Active Control of Vibration
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Table of contents
- Contentsiii
- Prefaceix
- Chapter 1. Introduction to Mechanical Vibrations1
- 1.1 Introduction1
- 1.2 Terminology1
- 1.3 Single-degree-of-freedom (SDOF) systems4
- 1.4 Free motion of SDOF systems5
- 1.5 Damped motion of SDOF systems6
- 1.6 Forced response of SDOF systems9
- 1.7 Transient response of SDOF systems and the use of the Laplace transform11
- 1.8 Multi-degree-of-freedom (MDOF) systems15
- 1.9 Free motion of MDOF systems16
- 1.10 Forced response of MDOF systems20
- 1.11 Damped motion of MDOF systems20
- 1.12 Finite element analysis of vibrating mechanical systems21
- Chapter 2. Introduction to Waves in Structures25
- 2.1 Introduction25
- 2.2 Longitudinal waves27
- 2.3 Flexural waves30
- 2.4 Flexural response of an infinite beam to an oscillating point force33
- 2.5 Flexural wave power flow34
- 2.6 Flexural response of an infinite thin beam to an oscillating line moment35
- 2.7 Free flexural motion of finite thin beams36
- 2.8 Response of a finite thin beam to an arbitrary oscillating force distribution39
- 2.9 Vibration of thin plates43
- 2.10 Free vibration of thin plates45
- 2.11 Response of a thin rectangular simply supported plate to an arbitrary oscillating force distrib46
- 2.12 Vibration of infinite thin cylinders48
- 2.13 Free vibration of finite thin cylinders52
- 2.14 Harmonic forced vibration of infinite thin cylinders53
- Chapter 3. Feedback Control59
- 3.1 Introduction59
- 3.2 Single-channel feedback control60
- 3.3 Stability of a single-channel system62
- 3.4 Modification of the response of an SDOF system64
- 3.5 The effect of delays in the feedback loop66
- 3.6 The state variable approach68
- 3.7 Example of a two-degree-of-freedom system72
- 3.8 Output feedback and state feedback76
- 3.9 State estimation and observers80
- 3.10 Optimal control83
- 3.11 Modal control86
- Chapter 4. Feedforward Control91
- 4.1 Introduction91
- 4.2 Single channel feedforward control92
- 4.3 The effect of measurement noise95
- 4.4 Adaptive digital controllers97
- 4.5 Multichannel feedforward control102
- 4.6 Adaptive frequency domain controllers103
- 4.7 Adaptive time domain controllers107
- 4.8 Equivalent feedback controller interpretation111
- Chapter 5. Distributed Transducers for Active Control of Vibration115
- 5.1 Introduction115
- 5.2 Piezoelectric material and definitions116
- 5.3 Piezoelectric stack actuators118
- 5.4 Piezoelectric one-dimensional asymmetric wafer actuators120
- 5.5 Piezoelectric one-dimensional anti-symmetric wafer actuators127
- 5.6 Piezoelectric two-dimensional anti-symmetric wafer actuators131
- 5.7 Piezoelectric distributed sensors138
- 5.8 Modal estimation with arrays of point sensors141
- 5.9 Wavenumber estimation with arrays of point sensors143
- 5.10 Wave vector filtering with arrays of point sensors144
- 5.11 Shape memory alloy actuators and sensors147
- Chapter 6. Active Control of Vibration in Structures153
- 6.1 Introduction153
- 6.2 Feedforward control of finite structures154
- 6.3 Feedback control of finite structures161
- 6.4 Feedforward control of wave transmission165
- 6.5 Actuator arrays for control of flexural waves168
- 6.6 Sensor arrays for control of flexural waves172
- 6.7 Feedforward control of flexural waves174
- 6.8 Feedback control of flexural waves178
- Chapter 7. Active Isolation of Vibrations185
- 7.1 Introduction185
- 7.2 Isolation of periodic vibrations of an SDOF system186
- 7.3 Vibration isolation from a flexible receiver; the effects of secondary force location190
- 7.4 Active isolation of periodic vibrations using multiple secondary force inputs193
- 7.5 Finite element analysis of an active system for the isolation of periodic vibrations197
- 7.6 Practical examples of multi-channel feedforward control for the isolation of periodic vibrations202
- 7.7 Isolation of unpredictable vibrations from a receiving structure206
- 7.8 Isolation of vibrating systems from random external excitation; the possibilities for feedforwar211
- 7.9 Isolation of vibrating systems from random external excitation; analysis of feedback control str213
- 7.10 Isolation of vibrating systems from random external excitation; formulation in terms of modern216
- 7.11 Active isolation of vehicle vibrations from road and track irregularities217
- Chapter 8. Active Structural Acoustic Control. I Plate Systems223
- 8.1 Introduction223
- 8.2 Sound radiation by planar vibrating surfaces; the Rayleigh integral224
- 8.3 The calculation of radiated sound fields by using wavenumber Fourier transforms230
- 8.4 Sound power radiation from structures in terms of their multi-modal response236
- 8.5 General analysis of Active Structural Acoustic Control (ASAC) for plate systems240
- 8.6 Active control of sound transmission through a rectangular plate using point force actuators251
- 8.7 Active control of structurally radiated sound using multiple piezoelectric actuators; interpreta254
- 8.8 The use of piezoelectric distributed structural error sensors in ASAC261
- 8.9 An example of the implementation of feedforward ASAC265
- 8.10 Feedback control of sound radiation from a vibrating baffled piston267
- 8.11 Feedback control of sound radiation from distributed elastic structures272
- Chapter 9. Active Structural Acoustic Control. II Cylinder Systems277
- 9.1 Introduction277
- 9.2 Coupled cylinder acoustic fields277
- 9.3 Response of an infinite cylinder to a harmonic forcing function279
- 9.4 Active control of cylinder interior acoustic fields using point forces282
- 9.5 Active control of vibration and acoustic transmission in fluid-filled piping systems287
- 9.6 Active control of sound radiation from vibrating cylinders294
- 9.7 Active control of sound in finite cylinder systems298
- 9.8 Control of interior noise in a full scale jet aircraft fuselage302
- Appendix. State Variables307
- A.1 Introduction307
- A.2 General solution to the state variable equation307
- A.3 The transient response308
- A.4 Transformation of variables309
- A.5 Modal coordinates311
- References313
- Index327
This book is a companion text to Active Control of Sound by P.A. Nelson and S.J. Elliott, also published by Academic Press. It summarizes the principles underlying active vibration control and its practical applications by combining material from vibrations, mechanics, signal processing, acoustics, and control theory. The emphasis of the book is on the active control of waves in structures, the active isolation of vibrations, the use of distributed strain actuators and sensors, and the active control of structurally radiated sound. The feedforward control of deterministic disturbances, the active control of structural waves and the active isolation of vibrations are covered in detail, as well as the more conventional work on modal feedback. The principles of the transducers used as actuateors and sensors for such control strategies are also given an in-depth description. The reader will find particularly interesting the two chapters on the active control of sound radiation from structures: active structural acoustic control. The reason for controlling high frequency vibration is often to prevent sound radiation, and the principles and practical application of such techniques are presented here for both plates and cylinders. The volume is written in textbook style and is aimed at students, practicing engineers, and researchers.
Key Features
* Combines material from vibrations, signal processing, mechanics, and controls
* Summarizes new research in the field
Key Features
* Combines material from vibrations, signal processing, mechanics, and controls
* Summarizes new research in the field