Introduction

Noise and vibration are often treated separately in the study of dynamics, and it is sometimes forgotten that the two are inter-related – i.e. they simply relate to the transfer of molecular motional energy in different media (generally fluids and solids respectively). It is the intention of this book to bring noise and vibration together within a single volume instead of treating each topic in isolation. Central to this is the concept of wave–mode duality; it is generally convenient for engineers to think of noise in terms of waves and to think of vibration in terms of modes. A fundamental understanding of noise, vibration and interactions between the two therefore requires one to be able to think in terms of waves and also in terms of modes of vibration.

This chapter reviews the fundamentals of vibrating mechanical systems with reference to both wave and mode concepts since the dynamics of mechanical vibrations can be studied in terms of either. Vibration deals (as does noise) with the oscillatory behaviour of bodies. For this oscillatory motion to exist, a body must possess inertia and elasticity. Inertia permits an element within the body to transfer momentum to adjacent elements and is related to density. Elasticity is the property that exerts a force on a displaced element, tending to return it to its equilibrium position. (Noise therefore relates to oscillatory motion in fluids whilst vibration relates to oscillatory motion in solids.)

Introduction

A time history of a noise or vibration signal is just a direct recording of an acoustic pressure fluctuation, a displacement, a velocity, or an acceleration waveform with time – it allows a view of the signal in the time domain. A basic noise or vibration meter would thus provide a single root-mean-square level of the time history measured over a wide frequency band which is defined by the limits of the meter itself. These single root-mean-square levels of the noise or vibration signals generally represent the cumulative total of many single frequency waves since the time histories can be synthesised by adding single frequency (sine) waves together using Fourier analysis procedures. Quite often, it is desirable for the measurement signal to be converted from the time to the frequency domain, so that the various frequency components can be identified, and this involves frequency or spectral analysis. It is therefore important for engineers to have a basic understanding of spectral analysis techniques. The appropriate measurement instrumentation for monitoring noise and vibration signals were discussed in section 4.3 in chapter 4. The subsequent analysis of the output signals, in both the time and frequency domains, forms the basis of this chapter.

Just as any noise or vibration signal that exists in the real world can be generated by adding up sine waves, the converse is also true in that the real world signal can be broken up into sine waves such as to describe its frequency content.

Introduction

It is becoming increasingly apparent to engineers that condition monitoring of machinery reduces operational and maintenance costs, and provides a significant improvement in plant availability. Condition monitoring involves the continuous or periodic assessment of the condition of a plant or a machine component whilst it is running, or a structural component whilst it is in service. It allows for fault detection and prediction of any anticipated failure, and it has significant benefits including (i) decreased maintenance costs, (ii) increased availability of machinery, (iii) reduced spare part stock holdings and (iv) improved safety.

Criticality and failure mode analysis techniques are commonly used to identify where improvements in machinery availability and reductions in maintenance costs can be achieved through the integration of condition monitoring techniques. This involves selecting the appropriate modes of condition monitoring (safety, online or offline vibration monitoring, and/or online or offline performance monitoring) based on the machine criticality and modes of failure, and also focuses on optimising the condition monitoring system to achieve specified objectives effectively and at least total cost. Criticality and failure mode analysis now also includes consideration of total production output and plant efficiency (in addition to breakdown/reliability), since these aspects of plant operation are equally important to total operating costs and production output, and hence bottom-line profits of large-scale petrochemical and power generation facilities. Consideration of total production output and plant efficiency represents the latest development in condition monitoring systems and is generically referred to as performance monitoring.

A significant amount of applied technology pertaining to noise and vibration analysis and control has emerged over the last thirty years or so. It would be an impossible task to attempt to cover all this material in a text book aimed at providing the reader with a fundamental basis for noise and vibration analysis. This book is therefore only concerned with some of the more important fundamental considerations required for a systematic approach to engineering noise and vibration analysis and control, the main emphasis being the industrial environment. Thus, this book is specifically concerned with the fundamentals of noise and vibration analysis for mechanical engineers, structural engineers, mining engineers, production engineers, maintenance engineers, etc. It embodies eight self-contained chapters, each of which is summarised here.

The first chapter, on mechanical vibrations, is a review of some fundamentals. This part of the book assumes no previous knowledge of vibration theory. A large part of what is presented in this chapter is covered very well in existing text books. The main difference is the emphasis on the wave–mode duality, and the reader is encouraged to think in terms of both waves and modes of vibration. As such, the introductory comments relate to both lumped parameter models and continuous system models. The sections on the dynamics of a single oscillator, forced vibrations with random excitation and multiple oscillator are presented using the traditional ‘mechanical vibrations’ approach. The section on continuous systems utilises both the traditional ‘mechanical vibrations’ approach and the wave impedance approach.

Introduction

At the very beginning of this book, the concept of wave–mode duality was emphasised. Its importance to engineering noise and vibration analysis will be illustrated in this chapter via a specific case study relating to pipe flow noise.

The general subject of flow-induced noise and vibrations is a large and complex one. The subject includes: (i) internal axial pipe flows – the transmission of large volume flows of gases, liquids or two phase mixtures across high pressure drops through complex piping systems comprising bends, valves, tee-junctions, orifice plates, expansions, contractions, etc.; (ii) internal cross-flows in heat exchangers, etc. with the associated vortex shedding, acoustic resonances and fluid-elastic instabilities; (iii) external axial and cross-flows – e.g. vortex shedding from chimney stacks; (iv) cavitation; and (v) structure-borne sound associated with some initial aerodynamic type excitation. The reader is referred to Naudascher and Rockwell, a BHRA (British Hydromechanics Research Association) conference publication and Blake for discussions on a wide range of practical experiences with flow-induced noise and vibrations.

This chapter is, in the main, only concerned with the study of noise and vibration from steel pipelines with internal gas flows – this noise and vibration is flow-induced and is of considerable interest to the process industries. There are many instances of situations where flow-induced noise and vibration in cylindrical shells have caused catastrophic failures. The mechanisms of the generation of the vibrational response of and the external sound radiation from pipes due to internal flow disturbances are discussed in this chapter.

Introduction

Sound is a pressure wave that propagates through an elastic medium at some characteristic speed. It is the molecular transfer of motional energy and cannot therefore pass through a vacuum. For this wave motion to exist, the medium has to possess inertia and elasticity. Whilst vibration relates to such wave motion in structural elements, noise relates to such wave motion in fluids (gases and liquids). Two fundamental mechanisms are responsible for sound generation. They are:

1. the vibration of solid bodies resulting in the generation and radiation of sound energy – these sound waves are generally referred to as structure-borne sound;

2. flow-induced noise resulting from pressure fluctuations induced by turbulence and unsteady flows – these sound waves are generally referred to as aerodynamic sound.

With structure-borne sound, the regions of interest are generally in a fluid (usually air) at some distance from the vibrating structure. Here, the sound waves propagate through the stationary fluid (the fluid has a finite particle velocity due to the sound wave, but a zero mean velocity) from a readily identifiable source to the receiver. The region of interest does not therefore contain any sources of sound energy – i.e. the sources which generated the acoustic disturbance are external to it. A simple example is a vibrating electric motor. Classical acoustical theory (analysis of the homogeneous wave equation) can be used for the analysis of sound waves generated by these types of sources.

Introduction

Statistical energy analysis (S.E.A.) is a modelling procedure for the theoretical estimation of the dynamic characteristics of, the vibrational response levels of, and the noise radiation from complex, resonant, built-up structures using energy flow relationships. These energy flow relationships between the various coupled subsystems (e.g. plates, shells, etc.) that comprise the built-up structure have a simple thermal analogy, as will be seen shortly. S.E.A. is also used to predict interactions between resonant structures and reverberant sound fields in acoustic volumes. Many random noise and vibration problems cannot be practically solved by classical methods and S.E.A. therefore provides a basis for the prediction of average noise and vibration levels particularly in high frequency regions where modal densities are high. S.E.A. has evolved over the past two decades and it has its origins in the aero-space industry. It has also been successfully applied to the ship building industry, and it is now being used (i) as a prediction model for a wide range of industrial noise and vibration problems, and (ii) for the subsequent optimisation of industrial noise and vibration control.

Lyon's book on the general applicability of S.E.A. to dynamical systems was the first serious attempt to bring the various aspects of S.E.A. into a single volume. It is a useful starting point for anyone with a special interest in the topic.

Introduction

Wave–mode duality concepts were introduced and discussed in some detail in chapter 1. It was pointed out that, whilst the lumped-parameter approach to mechanical vibrations is adequate to describe mode shapes and natural frequencies, it is not suitable for relating vibrations to radiated noise. One therefore has to use the fundamental wave approach to obtain an understanding of the essential features of mechanical vibrations as they relate to sound radiation and sound transmission. These interactions between sound waves and the mechanical vibrations of solid structures form a very important part of engineering noise and vibration control.

Because solids can store energy in shear and compression, all types of waves can be sustained in structures – i.e. compressional (longitudinal) waves, flexural (transverse or bending) waves, shear waves and torsional waves. On the other hand, since fluids can only store energy in compression, they can only sustain compressional (longitudinal) waves. For reasons which will become evident later on in this chapter, flexural (bending) waves are the only type of structural wave that plays a direct part in sound radiation and transmission. At this stage it is sufficient to note that the primary reason for this is that the bending wave particle velocities are perpendicular to the direction of wave propagation (see Figure 1.1b) resulting in an effective exchange of energy between the structure and the fluid.

The study of noise and vibration and the interactions between the two is now fast becoming an integral part of mechanical engineering courses at various universities and institutes of technology around the world. There are many undergraduate text books available on the subject of mechanical vibrations and there are also a relatively large number of books available on applied noise control. There are also several text books available on fundamental acoustics and its physical principles. The books on mechanical vibrations are inevitably only concerned with the details of vibration theory and do not cover the relationships between noise and vibration. The books on applied noise control are primarily designed for the practitioner and not for the engineering student. The books on fundamental acoustics generally concentrate on physical acoustics rather than on engineering noise and vibration and are therefore not particularly well suited to the needs of engineers. There are also several excellent specialist texts available on structural vibrations, noise radiation and the interactions between the two. These texts do not, however, cover the overall area of engineering noise and vibration, and are generally aimed at the postgraduate research student or the practitioner. There are also a few specialist reference handbooks available on shock and vibration and noise control – these books are also aimed at the practitioner rather than the engineering student.

A list of several international journals that publish research and development articles related to various aspects of engineering noise and vibration control is presented below.

1. Acustica – S. Hirzel Verlag

2. Applied Acoustics – Elsevier Applied Science

3. Current Awareness Abstracts – Vibration Institute

4. Journal of the Acoustical Society of America – Acoustical Society of America

5. Journal of Fluid Mechanics – Cambridge University Press

6. Journal of Fluids and Structures – Academic Press

7. Journal of Sound and Vibration – Academic Press

8. Journal of Vibration, Acoustics, Stress, and Reliability in Design – American Society of Mechanical Engineers

9. Mechanical Systems and Signal Processing – Academic Press

10. Noise and Vibration in Industry – Multi-Science

11. Noise Control Engineering Journal – Institute of Noise Control Engineers

12. Shock and Vibration Digest – Vibration Institute

13. Sound and Vibration – Acoustical Publications, Inc.

Introduction

A vast amount of applied technology relating to noise and vibration control has emerged over the last twenty years or so. It would be an impossible task to attempt to cover all this material in a text book aimed at providing the reader with a fundamental basis for noise and vibration analysis, let alone in a single chapter! This chapter is therefore only concerned with some of the more important fundamental considerations required for a systematic approach to engineering noise and vibration control, the main emphasis being the industrial environment. The reader is referred to Harris4.1 for a detailed engineering-handbook-type coverage of existing noise control procedures, and to Harris and Crede4.2 for a detailed engineering-handbook-type coverage of existing shock and vibration control procedures. Beranek4.3 also covers a wide range of practical noise and vibration control procedures. Some of the more recent advances relating to specific areas of noise and vibration control are obviously not available in the handbook-type literature, and one has to refer to specialist research journals. A list of major international journals that publish research and development articles in noise and vibration control is presented in Appendix 1.

This chapter commences with a discussion on noise and vibration measurement units. The emphasis is on the fundamental principles involved with the selection of objective and subjective sound measurement scales, vibration measurement scales, frequency analysis bandwidths, and the addition and subtraction of decibels.