Sub-Band Cancellation Path Modelling
513(1)
6.9.7.1.3 Sub-Band Adaptive Coefficient Update
513(1)
6.9.7.1.4 Sub-Band/Full-Band Coefficient Transformation
514(1)
6.9.7.1.5 Full-Band Control Signal Generation
515(1)
6.9.7.2 Multi-Channel Delayless Sub-Band Filtered-X Lms Algorithm
516(3)
6.9.7.3 Implementation Issues Associated With Delayless Sub-Band Filtered-X Lms Algorithms
519(1)
6.9.8 Delayed-X Lms Algorithm
520(2)
6.9.9 Delayed-X Harmonic Synthesiser Algorithm
522(3)
6.9.10 Algorithms For Active Control Of Impulsive Disturbances
525(5)
6.9.11 Algorithms Not Sensitive To Other Uncorrected Disturbances
530(1)
6.10 Cancellation Path Transfer Function Estimation
531(42)
6.10.1 On-Line Cancellation Path Modelling By Injecting An Additional Uncorrelated Disturbance
532(4)
6.10.2 Extended On-Line Cancellation Path Modelling By Using The Control Signal
536(3)
6.10.3 Comparison Of Two On-Line Cancellation Path Modelling Approaches
539(1)
6.10.4 Cross-Updated System With On-Line Cancellation Path Modelling
540(4)
6.10.5 Variable Step Size Lms Algorithms For On-Line Cancellation Path Modelling
544(3)
6.10.6 Auxiliary Disturbance Power Scheduling Algorithms
547(3)
6.10.7 Modelling Signals
550(3)
6.10.8 Phase Error For Deficient Order Cancellation Path Modelling
553(3)
6.10.9 Simultaneous Equation Method For On-Line Cancellation Path Modelling
556(3)
6.10.10 Active Control Algorithms Without Cancellation Path Modelling
559(5)
6.10.11 Feedback Path Modelling In Feedforward Control
564(6)
6.10.12 Re-Modelling Algorithm For Periodic Primary Disturbance Cancellation
570(2)
6.10.13 Multiple Channel Cancellation Path Modelling
572(1)
6.11 Leaky Algorithms And Output Effort Constraint
573(9)
6.11.1 Leaky Filtered-X Lms Algorithm
574(3)
6.11.2 Lyapunov Tuning Leaky Lms Algorithm
577(2)
6.11.3 Output Constraint Algorithms
579(3)
6.12 Adaptive Filtering In The Frequency Domain
582(23)
6.12.1 Frequency Domain Lms Algorithm
583(3)
6.12.2 Frequency Domain Filtered-X Lms Algorithm
586(5)
6.12.3 Frequency Domain Implementation Of Delayless Sub-Band Lms Algorithm
591(7)
6.12.4 Multi-Delay Frequency Domain Algorithm For Active Control
598(7)
6.13 Adaptive Signal Processing Using Recursive (Iir) Filters
605(9)
6.13.1 Why Use An Iir Filter?
605(2)
6.13.2 Error Formulations
607(3)
6.13.3 Formulation Of A Gradient-Based Algorithm
610(2)
6.13.4 Simplifications To The Gradient Algorithm
612(2)
6.14 Application Of Adaptive Iir Filters To Active Control Systems
614(35)
6.14.1 Basic Algorithm Development
615(5)
6.14.2 Simplification Through System Identification
620(1)
6.14.3 Sharf Smoothing Filter Implementation
621(2)
6.14.4 Comparison Of Algorithms
623(9)
6.14.5 Lattice Form Of Iir Algorithms
632(10)
6.14.6 Lattice Form Steiglitz-Mcbride Algorithms
642(7)
6.15 Alternative Approach To Using Iir Filters
649(4)
6.16 Adaptive Filtering Using Artificial Neural Networks
653(9)
6.16.1 Perceptron
654(3)
6.16.2 Back-Propagation Algorithm
657(5)
6.17 Neural Network-Based Feedforward Active Control Systems
662(15)
6.17.1 Algorithm Development: Simplified Single Path Model
665(3)
6.17.2 Generalisation Of The Algorithm
668(5)
6.17.3 Comparison With The Filtered-X Lms Algorithm
673(1)
6.17.4 Example
674(3)
6.18 Adaptive Filtering Using A Genetic Algorithm
677(20)
6.18.1 Algorithm Implementation
679(1)
6.18.1.1 Killing Selection Instead Of Survivor Selection
680(1)
6.18.1.2 Weight String Instead Of Binary Encoding
681(1)
6.18.1.3 Mutation Probability And Amplitude
681(1)
6.18.1.4 Rank-Based Selection (Killing And Breeding)
681(1)
6.18.1.5 Uniform Crossover
682(1)
6.18.1.6 Genetic Algorithm Parameter Adjustment
682(1)
6.18.1.7 Performance Measurement
682(1)
6.18.2 Implementation Example
682(3)
References
685(12)
Chapter 7 Active Control Of Noise Propagating In Ducts
697(126)
7.1 Introduction
697(3)
7.1.1 Active Versus Passive Control
699(1)
7.2 Control System Implementation
700(19)
7.2.1 Feedback Control
700(1)
7.2.2 Feedforward Control
701(2)
7.2.2.1 Independent Reference Signal
703(1)
7.2.2.2 Waveform Synthesis
704(1)
7.2.2.3 Acoustic Feedback
704(15)
7.3 Harmonic (Or Periodic) Plane Waves
719(32)
7.3.1 Constant Volume Velocity Primary Source
724(1)
7.3.1.1 Optimum Control Source Volume Velocity: Idealised Rigid Primary Source Termination
725(1)
7.3.1.2 Optimum Control Source Volume Velocity: Arbitrary Uniform Impedance Termination At The Primary Source
726(1)
7.3.1.3 Effect Of Control Source Location
727(1)
7.3.1.4 Effect Of Control Source Size
727(2)
7.3.1.5 Effect Of Error Sensor Location
729(1)
7.3.2 Constant Pressure Primary Source
729(3)
7.3.3 Primary Source In The Duct Wall
732(8)
7.3.4 Finite Length Ducts
740(2)
7.3.5 Acoustic Control Mechanisms
742(1)
7.3.5.1 Constant Volume Velocity Primary Source
742(3)
7.3.5.2 Constant Pressure Primary Source
745(1)
7.3.6 Effect Of Mean Flow
746(1)
7.3.7 Multiple Control Sources
747(1)
7.3.8 Random Noise
747(4)
7.4 Higher-Order Modes
751(23)
7.4.1 Constant Volume Velocity Primary Source, Single Control Source
758(1)
7.4.1.1 Optimum Control Source Volume Velocity: Idealised Rigid Primary Source Termination
758(1)
7.4.1.2 Optimum Control Source Volume Velocity: Arbitrary Uniform Impedance Termination At The Primary Source
759(1)
7.4.1.3 Dual Control Sources
760(1)
7.4.2 Constant Pressure Primary Source
761(1)
7.4.3 Finite Length Duct
761(2)
7.4.4 Effect Of Control Source Location And Size
763(1)
7.4.5 Effect Of Error Sensor Type And Location
764(5)
7.4.6 Example Of Higher-Order Mode Control In A Spray Dryer Exhaust
769(5)
7.5 Acoustic Measurements In Ducts
774(8)
7.5.1 Duct Termination Impedance
775(1)
7.5.2 Sound Pressure Associated With Waves Propagating In One Direction
776(3)
7.5.3 Turbulence Measurement
779(1)
7.5.4 Total Power Transmission Measurements
780(1)
7.5.5 Measurement Of Control Source Power Output
780(2)
7.6 Sound Radiated From Ic Engine Exhaust Outlets
782(9)
7.7 Active / Passive Mufflers
791(1)
7.8 Control Of Pressure Pulsations In Liquid Filled Ducts
791(2)
7.9 Active Headsets And Hearing Protectors
793(30)
7.9.1 Feedback Systems
795(1)
7.9.1.1 Analogue Systems
795(9)
7.9.1.2 Adaptive Digital Feedback Systems
804(3)
7.9.2 Adaptive Digital Feedforward Systems
807(5)
7.9.3 Hybrid Feedback/Feedforward Systems
812(1)
7.9.3.1 Hybrid Analogue And Digital Feedback Systems
812(1)
7.9.3.2 Hybrid Analogue Feedback And Digital Feedforward Systems
813(2)
7.9.3.3 Hybrid Digital Feedforward And Digital Feedback Systems
815(1)
7.9.4 Transducer Considerations
816(1)
References
816(7)
Chapter 8 Active Control Of Free-Field Sound Radiation
823(160)
8.1 Introduction
823(1)
8.2 Control Of Harmonic Sound Pressure At A Point
824(7)
8.3 Minimum Acoustic Power Output Of Two Free-Field Monopole Sources
831(14)
8.4 Active Control Of Acoustic Radiation From Multiple Primary Monopole Sources Using Multiple Control Monopole Sources
845(10)
8.5 Effect Of Transducer Location
855(7)
8.5.1 Comparison Of Near-Field Error Sensing Strategies
862(1)
8.6 Reference Sensor Location Considerations
862(8)
8.6.1 Problem Formulation
863(4)
8.6.2 Gain Margin
867(2)
8.6.3 Phase Margin
869(1)
8.7 Active Control Of Harmonic Sound Radiation From Planar Structures: General Problem Formulation
870(21)
8.7.1 Minimisation Of Acoustic Pressure At Discrete Locations Using Acoustic Monopole Sources
871(7)
8.7.2 Minimisation Of Total Radiated Acoustic Power Using Acoustic Monopole Sources
878(7)
8.7.3 Minimisation Of Acoustic Pressure At Discrete Locations Using Vibration Sources
885(3)
8.7.4 Minimisation Of Total Radiated Acoustic Power Using Vibration Sources
888(3)
8.8 Example: Control Of Sound Radiation From A Rectangular Plate
891(11)
8.8.1 Specialisation For Minimisation Of Acoustic Pressure At Discrete Locations
892(6)
8.8.2 Minimisation Of Radiated Acoustic Power
898(4)
8.9 Electrical Transformer Noise Control
902(3)
8.10 A Closer Look At Control Mechanisms And A Common Link Among All Active Control Systems
905(23)
8.10.1 Common Link
906(7)
8.10.2 Acoustic Control Source Mechanisms And The Common Link
913(5)
8.10.3 Mechanism Prelude: A Vibration Source Example
918(4)
8.10.4 Control Sources And Sources Of Control
922(1)
8.10.5 Vibration Source Control Mechanisms And The Common Link
922(6)
8.11 Minimising Sound Radiation By Minimising Acoustic Radiation Modes
928(12)
8.11.1 General Theory
930(2)
8.11.2 Minimising Vibration Versus Minimising Acoustic Power
932(2)
8.11.3 Example: Minimising Radiated Acoustic Power From A Rectangular Plate
934(6)
8.11.4 Alternative Methods For Minimising Sound Radiation From Vibrating Structures
940(1)
8.12 Some Notes On Approaching The Design Of An Active Control System For Sound Radiation From A Vibrating Surface
940(6)
8.12.1 Stepping Through The Design Of A System
941(2)
8.12.2 Shortcut: Determination Of The Optimum Control Source Amplitudes And Phases Using Multiple Regression
943(3)
8.13 Active Control Of Free-Field Random Noise
946(11)
8.13.1 Analytical Basis
946(4)
8.13.2 Minimum Sound Pressure Amplitude At The Error Sensor
950(2)
8.13.3 Minimisation Of Total Radiated Acoustic Power
952(4)
8.13.4 Calculation Of The Minimum Power Output
956(1)
8.14 Active Control Of Impact Acceleration Noise
957(11)
8.14.1 Method For Obtaining Optimum Control Source Pressure Output Schedules
959(4)
8.14.2 Example: Control Of A Sinusoidal Pulse From A Single Source
963(5)
8.15 Feedback Control Of Sound Radiation From Vibrating Structures
968(15)
8.15.1 Derivation Of Structural State Equations
968(3)
8.15.2 Modification For Acoustic Radiation
971(3)
8.15.3 Problem Statement In Terms Of Transformed Modes
974(3)
References
977(6)
Chapter 9 Active Control Of Enclosed Sound Fields
983(110)
9.1 Introduction
983(1)
9.2 Control Of Harmonic Sound Fields In Rigid Enclosures At Discrete Locations
984(8)
9.3 Global Control Of Sound Fields In Rigid Enclosures
992(13)
9.4 Control Of Sound Fields In Coupled Enclosures At Discrete Locations
1005(11)
9.5 Minimisation Of Acoustic Potential Energy In Coupled Enclosures
1016(9)
9.5.1 Multiple Regression As A Shortcut
1021(4)
9.6 Calculation Of Optimal Control Source Volume Velocities Using Boundary Element Methods
1025(2)
9.7 Control Mechanisms
1027(16)
9.7.1 Acoustic Control Source Mechanisms
1027(3)
9.7.2 Vibration Control Source Mechanisms
1030(2)
9.7.3 Specialisation Of Theory For The Rectangular Enclosure Case
1032(2)
9.7.4 Specialisation Of Theory For The Finite Length Circular Cylinder Case
1034(3)
9.7.5 Specialisation Of General Model For The Cylinder With Floor System
1037(2)
9.7.6 Examination Of Mechanisms
1039(4)
9.8 Influence Of Control Source And Error Sensor Arrangement
1043(6)
9.8.1 Control Source/Error Sensor Type
1044(1)
9.8.2 Effect Of Control Source Arrangement/Numbers
1045(1)
9.8.3 Effect Of Error Sensor Location
1046(3)
9.9 Controlling Vibration To Control Sound Transmission
1049(7)
9.10 Influence Of Modal Density
1056(9)
9.11 Control Of Sound At A Point In Enclosures With High Modal Densities
1065(8)
9.12 State-Space Models Of Acoustic Systems
1073(5)
9.12.1 Feedback Control Of Sound Transmission Into A Launch Vehicle
1077(1)
9.13 Aircraft Interior Noise
1078(6)
9.13.1 Introduction
1078(2)
9.13.2 Analytical Modelling
1080(3)
9.13.3 Control Sources And Error Sensors
1083(1)
9.14 Automobile Interior Noise
1084(9)
References
1086(7)
Chapter 10 Feedforward Control Of Vibration In Beams And Plates
1093(62)
10.1 Infinite Beam
1096(16)
10.1.1 Flexural Wave Control: Minimising Vibration
1098(4)
10.1.2 Flexural Wave Control: Minimising Power Transmission
1102(3)
10.1.3 Simultaneous Control Of All Wave Types: Power Transmission
1105(1)
10.1.3.1 Longitudinal Waves
1106(1)
10.1.3.2 Torsional Waves
1107(1)
10.1.3.3 Flexural Waves
1107(4)
10.1.4 Effect Of Damping
1111(1)
10.2 Finite Beams
1112(27)
10.2.1 Equivalent Boundary Impedance For An Infinite Beam
1113(3)
10.2.2 Response To A Point Force
1116(2)
10.2.3 Response To A Concentrated Line Moment
1118(1)
10.2.4 Active Vibration Control With A Point Force
1119(2)
10.2.4.1 Effect Of Boundary Impedance
1121(1)
10.2.4.2 Effect Of Control Force Location
1122(1)
10.2.4.3 Effect Of Error Sensor Location
1123(2)
10.2.4.4 Effect Of Forcing Frequency
1125(1)
10.2.4.5 Summary Of Control Results Using A Single Control Force
1125(1)
10.2.5 Minimising Vibration Using A Piezoceramic Actuator And An Angle Stiffener
1125(3)
10.2.5.1 Effect Of Variations In Forcing Frequency, Stiffener Flange Length And Control Location On The Control Force
1128(3)
10.2.5.2 Acceleration Distribution For Controlled And Uncontrolled Cases
1131(1)
10.2.5.3 Effect Of Control Location On Attenuation Of Acceleration Level
1132(1)
10.2.5.4 Effect Of Error Sensor Location On Attenuation Of Acceleration Level
1132(1)
10.2.6 Determination Of Beam End Impedances
1133(4)
10.2.6.1 Accuracy Of The Approximation
1137(1)
10.2.7 Measuring Amplitudes Of Waves Travelling Simultaneously In Opposite Directions
1138(1)
10.3 Active Control Of Vibration In A Semi-Infinite Plate
1139(16)
10.3.1 Response Of A Semi-Infinite Plate To A Line Of Point Forces Driven In-Phase
1139(5)
10.3.2 Minimisation Of Acceleration With A Line Of In-Phase Control Forces
1144(1)
10.3.3 Minimisation Of Acceleration With A Line Of N Independently Driven Control Forces
1145(1)
10.3.4 Power Transmission
1145(1)
10.3.5 Minimisation Of Power Transmission With A Line Of In-Phase Point Control Forces
1146(3)
10.3.6 Minimisation Of Power Transmission With A Line Of N Independently Driven Point Control Forces
1149(2)
10.3.7 Numerical Results
1151(2)
References
1153(2)
Chapter 11 Feedback Control Of Flexible Structures Described In Terms Of Modes
1155(64)
11.1 Introduction
1155(1)
11.2 Modal Control
1155(25)
11.2.1 Development Of The Governing Equations
1156(3)
11.2.2 Discrete Element Model Development
1159(2)
11.2.3 Transformation Into State-Space Form
1161(2)
11.2.4 Model Reduction
1163(1)
11.2.5 Modal Control
1164(4)
11.2.6 Spillover
1168(6)
11.2.7 Optimal Control Gains For Second-Order Matrix Equations
1174(3)
11.2.8 Brief Note On Passive Damping
1177(3)
11.3 Independent Modal Space Control
1180(10)
11.3.1 Control Law Development
1181(4)
11.3.2 Modal Filters
1185(5)
11.4 Model Reduction
1190(7)
11.4.1 Modal Cost Analysis
1191(2)
11.4.2 Optimal Truncated Model
1193(1)
11.4.2.1 Classical Optimal Truncation For Low Frequencies
1193(1)
11.4.2.2 Optimal Truncation For Specified Frequency Band
1194(2)
11.4.2.3 Optimisation For Robust Control Design
1196(1)
11.5 Effect Of Model Uncertainty
1197(3)
11.5.1 Modelling Of Unstructured Uncertainties
1197(1)
11.5.2 Robust Stability And Performance
1198(1)
11.5.2.1 Robust Stability
1198(1)
11.5.2.2 Robust Performance
1199(1)
11.6 Experimental Determination Of The System Model Through Subspace Model Identification
1200(1)
11.7 Sensor And Actuator Placement Considerations
1201(10)
11.7.1 Actuator Placement
1202(1)
11.7.1.1 Transient Excitation
1202(3)
11.7.1.2 Persistent Excitation
1205(1)
11.7.2 Sensor Placement
1205(1)
11.7.2.1 Transient Excitation
1206(2)
11.7.2.2 Persistent Excitation
1208(1)
11.7.3 Additional Comments
1208(1)
11.7.4 Collocated Sensors And Actuators
1209(2)
11.8 Centralised Versus Decentralised And Distributed Control
1211(8)
11.8.1 Biologically Inspired Control
1212(1)
References
1213(6)
Chapter 12 Vibration Isolation
1219(138)
12.1 Introduction
1219(5)
12.1.1 Feedforward Versus Feedback Control
1223(1)
12.1.2 Flexible Versus Stiff Support Structures
1223(1)
12.2 Feedback Control
1224(49)
12.2.1 Single-Degree-Of-Freedom Passive System
1224(3)
12.2.2 Feedback Control Of Single-Degree-Of-Freedom System
1227(2)
12.2.2.1 Displacement Feedback
1229(1)
12.2.2.2 Velocity Feedback
1230(1)
12.2.2.3 Acceleration Feedback
1231(1)
12.2.2.4 Theoretical Closed-Loop Stability
1232(1)
12.2.2.5 Closed-Loop Instabilities In Practical Systems
1233(2)
12.2.3 Base Excited Second-Order System
1235(2)
12.2.3.1 Relative Displacement Feedback
1237(2)
12.2.3.2 Absolute Displacement Feedback
1239(1)
12.2.3.3 Relative Velocity Feedback
1240(2)
12.2.3.4 Absolute Velocity Feedback
1242(2)
12.2.3.5 Relative Acceleration Feedback
1244(1)
12.2.3.6 Absolute Acceleration Feedback
1244(2)
12.2.3.7 Force Feedback
1246(3)
12.2.3.8 Integral Force Feedback
1249(1)
12.2.3.9 Effects Of Isolator Mass
1250(1)
12.2.3.10 Closed-Loop Stability Of The Base Excited System
1250(1)
12.2.4 Multiple-Mount Vibration Isolation
1251(1)
12.2.5 Tuned Vibration Absorber
1252(1)
12.2.5.1 Tuned Mass Damper
1252(2)
12.2.5.2 Adaptive, Semi-Active And Active Tuned Mass Dampers
1254(2)
12.2.5.3 Adaptive Tuned Vibration Neutraliser
1256(1)
12.2.6 Vibration Isolation Of Equipment From A Rigid Or Flexible Support Structure
1256(1)
12.2.6.1 Rigid Support Structure
1256(1)
12.2.6.1.1 Displacement Feedback
1257(1)
12.2.6.1.2 Velocity Feedback
1258(1)
12.2.6.1.3 Acceleration Feedback
1259(1)
12.2.6.1.4 Force Feedback
1260(2)
12.2.6.1.5 Force Feedback: Control Force Applied Only To Mass
1262(2)
12.2.6.1.6 Force Feedback: Control Force Applied Only To Support
1264(3)
12.2.6.1.7 Flexible Support Structure
1267(4)
12.2.6.2 Use Of An Intermediate Mass
1271(2)
12.3 Applications Of Feedback Control
1273(35)
12.3.1 Vehicle Suspension Systems
1273(4)
12.3.1.1 Fully Active Suspensions
1277(11)
12.3.1.1.1 Preview Control
1288(4)
12.3.1.2 Slow-Active Systems
1292(1)
12.3.1.3 Semi-Active Damping Suspension Systems
1293(5)
12.3.1.4 Semi-Active Systems Incorporating Variable Stiffness
1298(1)
12.3.1.5 Switchable Damper
1298(1)
12.3.1.6 Maglev Vehicle Suspensions
1299(1)
12.3.1.7 Sensors And Actuators
1299(1)
12.3.2 Rigid Mount Active Isolation
1300(1)
12.3.3 Vibration Isolation Of High-Precision Equipment
1301(1)
12.3.3.1 Vibration Isolation Systems For Microgravity Experiments
1301(1)
12.3.4 Vibration Reduction In Tall Buildings
1302(1)
12.3.5 Active Isolation Of Machinery From Flexible Structures: Engine Mounts
1303(2)
12.3.6 Helicopter Vibration Control
1305(3)
12.4 Feedforward Control: Basic Sdof System
1308(4)
12.4.1 Control Force Acting On The Rigid Body
1309(1)
12.4.2 Control Force Acting On The Support Structure
1309(2)
12.4.3 Control Force Acting On The Rigid Body And Reacting On The Support Structure
1311(1)
12.4.4 Summary
1312(1)
12.5 Feedforward Control: Single Isolator Between A Rigid Body And A Flexible Beam
1312(11)
12.5.1 Rigid Body Equation Of Motion
1315(2)
12.5.2 Supporting Beam Equation Of Motion
1317(2)
12.5.3 System Equation And Power Transmission
1319(2)
12.5.4 Optimum Control Force And Minimum Power Transmission
1321(2)
12.6 Feedforward Control: Multiple Isolators Between A Rigid Body And A Flexible Panel
1323(14)
12.6.1 Vertical Excitation Forces Only
1324(2)
12.6.2 Generalised Excitation Forces
1326(1)
12.6.2.1 Rigid Body Equation Of Motion
1327(1)
12.6.2.2 Supporting Panel Equations Of Motion
1328(3)
12.6.2.3 System Equations Of Motion
1331(2)
12.6.2.4 Optimal Control Forces And Minimum Power Transmission
1333(3)
12.6.3 Rigid Mass As The Intermediate Structure
1336(1)
12.7 Feedforward Control: Multiple Isolators Between A Rigid Body And A Flexible Cylinder
1337(9)
12.7.1 Rigid Body Equation Of Motion
1338(1)
12.7.2 Supporting Thin Cylinder Equations Of Motion
1338(5)
12.7.3 System Equation Of Motion
1343(2)
12.7.4 Minimisation Of Power Transmission Into The Support Cylinder
1345(1)
12.8 Feedforward Control: Summary
1346(11)
References
1346(11)
Chapter 13 Control System Implementation
1357(28)
13.1 Hierarchy Of Active Control System Implementation
1357(3)
13.2 Analogue Circuit Controllers
1360(4)
13.2.1 Feedforward Controller
1360(2)
13.2.2 Feedback Controller
1362(2)
13.3 Digital Controllers
1364(15)
13.3.1 Analogue/Digital Interface
1365(2)
13.3.1.1 Sample Rate Selection
1367(4)
13.3.1.2 Converter Type And Group Delay Considerations
1371(1)
13.3.1.3 Input/Output Filtering
1372(1)
13.3.2 Micro-Processor Selection
1373(2)
13.3.3 Software Considerations
1375(1)
13.3.4 Controller Architectures
1376(2)
13.3.5 Procedures For Implementing Digital Active Controllers
1378(1)
13.4 An Example Of Active Control System Implementation
1379(6)
13.4.1 Reference Sensor
1380(1)
13.4.2 Error Sensors
1380(1)
13.4.3 Sound Sources
1381(1)
13.4.4 Controller
1381(1)
13.4.5 Control System Performance
1382(1)
References
1382(3)
Chapter 14 Sound Sources And Sound Sensors
1385(56)
14.1 Loudspeakers
1385(11)
14.1.1 Traditional Moving-Coil Loudspeakers
1385(5)
14.1.2 Electrostatic Loudspeakers
1390(2)
14.1.2.1 Electrostrictive Loudspeakers
1392(1)
14.1.3 Optical Loudspeakers
1393(2)
14.1.4 Parametric Array
1395(1)
14.2 Horns
1396(2)
14.3 Omni-Directional Microphones
1398(5)
14.3.1 Condenser Microphone
1398(2)
14.3.2 Piezoelectric Microphone
1400(2)
14.3.3 Optical Microphones
1402(1)
14.3.4 Microphone Sensitivity
1402(1)
14.4 Directional Microphones
1403(7)
14.4.1 Tube Microphones
1403(2)
14.4.2 Microphone Arrays
1405(2)
14.4.2.1 Summary Of The Underlying Beamforming Theory
1407(1)
14.4.3 Gradient Microphones
1408(2)
14.5 Turbulence Filtering Sensors
1410(7)
14.5.1 Probe Tube Microphones
1410(1)
14.5.1.1 Effect Of Slit Flow Resistance On Acoustic Sensitivity
1411(1)
14.5.1.2 Effect Of Flow Speed On Acoustic Sensitivity
1412(1)
14.5.1.3 Effect Of Probe Tube Orientation
1413(1)
14.5.1.4 Effect Of Probe Tube Diameter
1413(1)
14.5.1.5 Effect Of A Reflective Duct Termination
1413(1)
14.5.1.6 Probe Tube Design Guidelines
1413(1)
14.5.1.7 Other Probe Tube Designs
1414(1)
14.5.2 Microphone Arrays
1415(1)
14.5.3 Use Of Two Microphones And A Recursive Linear Optimal Filter
1415(1)
14.5.4 Microphone Boxes
1415(2)
14.6 Virtual Sensing Algorithms For Active Noise Control
1417(24)
14.6.1 Virtual Sensing Problem Formulation
1417(1)
14.6.2 Spatially Fixed Virtual Sensing Algorithms
1418(1)
14.6.2.1 Virtual Microphone Arrangement
1418(1)
14.6.2.2 Remote Microphone Technique
1419(1)
14.6.2.3 Forward Difference Prediction Technique
1420(2)
14.6.2.4 Adaptive Lms Virtual Microphone Technique
1422(2)
14.6.2.5 Kalman Filtering Virtual Sensing Method
1424(4)
14.6.2.6 Stochastically Optimal Tonal Diffuse Field (Sotdf) Virtual Sensing Method
1428(3)
14.6.3 Moving Virtual Sensing Algorithms
1431(1)
14.6.3.1 Remote Moving Microphone Technique
1431(2)
14.6.3.2 Adaptive Lms Moving Virtual Microphone Technique
1433(1)
14.6.3.3 Kalman Filtering Moving Virtual Sensing Method
1434(1)
14.6.3.4 Stochastically Optimal Tonal Diffuse Field (Sotdf) Moving Virtual Sensing Method
1435(1)
References
1436(5)
Chapter 15 Vibration Sensors And Vibration Sources
1441(80)
15.1 Accelerometers
1441(7)
15.1.1 Accelerometer Mounting
1445(2)
15.1.2 Phase Response
1447(1)
15.1.3 Temperature Effects
1447(1)
15.1.4 Earth Loops
1447(1)
15.1.5 Handling
1448(1)
15.2 Velocity Transducers
1448(2)
15.3 Displacement Transducers
1450(2)
15.3.1 Proximity Probe
1450(1)
15.3.2 Linear Variable Differential Transformer (Lvdt)
1451(1)
15.3.3 Linear Variable Inductance Transducers (Lvit)
1452(1)
15.4 Strain Sensors
1452(13)
15.4.1 Resistive Strain Gauges
1453(2)
15.4.2 Pvdf Film
1455(3)
15.4.2.1 One-Dimensional Shaped Sensor
1458(1)
15.4.2.2 Two-Dimensional Shaped Sensor For Simply Supported Boundary Conditions
1459(2)
15.4.2.3 Two-Dimensional Shaped Sensor For Arbitrary Boundary Conditions
1461(1)
15.4.3 Optical Fibres
1461(4)
15.5 Hydraulic Actuators
1465(1)
15.6 Pneumatic Actuators
1466(1)
15.7 Proof Mass (Or Inertial) Actuator
1467(3)
15.8 Electrodynamic And Electromagnetic Actuators
1470(1)
15.9 Magnetostrictive Actuators
1471(3)
15.9.1 Magnetic Bias
1472(1)
15.9.2 Mechanical Bias Or Prestress
1473(1)
15.9.3 Frequency Response, Displacement And Force
1473(1)
15.9.4 Disadvantages Of Terfenol Actuators
1473(1)
15.10 Shape Memory Alloy Actuators
1474(1)
15.11 Piezoelectric (Electrostrictive) Actuators
1475(13)
15.11.1 Thin Actuators
1476(1)
15.11.1.1 One-Dimensional Actuator Model: Effective Moment
1477(4)
15.11.1.2 Two-Dimensional Actuator Analysis
1481(5)
15.11.2 Thick Actuators
1486(2)
15.12 Smart Structures
1488(20)
15.12.1 Novel Actuator Configurations
1488(1)
15.12.2 Shunted Piezoelectric Dampers
1488(6)
15.12.3 Piezoelectric Sensoriactuators
1494(7)
15.12.4 Energy Harvesting From Vibration
1501(7)
15.13 Electro-Rheological Fluids
1508(4)
15.14 Magneto-Rheological Fluids
1512(9)
References
1515(6)
Appendix A BRIEF REVIEW OF SOME RESULTS OF LINEAR ALGEBRA
1521(8)
A.1 Matrices And Vectors
1521(1)
A.2 Addition, Subtraction And Multiplication By A Scalar
1521(1)
A.3 Multiplication Of Matrices
1522(1)
A.4 Transposition
1523(1)
A.5 Determinants
1524(1)
A.6 Matrix Inverses
1525(1)
A.7 Rank Of A Matrix
1526(1)
A.8 Positive And Non-Negative Definite Matrices
1526(1)
A.9 Eigenvalues And Eigenvectors
1526(1)
A.10 Orthogonality
1527(1)
A.11 Vector Norms
1528(1)
References
1528(1)
Index 1529
Colin Hansen is professor emeritus in the School of Mechanical Engineering at the University of Adelaide. He established the ANVC group at the university in 1987 and led the group until his retirement at the end of 2011. The group is internationally recognized for its extensive contributions to the advancement of scientific knowledge in many aspects of active noise and vibration control. In 2012 he was made the 15th honorary fellow of the International Institute of Acoustics and Vibration (IIAV) in recognition of his "outstanding contributions to scientific knowledge in acoustics, noise and vibration" and in 2009 was awarded the Rayleigh Medal by the British Institute of Acoustics for "outstanding contributions to acoustics".

Scott Snyder is currently pro vice-chancellor, strategy and planning, at Charles Darwin University (CDU). He has also been the Executive Director, Corporate Services and an Executive Dean at that institution. Prior to moving to CDU, Snyder was a member of academic staff in the School of Mechanical Engineering at the University of Adelaide, and later head of IT Services at that organization. His Ph.D. was in the area of active noise and vibration control and he spent a number of years undertaking further research on ANVC in Japan and at the University of Adelaide prior to being appointed to Academic Staff.

Xiaojun Qiu is a professor in acoustics and signal processing and head of the Institute of Acoustics, Nanjing University. He worked with Colin Hansen in the School of Mechanical Engineering at the University of Adelaide, Australia, as a research fellow from 1997 to 2002. He is a member of the Audio Engineering Society and the International Institute of Acoustics and Vibration. He has authored and co-authored two books and more than 250 technical papers, and holds more than 70 patents on audio acoustics and audio signal processing.

Laura Brooks is an adjunct lecturer at the School of Mechanical Engineering at the University of Adelaide. She was selected by Engineers Australia for inclusion in the list of Australia's Most Inspiring Young Engineers in 2005 and was awarded the 2006 Fulbright Postgraduate Award in Engineering. Her research interests include aeroacoustics, ocean acoustics, seismic noise, vibrations, active control, signal processing, and engineering education.

Danielle Moreau is a postdoctoral research associate at the School of Mechanical Engineering at the University of Adelaide, where she received a University Postdoctoral Research Medal for her Ph.D. research on virtual sensing in active control. The focus of Dr Moreaus current work is on the understanding and control of flow-induced noise. She has more than 20 publications and has given seminars to research groups in Japan and the United States.
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