Acoustic Waves Part 1 pdf

Abbasov Acoustic Waves in Phononic Crystal Plates 91 Xin-Ye Zou, Xue-Feng Zhu, Bin Liang and Jian-Chun Cheng Frequency-Domain Numerical Modelling of Visco-Acoustic Waves with Finite-Dif

Acoustic Waves

edited by

Don W Dissanayake

SCIYO

Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher No responsibility is accepted for the accuracy of information contained in the published articles The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods

or ideas contained in the book

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Technical Editor Teodora Smiljanic

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First published September 2010

Printed in India

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Acoustic Waves, Edited by Don W Dissanayake

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ISBN 978-953-307-111-4

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Reverberation-Ray Matrix Analysis of Acoustic Waves

in Multilayered Anisotropic Structures 25

Yongqiang Guo and Weiqiu Chen

Rectifying Acoustic Waves 47

Yukihiro Tanaka, Takahiro Murai, and Norihiko Nishiguchi

Dispersion Properties of Co-Existing Low Frequency Modes

in Quantum Plasmas 57

S A Khan and H Saleem

Research of the Scattering of Non-linearly Interacting

Plane Acoustic Waves by an Elongated Spheroid 73

Iftikhar B Abbasov

Acoustic Waves in Phononic Crystal Plates 91

Xin-Ye Zou, Xue-Feng Zhu, Bin Liang and Jian-Chun Cheng

Frequency-Domain Numerical Modelling

of Visco-Acoustic Waves with Finite-Difference

and Finite-Element Discontinuous Galerkin Methods 125

Romain Brossier, Vincent Etienne, Stéphane Operto and Jean Virieux

Shear Elastic Wave Refraction on a Gap between Piezoelectric Crystals with Uniform Relative Motion 159

Nick Shevyakhov and Sergey Maryshev

Surface Acoustic Wave Based Wireless MEMS Actuators

for Biomedical Applications 181

Don W Dissanayake, Said Al-Sarawi and Derek Abbott

Surface Acoustic Wave Motors and Actuators: Mechanism,

Structure, Characteristic and Application 207

Shu-yi Zhang and Li-ping Cheng

Contents

Real Time Methods for Wideband Data Processing Based

on Surface Acoustic Waves 233

N V Masalsky

Aluminium Nitride thin Film Acoustic Wave Device

for Microfl uidic and Biosensing Applications 263

Y.Q Fu, J S Cherng, J K Luo, M.P.Y Desmulliez, Y Li,

A J Walton and F Placido

Application and Exploration of Fast Gas Chromatography - Surface Acoustic Wave Sensor to the Analysis of Thymus Species 299

Se Yeon Oh, Sung-Sun Park, and Jongki Hong

Application of Acoustic Waves to Investigate

the Physical Properties of Liquids at High Pressure 317

Piotr Kiełczyński

Pressure and Temperature Microsensor Based

on Surface Acoustic Wave in TPMS 341

Tianli Li, Hong Hu, Gang Xu, Kemin Zhu and Licun Fang

Analysis and Modelling of Surface Acoustic Wave

Chemical Vapour Sensors 359

Marija Hribšek and Dejan Tošić

Laser-Based Determination of Decohesion and Fracture Strength

of Interfaces and Solids by Nonlinear Stress Pulses 377

Peter Hess

Ultrasonics: A Technique of Material Characterization 397

Dharmendra Kumar Pandey and Shri Pandey

Dissipation of Acoustic Waves in Barium Monochalcogenides 431

Rajendra Kumar Singh

Statistical Errors in Remote Passive Wireless SAW Sensing

Employing Phase Differences 443

Y.S Shmaliy, O.Y Shmaliy, O Ibarra-Manzano,

J Andrade-Lucio, and G Cerda-Villafana

VI

Surface Acoustic Wave (SAW) devices are widely used in multitude of device concepts mainly

in Micro Electro Mechanical Systems (MEMS) and communication electronics As such, SAW based micro-sensors, actuators and communication electronic devices are well known applications of SAW technology Due to their solid state design and fabrication compatible with other modern technologies such as Microwave Integrated Circuits (MIC), MEMS, (Charge Coupled Devices) CCD and integrated optic devices, SAW based sensors are considered to be extremely reliable For example, SAW based passive micro sensors are capable of measuring physical properties such as temperature, pressure, variation in chemical properties, and SAW based communication devices perform a range of signal processing functions, such as delay lines, fi lters, resonators, pulse compressors, and convolvers In recent decades, SAW based low-powered actuators and microfl uidic devices have signifi cantly contributed towards their popularity

SAW devices are based on propagation of acoustic waves in elastic solids and the coupling

of these waves to electric charge signals via an input and an output Inter Digital Transducers (IDT) that are deposited on the piezoelectric substrate Since the introduction of the fi rst SAW devices in the 1960s, this fl exibility has facilitated a great level of creativity in the design of different types of devices, which has resulted in low cost mass production alongside with modern electronic, biomedical and similar systems

In recent times, SAW devices have become an indispensable part of the modern electronic communication industry due to their usefulness as IF, RF, and GPS fi lters for various applications Over the years, SAW devices are known to offer superior performance in communication due to a range of factors such as high stability, excellent aging properties, low insertion attenuation, high stopband rejection and processing gain, and narrow transition width from passband to the stopband Therefore, it is evident that SAW based wireless communication is a well-established fi eld in RF–MEMS and Bio–MEMS devices, and has a great potential to incorporate with modern biosensors, micro actuators and biological implants Furthermore, passive SAW sensors can be RF controlled wirelessly through a transceiver unit over distances of several meters, without the need of a battery Hence, such devices are well suited for use in a wide range of sensor and identifi cation systems

This book consists of 20 exciting chapters composed by researchers and engineers active in the fi eld of SAW technology, biomedical and other related engineering disciplines The topics range from basic SAW theory, materials and phenomena to advanced applications such as sensors actuators, and communication systems As such, fi rst part of this book is dedicated to several chapters that present the theoretical analysis and numerical modelling such as Finite Element Modelling (FEM) and Finite Difference Methods (FDM) of SAW devices Then, some exciting research contributions in SAW based actuators and micro motors are presented in

Preface

Don W Dissanayake,

The School of Electrical and Electronic Engineering,

The University of Adelaide,

Australia

1899 The existence of the P-wave and the S-wave was also verified by the classical elastic theory However, with the discovery of some new phenomena of elastic waves in anisotropic solids, it is found that the limitations of classical elastic theory have become obvious Furthermore, the current concepts and theories of elastic waves can not answer several basic questions of elastic wave propagation in anisotropic solids For example, how many elastic waves are there? How many wave types are there? What is the space pattern of elastic waves? As we know, the Christoffel’s equation, which is often used to describe anisotropic elastic waves in the classical elastic theory, can not indicate the space pattern and the complete picture of elastic wave propagation in anisotropic solids, but only show the difference of propagation in the different directions along an axis or a section (Vavrycuk, 2005) The reason for this is that the classical elastic wave equations, expressed by displacements can not distinguish the different elastic sub-waves (except for isotropic solids), because the elasticity and anisotropy of solids are synthesized in an elastic matrix Similarly, for the electromagnetic fields, except for the Helmholtz’s equation of electromagnetic waves in isotropic media, the laws of propagation of electromagnetic waves

in anisotropic media are also not clear to us From the Maxwell’s equation, the explicit equations of electromagnetic waves in anisotropic media could not be obtained because the dielectric permittivity matrix and magnetic permeability matrix were all included in these equations, so that only local behaviour of electromagnetic waves, for example, in a certain plane or along a certain direction, can be studied (Yakhno et al., 2006)

The theory of linear piezoelectricity is based on a quasi-static approximation (Tiersten et al., 1962) In this theory, although the mechanical equations are dynamic, the electromagnetic equations are static and the electric field and the magnetic field are not coupled Therefore it does not describe the wave behaviour of electromagnetic fields Electromagnetic waves generated by mechanical fields (Mindlin, 1972) need to be studied in the calculation of radiated electromagnetic power from a vibrating piezoelectric device (Lee et al., 1990), and are also relevant in acoustic delay lines (Palfreeman, 1965) and wireless acoustic wave sensors (Sedov et al., 1986), where acoustic waves produce electromagnetic waves or vise versa When electromagnetic waves are involved, the complete set of Maxwell equation needs to be used,

Acoustic Waves

2

coupled to the mechanical equations of motion Such a fully dynamic theory is called

piezoelectromagnetism by some researchers (Lee, 1991) Piezoelectromagnetic SH waves were

studied by Li (Li, 1996) using scalar and vector potentials, which results in a relatively

complicated mathematical model of four equations Two of these equations are coupled, and

the other two are one-way coupled In addition, a gauge condition needs to be imposed A

different formulation was given by Yang and Guo (Yang et al., 2006), which leads to two

uncoupled equations Piezoelectromagnetic SH waves over the surface of a circular cylinder of

polarized ceramics were analyzed Although many works have been done for the

piezoelectromagnetic waves in piezoelectric solids, the explicit uncoupled equations of

piezoelectromagnetic waves in the anisotropic media could not be obtained because of the

limitations of classical theory In this chapter, the idea of eigen theory presented by author

(Guo, 1999; 2000; 2001; 2002; 2005; 2007; 2009; 2009; 2010; 2010; 2010) is used to deal with both

the Maxwell’s electromagnetic equation and the Newton’s motion equation By this method,

the classical Maxwell’s equation and Newton’s equation under the geometric presentation can

be transformed into the eigen Maxwell’s equation and Newton’s equation under the physical

presentation The former is in the form of vector and the latter is in the form of scalar As a

result, a set of uncoupled modal equations of electromagnetic waves and elastic waves are

obtained, each of which shows the existence of electromagnetic and elastic sub-waves,

meanwhile the propagation velocity, propagation direction, polarization direction and space

pattern of these sub-waves can be completely determined by the modal equations

In section 2, the elastic waves in anisotropic solids were studied under six dimensional eigen

spaces It was found that the equations of elastic waves can be uncoupled into the modal

equations, which represent the various types of elastic sub-waves respectively In section 3, the

Maxwell’s equations are studied based on the eigen spaces of the physical presentation, and

the modal electromagnetic wave equations in anisotropic media are deduced In section 4, the

quasi-static theory of waves in piezoelectric solids (mechanical equations of motion, coupled to

the equations of static electric field, or Maxwell’s equations, coupled to the mechanical

equations of equilibrium) are studied based on the eigen spaces of the physical presentation

The complete sets of uncoupled elastic or electromagnetic dynamic equations for piezoelectric

solids are deduced In section 5, the Maxwell’s equations, coupled to the mechanical equations

of motion, are studied based on the eigen spaces of the physical presentation The complete

sets of uncoupled fully dynamic equations for piezoelectromagnetic waves in anisotropic

media are deduced, in which the equations of electromagnetic waves and elastic ones are both

of order 4 The discussions are given in section 6

2 Elastic waves in anisotropic solids

2.1 Concepts of eigen spaces

The eigen value problem of elastic mechanics can be written as

1,2, ,6

i=λi i i= "

where C is a standarded matrix of elastic coefficients, λi is eigen elasticity, and is

invariables of coordinates, ϕi is the corresponding eigen vector, and satisfies the

orthogonality condition of basic vectors

Τ

=

The Eigen Theory of Waves in Piezoelectric Solids 3

where Λ=diag⎡⎣λ λ1, , ,2"λ6⎤⎦, Φ ={ϕ ϕ1, , ,2"ϕ6}is the modal matrix of elastic solids, it is

orthogonal and positive definite one, satisfies Φ ΦT =I

The eigen spaces of anisotropic elastic solids consist of independent eigen vectors, it has the

structure as follows

1[ 1] m[ m ]

where the possible overlapping roots are considered, and m ≤( )6 is used to represent the

number of independent eigen spaces Projecting the stress vector σ and strain vector ε on

the eigen spaces, we get

ε are modal stress and modal strain, which are stress and strain under the

eigen spaces respectively, and are different from the traditional ones in the physical meaning

Eqs.(4) and (5) are also regarded as a result of the sum of finite number of normal modes

The modal stress and modal strain satisfy the normal Hook’s law

2.2 Modal elastic wave equations

When neglecting body force, the dynamics equation and displacement equation of elastic

solids are the following respectively

It is proved by author that the elastic dynamics equation (10) under the geometrical spaces

of three dimension can be converted into the modal equations under the eigen spaces of six

The calculation shows that the stress operators are the same as Laplace’s operator (either

two dimensions or three dimensions) for isotropic solids, and for most of anisotropic solids

In the modal equations of elastic waves, the speeds of propagation of elastic waves are the

following

i i

ρ

Eqs.(14) and (15) show that the number of elastic waves in anisotropic solids is equal to that

of eigen spaces of anisotropic solids, and the speeds of propagation of elastic waves are

related to the eigen elasticity of anisotropic solids

2.3 Elastic waves in isotropic solids

There are two independent eigen spaces in isotropic solids

where ξi is a vector of order 6, in which i th element is 1 and others are 0

The eigen elasticity and eigen operator of isotropic solids are the following

The Eigen Theory of Waves in Piezoelectric Solids 5

where λandμare Lame constants,∇ is Laplace’s operator of three dimention Thus, there 2III

exist two independent elastic waves in isotropic solids, which can be described by the

following equations

2 * * III 1 1

2 * * III 2 ( , )x t 2( , )x t

Eq (21) represents the relative change of the volume of elastic solids So Eq (19) shows the

motion of pure longitudinal wave

Also from Eq (5), the modal strain of order 2 of isotropic solids is

Eq (23) represents the pure shear strain on elastic solids So Eq (20) shows the motion of

pure transverse wave

2.4 Elastic waves in anisotropic solids

The eigenelasticity and eigenoperator of cubic solids are