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Über dieses Buch

Control of Noise and Structural Vibration presents a MATLAB®-based approach to solving the problems of undesirable noise generation and transmission by structures and of undesirable vibration within structures in response to environmental or operational forces. The fundamentals of acoustics, vibration and coupling between vibrating structures and the sound fields they generate are introduced including a discussion of the finite element method for vibration analysis. Following this, the treatment of sound and vibration control begins, illustrated by example systems such as beams, plates and double walls. Sensor and actuator placement is explained as is the idea of modal sensor–actuators. The design of appropriate feedback systems includes consideration of basic stability criteria and robust active structural acoustic control. Positive position feedback (PPF) and multimode control are also described in the context of loudspeaker–duct and loudspeaker–microphone models. The design of various components is detailed including the analog circuit for PPF, adaptive (semi-active) Helmholtz resonators and shunt piezoelectric circuits for noise and vibration suppression. The text makes extensive use of MATLAB® examples and these can be simulated using files available for download from the book’s webpage at End-of-chapter exercises will help readers to assimilate the material as they progress through the book. Control of Noise and Structural Vibration will be of considerable interest to the student of vibration and noise control and also to academic researchers working in the field. It’s tutorial features will help practitioners who wish to update their knowledge with self-study.



Chapter 1. Introduction

The presence of structure-borne sound is a persistent problem in acoustics. Various noise control techniques, such as passive, active, or a combination of the two control techniques (hybrid), have been developed in different fields to reduce the noise. Among those techniques, the traditional passive noise reduction techniques are widely used in industries and commercial products. Passive control methods typically use absorptive materials or vibration absorbers to achieve noise reduction. They are proved to be very effective in the middle and high frequency ranges. However, in the low frequency range, passive noise control often makes noise elimination equipment very bulky and inefficient. For example, absorptive materials are not a practical means of attenuation at low frequencies because of the thickness requirement to absorb the large acoustic wavelengths. Similarly, damping materials typically are not effective in attenuating low-frequency vibrations and radiating sound. Thick and massive viscous materials are required, which again presents a practicality problem with implementing this traditional control technique to realistic applications. Efficient vibration and noise reduction approach in the low frequency range thus poses a challenging topic to noise control engineers.
Qibo Mao, Stanislaw Pietrzko

Chapter 2. Vibration and Sound Radiation

In this chapter, we discuss the general structural–acoustic problem. Before we begin to investigate the active control of structural–acoustic system, it is important to review some of the basic theory of structural–acoustics and the coupling between vibrating structures and the radiated sound field. The dynamics of continuous systems (such as beam and plate) is the focus of this chapter. Firstly, the structural modes and natural frequencies for beam- and plate-type structures are presented. The results will be used in the analysis and design of active control of vibration and sound radiation from these structural types throughout this book. Secondly, by using the Fourier transform, the sound pressures and sound powers of the vibrating structures are discussed in the wave-number domain. Finally, the calculation of sound power by using radiation mode approach is presented. Additionally, some information for several basic commands from GUI, which are used in the design of the interface of the program used throughout this book, will be given in this chapter. It is hoped that this chapter serves as a tutorial introduction not only to structural–acoustic analysis but also to the use of MATLAB and GUI.
Qibo Mao, Stanislaw Pietrzko

Chapter 3. Introduction Examples on Control of Sound and Vibration

In this chapter, the physical basics for active control of sound and vibration are presented. Some examples of the active control of one-dimensional acoustic pressure and structural–acoustic systems (such as beam, plate, and double plate) will be presented. It should be noted that we focus on the control performance due to the physical aspects in this chapter, so the disturbance sources are assumed tonal and constant. Sections 3.1 and 3.2 describe the control performance for a one-dimensional duct by using single or double control sources; then the control performance due to the different cost functions (such as cancellation of pressure or absorbing reflected wave) is discussed. Section 3.3 describes several active control strategies for structural–acoustic problems, such as minimization of the sound power, cancellation of the volume velocity, and cancellation of the first few radiation modes. Section 3.4 discusses the control performances for beam-type structures by using point forces as control sources. Section 3.5 discusses the control performances for plate-type structures by using the piezoelectric actuators and point forces as control sources. Section 3.6 discusses the sound transmission loss for double-plate structures by using different control sources.
Qibo Mao, Stanislaw Pietrzko

Chapter 4. Distributed Transducers by Using Smart Materials

In this chapter, we consider the design of piezoelectric sensors and actuators for structural vibration and sound control. Firstly, the robust stability analysis of the collocated sensor/actuator pair is discussed. Secondly, the design of modal sensors by using shaped PVDF films for beam-type structures is presented. Thirdly, the modal sensor by using a PVDF array is discussed. Finally, the design of 2-D modal sensor/actuator is also discussed.
Qibo Mao, Stanislaw Pietrzko

Chapter 5. Feedback Control

The aim of this chapter is to illustrate the design of the feedback control system for beam and plate structures. In Sect. 5.1, the linear quadratic regulator (LQR) problem is presented. In Sect. 5.2, the linear quadratic Gaussian (LQG) problem is discussed with vibrating beam and plates. One GUI program is given to compare the control performance between LQR and LQG controllers. In Sect. 5.3, the basic principle of modal control is given. In Sect. 5.4, we review SISO analytical models for a structure and closed-loop analysis techniques. Basic stability criteria tools for feedback control system, such as root locus criterion and Bode plot and Nyquist criterion, and their use in identification of gain and phase margins are discussed. In Sect. 5.5, the internal model control (IMC) is presented. In some special cases, the feedback control system can be seen as a feedforward system by using IMC. In Sect. 5.6, the design of a robust control system is discussed. In this section, the theory of robust control is not presented but the preparation for control design for several practical design cases by using MATLAB is given extensively. Two tutorial examples, i.e., control of vibration of a vibrating beam and control of sound radiation of a plate, are given and discussed in detail. How to generate the generalized plant and how to select the weighting functions are the main topics in this section.
Qibo Mao, Stanislaw Pietrzko

Chapter 6. Positive Position Feedback (PPF) Control

This chapter presents the design of a positive position feedback (PPF) controller based on low-pass filters and band-pass filters. In Sect. 6.1, the principle of the PPF controller is presented based on the single degree of freedom (SDOF) case. In Sect. 6.2, the loudspeaker–duct model is developed, several model interconnection methods in MATLAB are presented, and then the influence of loudspeaker dynamics is discussed. In Sect. 6.3, for the loudspeaker/microphone pair at the same location, the design of a PPF controller with an all-pass filter as phase compensation is presented. The Nyquist diagram, gain and phase margin, and root locus analysis are used to analyze the stability of the PPF controller. In Sect. 6.4, the PPF controller is extended for non-collocated loudspeaker/microphone pair. The calculation results show that the similar sound pressure reduction can be obtained by using a PPF controller with a non-collocated loudspeaker/microphone pair. In Sect. 6.5, the multimode control is discussed by using a single loudspeaker/microphone pair. In Sect. 6.6, a GUI program is given to design and analyze the PPF controller for a loudspeaker–duct model. And then we discuss how to share data between Simulink and GUI programs. In Sect. 6.7, the analog circuit for design of PPF controllers and all-pass filters are presented. Finally, some experimental results are presented to verify the simulation results.
Qibo Mao, Stanislaw Pietrzko

Chapter 7. Semi-active Control Using Adaptive Helmholtz Resonators

Active control systems want external power to operate the actuators and controller. Large power sources may be required in some applications, and it may make the control systems very bulky. In addition, the usual concerns associated with all active systems, i.e., stability robustness and actuator saturation, hold true for active sound and vibration control systems too. Semi-active devices require less energy than active devices. The main advantages of semi-active control are that it requires less power, costs less, and has reduced complexity in comparison to active system. Furthermore, the semi-active control is nearly as effective as active system. Semi-active systems are inherently passive and always stable. They are also less vulnerable to power failure. In this chapter, adaptive (semi-active) Helmholtz resonators for noise control are presented. In Sects. 7.1 and 7.2, the basic theory of the Helmholtz resonator (HR) is presented, and then an experimental setup is designed to measure the frequency response of the HR to verify the numerical results. In Sect. 7.3, the theoretical and experimental studies are presented for the sound control in rigid duct structures by using HRs. In Sects. 7.4 and 7.5, control sound transmission through double-plate structures using optimally tuned HRs is discussed, an analytical model of fully coupled structural–acoustic-HRs inside a double-plate structure is established, and then some experimental results are presented. In Sect. 7.6, the design of adaptive HRs is presented and experimentally verified.
Qibo Mao, Stanislaw Pietrzko

Chapter 8. Shunt Piezoelectric Circuits

In this chapter, the shunt piezoelectric circuits are discussed for vibration/noise suppression. In Sect. 8.1, a brief review of development of shunt piezoelectric damping techniques is given. In Sect. 8.2, the general modelling for the different shunt piezoelectric damping (such as RL series circuit, RL parallel circuit, RL-C circuit, and negative capacitance circuit) is presented. In Sect. 8.3, based on minimizing sound power of structure, the optimal parameters for shunt circuits are discussed. In Sect. 8.4, the switch law for the state- and pulse-switching circuits is discussed. In Sect. 8.5, the detail numerical calculations are given and discussed. In Sect. 8.6, with the example of clamped plate, experimental results are given by using RL series/parallel circuit and pulse-switching circuit.
Qibo Mao, Stanislaw Pietrzko


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