Vibration, Acoustics and Strain Measurement: Theory and Experiments

Preface
Acknowledgement
About the Book
Contents
About the Author
1 Introduction
2 Theory of Vibration
	2.1 Introduction
	2.2 Single-Degree-of-Freedom System
		2.2.1 Translatory System
		2.2.2 Torsional System
		2.2.3 Damping
		2.2.4 Free Damped Vibration
		2.2.5 Structural/Hysteretic Damping
		2.2.6 Forced Vibration
		2.2.7 Response with Unbalanced Forces
		2.2.8 Vibration Isolation
	2.3 Two-Degree-of-Freedom System
		2.3.1 Translatory System
		2.3.2 Coupled Translation and Rotation
		2.3.3 Undamped Vibration Absorber
	2.4 Multi-degree-of-Freedom System
		2.4.1 Free Vibration of Undamped Multi-degree-of-Freedom System
		2.4.2 Free Vibration of Multi-degree-of-Freedom System with Damping
		2.4.3 Orthogonality of Natural Modes
		2.4.4 Free Vibration of Multi-degree-of-Freedom System in Terms of Modal Coordinates
		2.4.5 Forced Response to Harmonic Excitation: Frequency Response Function (FRF)
	2.5 Vibrations of Continuous Systems
		2.5.1 Introduction to Continuous Systems
		2.5.2 Longitudinal Vibration of a Rod
		2.5.3 Transverse Vibration of Euler–Bernoulli Beam
	List of Symbols
	Abbreviations
	Questions
	Bibliography
3 Equipment for Measurement and Generation of Vibration
	3.1 Introduction to Vibration Transducers
		3.1.1 Choice of Vibration Parameter—Displacement, Velocity, and Acceleration
		3.1.2 Active and Passive Transducers
		3.1.3 Absolute and Relative Measuring Instruments
		3.1.4 Contact and Non-contact Transducers
		3.1.5 Earliest Vibration Transducer: The Hand Vibrograph
	3.2 Absolute Measuring Transducers or Seismic Transducers
		3.2.1 Seismic Transducer Theory
		3.2.2 Seismic Displacement Transducer of the Inductive Type
		3.2.3 Seismic Velocity Transducer: Electrodynamic Pickup
		3.2.4 Seismic Inductive Accelerometer
	3.3 Displacement Transducers
		3.3.1 Eddy Current Transducer
		3.3.2 Capacitance Pickup/Condenser Vibrometer
		3.3.3 Fibre Optic Probe
		3.3.4 Holography
	3.4 Velocity Transducers
		3.4.1 Electromagnetic Transducer
		3.4.2 Laser Doppler Vibrometer
	3.5 Acceleration Transducers
		3.5.1 Piezoelectric Accelerometer
		3.5.2 Microelectro-Mechanical Systems (MEMS)-Based Accelerometers
		3.5.3 Servo Accelerometer
	3.6 Rotary Vibration Transducers
		3.6.1 Rotary Variable Differential Transformer (RVDT)/Torsional Vibration Pickup
		3.6.2 Laser-Based Torsional Vibration Transducer
	3.7 Smart Sensors (Plug-and-Play Devices) …
	3.8 Comparison of Transducers
	3.9 Introduction to Vibration Excitation Techniques
		3.9.1 Choice of Excitation Technique
	3.10 Vibration Exciters of the Contact Type
		3.10.1 Electrodynamic Vibration Shaker
		3.10.2 Modal Thrusters
		3.10.3 Mechanical Exciters of the Direct Drive Type
		3.10.4 Reaction-Type Exciters
		3.10.5 Inertial Systems
		3.10.6 Electrohydraulic/Hydraulic Exciters
		3.10.7 Lead Zirconate Titanate Actuators
		3.10.8 Summary of Intrusive Excitation Techniques
	3.11 Non-intrusive (Non-contact) Excitation Techniques
		3.11.1 Near Non-intrusive Excitation Using Electrodynamic Shaker
		3.11.2 Operational Excitation/Ambient Testing
		3.11.3 Step Relaxation
		3.11.4 Impact Testing Using Modal Hammers
		3.11.5 Acoustic Excitation
		3.11.6 Electromagnetic Exciter
		3.11.7 Assessment of Non-intrusive Excitation Techniques
	3.12 Signal Conditioning Amplifiers
	List of Symbols
	Abbreviations
	Questions
	Bibliography
4 Fundamentals of Acoustics
	4.1 Human Perception of Sound
		4.1.1 Sound Pressure and Sound Pressure Level (SPL)
		4.1.2 Frequencies of Interest and Frequency Weighting
	4.2 Sound Wave Propagation in 1-Dimension (1-D)
		4.2.1 Longitudinal Waves in a Column of Gas
	4.3 Sound Propagation in 3-Dimensional (3-D) Space: The 3-D Wave Equation
	4.4 Some Important Acoustic Quantities and Relations
		4.4.1 Velocity of Sound
		4.4.2 Characteristic Impedance and Specific  Acoustic Impedance
		4.4.3 Energy Density and Intensity
		4.4.4 Sound Power
		4.4.5 Levels
		4.4.6 Additive Effects of Sound
		4.4.7 Radiation Fields of a Sound Source
	4.5 Sound Transmission from One Medium  to Another with Normal Incidence
		4.5.1 Sound Transmission Though a Solid Barrier  with Normal Incidence
	4.6 Acoustics of Enclosed Spaces
		4.6.1 Acoustic Field in a Small Rectangular Room
		4.6.2 Sound Pressure Level in a Large Enclosure
		4.6.3 Decay of a Sound Field in an Irregularly  Shaped Enclosure
	List of Symbols
	Abbreviations
	Questions
	Bibliography
5 Equipment for Measurements  in Acoustics
	5.1 Parameters to Be Considered in the Choice of Microphones
		5.1.1 Technical Considerations
	5.2 Various Types of Microphones
		5.2.1 The Carbon Granule Microphone
		5.2.2 Condenser Microphone
		5.2.3 Electret Capacitor Microphone (ECM)
		5.2.4 Electrodynamic/Moving Coil Microphone
		5.2.5 Piezoelectric Microphone
		5.2.6 The Ribbon Microphone
		5.2.7 MEMS Microphone
	5.3 Acoustic Exciters
		5.3.1 Technical Specifications of a Loudspeaker
		5.3.2 Electrodynamic/Moving Coil Loudspeaker
		5.3.3 Electrostatic Loudspeaker (ESL)
		5.3.4 Ribbon Driven Speakers
		5.3.5 Piezoelectric Speaker
		5.3.6 Electropneumatic Transducer
	5.4 Sound Level Measurement
		5.4.1 Sound Level Meter
		5.4.2 A, B, C, D and LIN Frequency Weighting Networks
		5.4.3 1/1 and 1/3 Octave Filters
		5.4.4 Time Averaging
		5.4.5 Integrating Sound Level Meters
		5.4.6 Acoustic Calibrators
	5.5 Acoustic Chambers
		5.5.1 Anechoic Chamber
		5.5.2 Reverberation Chambers
	List of Symbols
	Abbreviations
	Questions
	Bibliography
6 Theory of Stress Analysis
	6.1 Introduction
		6.1.1 Statically Determinate and Indeterminate Structures
	6.2 Axial Loading: Normal Stress and Strain
		6.2.1 Stress–Strain Relation for Steel
		6.2.2 Different Types of Materials
	6.3 Pure Shear
	6.4 Two-Dimensional Stress–Strain
	6.5 Thin-Walled Pressure Vessel
	6.6 Beams in Bending
	6.7 Torsional Stresses and Displacements
		6.7.1 Theory
	6.8 Buckling of Columns
	6.9 Stress Concentration for Flat Bars in Tension
	List of Symbols
	Questions
	Bibliography
7 Strain Gauge-Based Equipment
	7.1 Introduction
	7.2 Strain Gauges
		7.2.1 Electrical Wire Gauge
		7.2.2 Foil Gauge
		7.2.3 Thin Film Gauges
		7.2.4 Semiconductor Strain Gauges
		7.2.5 Error in Strain Gauge Measurements
	7.3 The Wheatstone Bridge
		7.3.1 The Instrumentation Carrier Frequency Amplifier
	7.4 Transducers for Force Measurement
		7.4.1 Strain Gauge Load Cell
		7.4.2 Piezoelectric Force Transducer
	7.5 Transducers for Torque Measurement
		7.5.1 Static Torque Measurement
		7.5.2 Strain Gauge-Based Transducer
	7.6 Pressure Transducers
		7.6.1 Strain Gauge-Based Pressure Transducers
	7.7 Equipment that Facilitate Measurements on Rotating Structures
		7.7.1 Stroboscope
		7.7.2 Slip Ring Unit
		7.7.3 Measurements Using Telemetry System
		7.7.4 Non-contact Rotary Transformer
	List of Symbols
	Abbreviations
	Questions
	Bibliography
8 Fundamentals of Signal Analysis
	8.1 Introduction
	8.2 Various Steps in Data Acquisition and Processing
		8.2.1 Data Acquisition Systems
		8.2.2 Analogue and Digital Signals
		8.2.3 Analogue-to-Digital Converter (A/D Converter or ADC)
		8.2.4 Digital-to-Analogue Conversion
	8.3 Some Important Signal Operations
		8.3.1 Amplitude Scaling
		8.3.2 Translation/Time Shifting
		8.3.3 Time Scaling
		8.3.4 Time Inversion/Reversal/Folding/Flipping
		8.3.5 Even and Odd Parts of a Signal
	8.4 Some Important Concepts Related to Signals and Systems
		8.4.1 Unit Impulse Function
		8.4.2 Impulse Response Function (IRF)
		8.4.3 Linear Time-Invariant System
		8.4.4 Causal Systems and Signals
		8.4.5 Stability
		8.4.6 Frequency Response Function
	8.5 Frequency Domain Analysis
		8.5.1 Symmetry Properties of the Fourier Transform
		8.5.2 Fourier Transform Theorems
		8.5.3 Fourier Transform of Sequences
	8.6 Sampling of Continuous-Time Signals
		8.6.1 Undersampling and Aliasing
		8.6.2 Anti-aliasing Filter
		8.6.3 Sampling Theory
		8.6.4 Nyquist–Shannon Sampling Theorem
		8.6.5 Mathematical Sampling and Aliasing: Harmonic Signal
		8.6.6 Band-Limited Sampling and Aliasing
		8.6.7 Reconstruction of Original Signal Using Reconstruction Filters
	8.7 The Fast Fourier Transform
	8.8 FFT Analyser Setup
		8.8.1 Setup for Spectrum Collection
		8.8.2 Setup for Analysing Time Waveforms
		8.8.3 Leakage and Windowing
		8.8.4 Averaging
		8.8.5 Zoom
	8.9 Dealing with Random Signals
		8.9.1 Introduction
		8.9.2 Modelling of Random Processes
		8.9.3 Probabilistic Model
		8.9.4 Some Common Distributions
		8.9.5 Statistical Descriptors for Random Signals
	8.10 Classification of Random Data
		8.10.1 Stationarity
		8.10.2 Ergodicity
	8.11 Frequency Domain Representation of Random Signals
		8.11.1 Relationship Between Autocorrelation Rxx(τ) and Power Spectral Density Sxx(f)
	8.12 Response of an SDOF System
		8.12.1 Response to Harmonic Excitation
		8.12.2 Response to Transient Excitation
		8.12.3 Response-to-Random Loading
	List of Symbols
	Special Operators
	Abbreviations
	Questions
	Bibliography
9 Basics of Experimental Modal Analysis
	9.1 Introduction
	9.2 Important Experimental Aspects of Modal Testing
		9.2.1 Support Conditions of Test Structure
		9.2.2 Choice of Exciters/Shakers
		9.2.3 Impact Testing and Difficulties
		9.2.4 Sensing Techniques
		9.2.5 Selection of Excitation Signals for Modal Testing
		9.2.6 Applications and Features of a Signal Generator
	9.3 Representation and Properties of FRF Data of SDOF and MDOF Systems
		9.3.1 Graphical Display of FRF Data for SDOF Systems
		9.3.2 Characteristics and Presentation of MDOF FRF Data
	9.4 Obtaining FRFs with True Random Excitation
		9.4.1 Single- and Multiple-Input System Response Models
		9.4.2 Issues Involved in Multiple-Input Multiple- Output (MIMO) Analysis
		9.4.3 Estimation of Frequency Response Functions
	9.5 Signal Processing Problems and Solutions in Modal Analysis
		9.5.1 Autoranging
		9.5.2 Removing Noise and Distortion from Measurements
		9.5.3 Windowing
	9.6 Modal Parameter Extraction Methods for SDOF  and MDOF Systems
		9.6.1 Preliminary Checks of FRF Data
		9.6.2 SDOF Modal Analysis
		9.6.3 MDOF Curve Fitting Methods
	List of Symbols
	Abbreviations
	Questions
	Bibliography
10 Vibration Experiments
	10.1 Free Vibration (Translation) Using Impact Excitation
	10.2 Forced Vibration (Translation) Using Stepped Sinusoidal Excitation
	10.3 Forced Vibration Experiment with Swept Sine Excitation
	10.4 Forced Vibration Using Random Excitation
	10.5 Free Vibration (Torsion) and Determination of Mass Moment …
	10.6 Determination of Effective Radius of Gyration of a Body …
	10.7 Measurement of Critical Speed of Shaft
	10.8 Determination of Force Transmissibility
	10.9 Measurement of Displacement Transmissibility
	10.10 Determination of Stiffness of Isolators
	10.11 Determination of Natural Frequencies and Damping Ratios …
	10.12 Calibration of Vibration Transducer
	10.13 Measurement of Complex Modulus of Elasticity
	10.14 Study of Dynamic Vibration Absorber
	10.15 Modal Analysis of Plates: Sand Patterns of Mode Shapes
	10.16 Modal Analysis: Roving Pickup and Fixed Shaker
	10.17 Modal Analysis: Roving Impact and Fixed Transducer
	Bibliography
11 Experiments in Acoustics
	11.1 Measurement of Sound Pressure Level
	11.2 Measurement of Sound Power from Sound  Pressure Levels: ISO 3744 and 3745
	11.3 Measurement of Sound Power from Sound Pressure Levels: ISO 3746 Engineering Method
	11.4 Measurement of Sound Power from Sound Pressure Levels in Diffuse Field Environment:  ISO 3741–3743
	11.5 Sound Intensity Measurement Using Two-Microphone Method
	11.6 Sound Intensity Measurement Using a Fast Fourier Transform (FFT) Analyser
	11.7 Sound Absorption Measurement Using a Standing Wave Tube
	11.8 Acoustic Impedance Measurement Using the Two-Microphone Method (The Transfer  Function Method)
	11.9 Absorption Coefficient Measurement Using a Reverberation Chamber
	11.10 Measurement of Reverberation Time of a Chamber
	11.11 Measurement of Sound Transmission Loss (TL) Using Sound Pressure Level and Reverberation Time: ASTM E-90
	11.12 Measurement of Transmission Loss Using Sound Pressure Level and Sound Intensity
	11.13 Measurement of Transmission Loss and Single Number Ratings (STC) Using Impedance Tube
	Bibliography
12 Common Experiments in Stress Analysis
	12.1 Strain Gauge Installation
	12.2 Axial Load: Quarter Bridge with Single Active Gauge
	12.3 Axial Load: Half Bridge with Two Active Gauges in Opposite Arms
	12.4 Axial Load: Half Poisson Bridge
	12.5 Axial Load: Full Poisson Bridge
	12.6 Bending Strain Analysis of Cantilever Beam with Quarter Bridge
	12.7 Measurement of Bending Strain: Half Bridge with Gauges in Adjacent Arms
	12.8 Measurement of Bending Strain: 1/2 Poisson Bridge
	12.9 Bending Strain: Full Bridge
	12.10 Bending Strain: Full Poisson Bridge
	12.11 Torsional Strain Measurement Using Half Bridge
	12.12 Torsional Strain Measurement with Full Bridge
	12.13 Determination of Longitudinal and Hoop Stresses and Fluid Pressure …
	12.14 Determination of Longitudinal and Hoop Stresses and Fluid Pressure …
	12.15 Determination of Young's Modulus of Elasticity and Poisson's Ratio …
		12.15.1 Determination of Poisson's Ratio
		12.15.2 Determination of Young's Modulus of Elasticity
	12.16 Three-Point Bending Experiment for Determination of Flexural Modulus …
	12.17 Measurement of Dynamic Strains
	12.18 Measurement of Strains Due to Combined Bending and Torsion
	12.19 Study of Buckling Behaviour of a Column
	12.20 Measurement of Stress Concentration Factors
	Bibliography
Appendix  Index
Index