Sound Waves and Acoustic Emission

59 Pages·2023·1.277 MB·English

by  Claudia Barile, Caterina Casavola, Giovanni Pappalettera, Vimalathithan Paramsamy Kannan

Synthesis Lectures on
Wave Phenomena in the Physical Sciences
Claudia Barile · Caterina Casavola ·
Giovanni Pappalettera ·
Vimalathithan Paramsamy Kannan
Sound Waves and
Acoustic Emission
Synthesis Lectures on Wave Phenomena
in the Physical Sciences
Series Editor
Sanichiro Yoshida, Department of Chemistry and Physics, Southeastern Louisiana
University, Hammond, LA, USA
The aim of this series is to discuss the science of various waves. An emphasis is laid on
graspingthebigpictureofeachsubjectwithoutdealingformalism,andyetunderstanding
thepracticalaspectsofthesubject.Tothisend,mathematicalformulationsaresimplified
as much as possible and applications to cutting edge research are included.
Claudia Barile Caterina Casavola
(cid:1)
(cid:129)
Giovanni Pappalettera
(cid:1)
Vimalathithan Paramsamy Kannan
Sound Waves and Acoustic
Emission
123
ClaudiaBarile Caterina Casavola
Department ofMechanics Department ofMechanics
Mathematics, andManagement Mathematics, andManagement
Polytechnic University ofBari Polytechnic University ofBari
Bari, Italy Bari, Italy
GiovanniPappalettera Vimalathithan Paramsamy Kannan
Department ofMechanics Department ofMechanics
Mathematics, andManagement Mathematics, andManagement
Polytechnic University ofBari Polytechnic University ofBari
Bari, Italy Bari, Italy
ISSN 2690-2346 ISSN 2690-2354 (electronic)
Synthesis Lectures onWave Phenomena inthe Physical Sciences
ISBN978-3-031-23788-1 ISBN978-3-031-23789-8 (eBook)
https://doi.org/10.1007/978-3-031-23789-8
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Contents
1 What is Sound? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Perception of Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 How Does Sound Travel? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Properties of Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Speed of Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Propagation of Sound Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Simple Harmonic Vibrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Damped Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Propagation of Waves on a String. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Solution for the Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.1 Wave Energy of the Transverse Wave . . . . . . . . . . . . . . . . . . . . 21
2.4.2 Reflection of the Transverse Wave at a Boundary. . . . . . . . . . . . 24
2.5 Longitudinal Wave Propagation in Bars . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.1 Longitudinal Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Transverse Wave Propagation in Bars. . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7 Dispersion of Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 Acoustic Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1 Propagation of Elastic Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.1 Longitudinal Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.2 Transverse Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1.3 Rayleigh Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.4 Lamb Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.5 Other Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Attenuation and Distortion of Elastic Waves . . . . . . . . . . . . . . . . . . . . . 40
4 Acousto-Ultrasonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1 Brief Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Stress Wave Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3 Attenuation and Dispersion of Acousto-Ultrasonic Stress Waves . . . . . . 46
References. .... .... .... .... .... ..... .... .... .... .... .... ..... .... 51
v
About the Authors
ClaudiaBarile isanAssociateProfessorofMechanicalDesignandExperimentalDesign
at Politecnico di Bari where she is also a lecturer at the Bachelor and Master Degree of
IndustrialDesignandattheMasterDegreeofMechanicalEngineering.Hermainresearch
interests are connected with material characterization and experimental mechanics
including strain gauges methods, acoustic emission, and residual stress analysis. She is a
member of the Ph.D. committee in Mechanical and Management Engineering at
Politecnico di Bari. She is the author of more than one hundred papers published in
international journals andconference proceedings. Sheistheco-author offive booksand
member of international and national associations including the Society of Experimental
Mechanics,theEuropeanSocietyofExperimentalMechanics,andtheSocietàScientifica
Italiana di Progettazione Meccanica e Costruzione di Macchine.
Prof.CaterinaCasavola isaFullProfessorofMechanicalDesignatPolitecnicodiBari,
and she teaches the Design of Innovative Materials, Experimentation on Aerostructures,
and Experimental Mechanics. Her research activity is concerned with mechanical
characterization of innovative materials, experimental stress analysis on real components
(1:1 scale) and in situ inspection, study of residual stress generation, evolution and
measurements (hole drilling method both with strain gage rosette and ESPI, X-Ray
diffractometer,Barkhausennoise),andmonitoringofelectronicboardandcomponentsby
meansofspeckleinterferometry.SheistheScientificDirectoroftheLaboratoryofStatic
and Dynamic tests, the Laboratory of Residual Stresses, the Laboratory of Experimental
StressAnalysis,theLaboratoryEMILIA(ExperimentalMechanicsIntegratedLaboratory
In Aerospace), and the Laboratory of Telemetry at Politecnico di Bari.
GiovanniPappalettera isanAssociateProfessoratPolitecnicodiBariwhereheisalsoa
lecturerattheBachelorandMasterDegreeofIndustrialDesignandattheMasterDegree
of Mechanical Engineering. His main research interests are connected with material
characterization and experimental mechanics including optical methods, acoustic emis-
sion, and residual stress analysis. He is a member of the Ph.D. committee in Mechanical
and Management Engineering at Politecnico di Bari. He is the author of more than one
hundred papers published in international journals and conference proceedings and is
vii
viii About theAuthors
co-inventorofthreepatents.Heistheco-authoroftwobooksandmemberofinternational
associations including the Society of Experimental Mechanics and the European Society
of Experimental Mechanics.
VimalathithanParamsamyKannan isaResearcheratPolitecnicodiBari,Italy,where
he obtained his Ph.D. degree with honours in 2021. His research interests include
Mechanical Characterization of Engineering Materials through Non-destructive Evalua-
tiontechniques,particularlyAcousticEmissiontechnique.Healsohasaspecialinterestin
theCharacterizationofPolymer-based CompositeMaterials. Hehaspublished morethan
30 articles in international conferences and peer-reviewed journals onAcoustic Emission
technique.
What is Sound? 1
Whether it is a symphony of Mozart from a stein piano or an unpleasant noise from a
pneumatic drill, both are recognized as sound. But what may be the definition of sound?
Soundisawave,indeed,becauseittransmitsenergyfromoneplacetoanotherbymeans
of a medium but the medium itself is not transported. Hence, before we search for the
definitionofsound,letustakeamomenttodiscussthedefinitionofawave.Awaveisa
self-sustainingdisturbanceofamedium.Itcanbesimplydefinedasadisturbanceofsome
kindorachangeinequilibrium.Whenthisdisturbanceoccursintheambientpressureor
the density, we perceive the sound wave. Therefore, sound is the disturbance of ambient
pressure, that we receive through our ears and perceive by our auditory system.
1.1 Perception of Sound
How do we perceive sound? Human auditory system is nothing more than an advanced
and integrated signal processing system. Figure 1.1 shows the section of a human ear.
A human or an animal auditory system has ear canal, which ends at the tympanic
membrane (or simply known as ear drum). The tympanic membrane is connected to the
inner ear through a mechanical linkage of three bones: malleus, incus, and stapes. These
mechanical linkages are connected to a liquid filled organ cochlea. When a sound wave
reaches our ear, the disturbances pass through the ear canal and vibrates the three bones.
The vibrations of these bones over cochlea generates signals for the brain, which pro-
cesses these nerve signals as sound. Consider it similar to the functioning of a telegram.
Now, we consider a microphone, which is one of the other mechanical systems com-
monlyusedforperceivingsound.Itworksonthesameprincipleofvibration/fluctuations
©The Author(s), underexclusive license to SpringerNature SwitzerlandAG2023 1
C. Barile et al.,SoundWaves andAcoustic Emission,Synthesis Lectures onWave
Phenomena inthe Physical Sciences, https://doi.org/10.1007/978-3-031-23789-8_1
2 1 WhatisSound?
Fig. 1.1 Human auditory
system (taken fromWikipedia)
duetothepressuredisturbances.Themechanicalresponseofthepressuredisturbancesdue
tosound isconverted into electrical signals via capacitors ora piezoelectric crystal.
1.2 How Does Sound Travel?
Sofar,wehaveseenhowthesoundisperceivedbuthowdoesthesoundtravel?Atypical
wave, with respect to the propagating direction, travels either as a longitudinal or a
transverse wave. In simple terms, the difference between longitudinal and transverse
wavescanbeexplainedbyonekeyfeature.Inlongitudinalwaves,thedisturbancesoccur
only in one direction, which is the direction of the wave propagation. Whereas in
transversewave,thereisaninfinitenumberofdirections,alllyinginaplanenormaltothe
direction of propagation, the disturbances can occur as shown in Fig. 1.2a. Longitudinal
waves propagate through the compression and rarefaction in the propagating medium, as
shown in Fig. 1.2b. By definition, sound waves propagate by the compression and rar-
efaction of pressure, density or particle displaced in all fluids. Therefore, in most cases,
soundtravelsasalongitudinalwave.However,soundcantravelasbothlongitudinaland
transverse waves in solids, which will discuss later in detail.
ConsidertheblackdotsinFig. 1.2basairmolecules,andwecanassociatethefigureto
the propagation of sound. It is worth repeating that the sound wave propagates by the
displacement of pressure in the air molecules. So obviously, sound needs molecules for
travel. Not surprisingly, sound does not travel in near-empty regions of space. In space,
eveniftwoastronautsarefloatingnexttoeachother,theironlywayofcommunicationis
radio devices (or sign language).