In the open ocean acoustic scattering by SONAR sources can be dominated by large fish schools. Multiple scattering effects are strong and the individual fish air-filled swimbladders scatter in the 1-10 kHz frequency range for most fish sizes. Furthermore, these schools are typically large in comparison to the acoustic wavelength and the individual fish typically swim in nearly periodic arrangements with a separation distance of approximately one body length. Hence, this work takes the perspective that fish schools can be studied simply and effectively by invoking the formalism of Bloch waves in periodic media. Analysis of the periodic school is aided through the Bloch theorem which reduces the study of the entire school to the study of a unit cell containing a single fish swimbladder. Application of the Bloch formalism to the school requires study of acoustic reflection from a semi-infinite half-space composed of an infinite tessellation of air-filled swimbladders in water. This media is denoted a fluid phononic crystal (PC). The reflection is considered, using a finite element discretization of the unit cell and an expansion of Bloch waves for the transmitted wave field. Next, scattering from a large finite school is studied through the context of the Helmholtz-Kirchhoff integral theorem where the semi-infinite PC pressure, determined by the Bloch wave expansion, is used as the surface pressure. Validation of results is accomplished via comparison with a finite element model (two dimensions) and a low frequency analytical multiple scattering model (three dimensions). Analysis of the dispersion relationship of the infinite PC yields useful information for a large school, namely, the frequency corresponding to target strength peaks, even as wave incidence angles and internal fish spacing are varied. The scattering effects attributed to the shape and weak internal disorder of the finite school were investigated with the surface integral method and a perturbation scheme. A general model using Bloch formalism, that encompasses the internal fish structure, fish biologic properties, and realistic school effects such as varying school geometry and disorder, was formulated. Transient analysis of the frequency dependent scattering, using the proposed approach developed in this thesis, may assist SONAR operators better classify large fish schools based on the observed characteristics of the scattered field.

¡§Phononic crystal,¡¨ a binary-composite medium composed of a square array of parallel circular steel cylinders in a air matrix is studied. Phononic crystal exists full band-gaps phenomenon which is caused by strongly constructive interference of Bragg reflection in their acoustic transmission spectrum. The Bragg reflection theorem is also a basis for searching the full band-gaps in this thesis. This thesis applies the boundary element simulation software BEASY to analyze the sound field characteristics of solid/fluid composite medium, phononic crystal. The forbidden bands of the band gap are shown by the relative amplitude in the incidence before and after. First, the study by Varadan and Faran aims at scattering sound field of the single rigid sphere and the circular cylinder in water which constructed a simulation of the boundary element model. It is compared to under the different kr change result of its scattering sound field and it has demonstrated that our simulation work was feasible. Second, the study constructs the boundary element model for a two-dimensional phononic crystal which was studied by Sánchez-Pérez etc. with experimentation, constituted of rectangular and triangular array of parallel circular stainless steel and aluminum cylinders in air. The study is compared with the forbidden bands of the band gap in the reference which performs the simulations with the mono-frequency by sweep. The full band gaps are determined from the combination of the results in both the [100] and [110] direction. Finally, the study aimed at the scattering pattern of sound field in phononic crystal to make discussion. In order to understand the sound source acts on the phononic crystal, the status of the sound pressure is distributed over the spatial. So it could get up to reduce the influence of the noise by way of the improvement the structure in phononic crystal. The study has successfully shown the boundary element simulation for the solid/fluid phononic crystal. The study of experiment in the reference is compared with the BEM simulation in this thesis. The results have demonstrated that the boundary element method is a good tool for the design of phononic crystal in application to new type sound absorption (isolation) material in the future.

¡§Phononic crystal,¡¨ a binary-composite medium composed of a square array of parallel circular brass cylinders in a water matrix is reported. Phononic crystal exists total band-gaps phenomenon which is caused by destructive interference of Bragg reflection in their acoustic transmission spectrum. This Bragg reflection theorem is also a basis for searching the total band-gaps in this thesis. Because of the band-gaps of the phononic crystal, it is very appropriate for applying phononic crystal in underwater absorptive materials. This research presents the Bragg theorem prediction of brass/water acoustic forbidden bands structure with three kinds of different filling fractions, 5 %, 10 %, and 20 %, and three kinds of transducers. Their central frequency are 300 kHz, 500 kHz, and 1 MHz, respectively, and their bandwidths are 210 kHz~390 kHz, 350 kHz~650 kHz, and 700 kHz~1300 kHz, respectively. Furthermore, in order to find total band-gaps, [100] and [110] directions are measured in this research. The band-gaps of phononic crystal in this research are designed by the couple probes of lowest frequencies 300 kHz in our laboratory. Although the devices of underwater acoustics usually operate in 15~200 kHz, it is also proved indirectly that to design and to apply phononic crystal in underwater absorptive materials are workable. In addition, the measurement results of band-gaps of single frequency are the same as broad-band frequencies using ultrasonic analyzer in this thesis. Therefore, it is a good way to survey the band-gaps with broad-band frequencies method first, and then to use single frequency method measuring deeply drop of the band-gaps. This research uses Bragg reflection theorem, to calculate approximate position of band-gaps, and predicts n=1~3 total band-gaps successfully in experiments. It is also proved that using this kind of underwater absorptive materials of phononic crystal has the effect of camouflaging submarine purpose with specific frequencies. This is an easiest theorem to survey band-gaps of phononic crystal, and must be a most useful tool to design all kinds of absorptive materials of phononic crystal.

Compared to the much more common photonic crystals that are used to manipulate light, phononic crystals (PnCs) with inclusions in a lattice can be used to manipulate sound. While trying to propagate in a periodically structured media, acoustic waves may experience geometries in which propagation forward is totally forbidden. Furthermore, defects in the periodicity can be used to confine acoustic waves to follow complicated routes on a wavelength scale. Using advanced fabrication methods, we aim to implement these structures to control surface acoustic wave (SAW) propagation on the piezoelectric surface and eventually interact SAWs with quantum structures. To investigate the interaction of SAWs with periodic elastic structures, SAW interdigital transducers (IDTs) and PnC fabrication procedures were developed. GaAs is chosen as a piezoelectric substrate for SAWs propagation. Lift-off photolithography processes were used to fabricate IDTs with finger widths as low as 1.5 micron. PnCs are periodic structures of shallow air holes created in GaAs substrate by means of a wet-etching process. The PnCs are square lattices with lattice constants of 8 and 4 micron. To predict the behavior of a SAW when interacting with the PnC structures, an FDTD simulator was used to calculate the band structures and SAW wave displacement on the crystal surface. The bandgap (BG) predicted for the 8 micron crystal ranges from 180 MHz to 220 MHz. Simulations show a shift in the BG position for 4 micron crystals ranging from 391 to 439 MHz. Two main waveguide geometries were considered in this work: a simple line waveguide and a funneling entrance line waveguide. Simulations indicated an increase in acoustic power density for the funneling waveguides. Fabricated device evaluated with electrical measurements. In addition, a scanning Sagnac interferometer is used to map the energy density of the SAWs. The Sagnac interferometer is designed to measure the outward displacement of a surface due to the SAW. Interferometric measurements confirmed waveguiding in the modified funnel entrance waveguide embedded in the 4 micron PnC. However, they also revealed strong dissipation of the SAW in the waveguide due to the non-vertical sidewalls resulting from the wet-etch process. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-11-29 15:53:46.369

In this work we apply the finite element method to analyze the wave transmission property of solid/fluid composite medium, phononic crystal. The sound attenuation spectrum is obtained to show the forbidden bands of the band gap. First, we construct the finite element model for a two-dimensional phononic crystal, studied by Sánchez-Pérez etc. with PWE and experimentally, constituted of a rectangular array of parallel circular stainless steel cylinders in air. It has demonstrated that our simulation work was feasible; then, we performed the experimental measurements and simulations by using the narrow and wide frequencies. The results show agreement between the experiments and the simulations. We also simulated the crystal samples of filling fraction 5 % and 10 % for square and hexagon lattice, respectively, in both the [100] and [110] direction. The full band gaps are determined from the combination of the results. We have investigated the finite element simulation for the solid/fluid phononic crystal successfully. Both work the results of experiment in the reference and in this work are compared with the FEM simulation. It demonstrates that the finite element method is a good tool for the design of phononic crystal in application to new type sound absorption (isolation) material.

The work presented in this thesis is concerned with the propagation of acoustic waves through phononic crystal systems and their ability to attenuate sound in the low frequency regime. The plane wave expansion method and finite element method are utilised to investigate the properties of conventional phononic crystal systems. The acoustic band structure and transmission measurements of such systems are computed and verified experimentally. Good agreement between band gap locations for the investigative methods detailed is found. The well known link between the frequency range a phononic crystal can attenuate sound over and its lattice parameter is confirmed. This leads to a reduction in its usefulness as a viable noise barrier technology, due to the necessary increase in overall crystal size. To overcome this restriction the concept of an acoustically resonant phononic crystal system is proposed, which utilises acoustic resonances, similar to Helmholtz resonance, to form additional band gaps that are decoupled from the lattice periodicity of the phononic crystal system. An acoustically resonant phononic crystal system is constructed and experimental transmission measurements carried out to verify the existence of separate attenuation mechanisms. Experimental attenuation levels achieved by Bragg formation and resonance reach 25dB. The two separate attenuation mechanisms present in the acoustically resonant phononic crystal, increase the efficiency of its performance in the low frequency regime, whilst maintaining a reduced crystal size for viable noise barrier technology. Methods to optimise acoustically resonant phononic crystal systems and to increase their performance in the lower frequency regime are discussed, namely by introducing the Matryoshka acoustically resonant phononic crystal system, where each scattering unit is composed of multiple concentric C-shape inclusions.

This dissertation contains research directed at investigating the behavior and properties of a class of composite materials known as phononic crystals. Two categories of phononic crystals are explicitly investigated: (I) elastic phononic crystals and (II) nano-scale phononic crystals. For elastic phononic crystals, attention is directed at two-dimensional structures. Two specific structures are evaluated (1) a two-dimensional configuration consisting of a square array of cylindrical Polyvinylchloride inclusions in air and (2) a two-dimensional configuration consisting of a square array of steel cylindrical inclusions in epoxy. For the first configuration, a theoretical model is developed to ascertain the necessary band structure and equi-frequency contour features for the realization of phase control between propagating acoustic waves. In contrasting this phononic crystal with a reference system, it is shown that phononic crystals with equifrequency contours showing non-collinear wave and group velocity vectors are ideal systems for controlling the phase between propagating acoustic waves. For the second configuration, it is demonstrated that multiple functions can be realized of a solid/solid phononic crystal. The epoxy/steel phononic crystal is shown to behave as (1) an acoustic wave collimator, (2) a defect-less wave guide, (3) a directional source for elastic waves, (4) an acoustic beam splitter, (5) a phase-control device and (6) a k-space multiplexer. To transition between macro-scale systems (elastic phononic crystals) and nano-scale systems (nano-phononic crystals), a toy model of a one-dimensional chain of masses connected with non-linear, anharmonic springs is utilized. The implementation of this model introduces critical ideas unique to nano-scale systems, particularly the concept of phonon mode lifetime. The nano-scale phononic crystal of interest is a graphene sheet with periodically spaced holes in a triangular array. It is found through equilibrium molecular dynamics simulation techniques, that phonon-boundary collision effects and coherent phononic effects (band-folding) are two competing scattering mechanisms responsible for the reduction of acoustic and optical phonon lifetimes. Conclusions drawn about the lifetime of thermal phonons in phononic crystal patterned graphene are linked with the anharmonic, one-dimensional crystal model.

The propagation of ultrasound through two- and three-dimensional strongly scattering media, with either random or ordered internal structures, has been investigated through experiments and finite element simulations. All media investigated have strong scattering resonances, leading to novel transport behaviour. The two-dimensional samples consist of nylon rods immersed in water. When the nylon rods are arranged in a triangular lattice to form two-dimensional phononic crystals, very unusual dispersion properties are observed when the lattice constant is adjusted so that Bragg and hybridization gaps overlap in frequency. This behaviour is attributed to the competition between two co-existing propagating modes, leading to a new method for tuning bandgap properties and adjusting the transmission by orders of magnitude. The scattering resonance of the nylon rods also leads to unusual Dirac cone properties at the K point of the triangular lattice. The three-dimensional media were fabricated by brazing aluminum beads together to form a disordered porous solid network, with either vacuum or air in the pores, depending on the experiment. This system is of particular interest because it has been shown to exhibit Anderson localization of ultrasound. Two experimental approaches were developed to investigate previously unstudied properties of this system. By directly counting the modes in the frequency domain, the density of states was measured. At intermediate frequencies, the density of states was found to be approximately independent of frequency, while at higher frequencies, the frequency dependence was consistent with traditional density-of-states models. The level statistics of the modes was also investigated to determine the conditions under which level repulsion occurs. By using a laser interferometer to measure the ultrasonic displacements on the surface of a large slab-shaped sample, sub-diffusive behaviour was observed, demonstrating the feasibility of using such measurements to investigate the transition to Anderson localization in these samples.

In this thesis, the propagation of transient waves in heterogeneous media and the tuning of periodic elastic materials are studied. The behaviour of time harmonic waves in complex media is a well understood phenomenon. The primary aim of this text is to gain a deeper understanding into the propagation of transient waves in periodic media. The secondary aim is to explore the time harmonic behaviour of two dimensional pre-stressed elastic media and investigate the plausibility of band gap tuning. We begin this text by investigating the reflection of pulses from a semi-infinite set of point masses (we call 'beads') on a string. The reflected pulse is formulated using Fourier transforms which involve the harmonic reflection coefficient. We find that the reflected amplitude of a harmonic wave depends on its frequency. We then ask whether it is possible to find an effective reflection coefficient by assuming the beaded portion of the string is given by some effective homogeneous medium. An effective reflection coefficient is found by assuming the homogeneous medium has the wavenumber given by the infinite beaded string. This effective reflection coefficient is compared to the exact reflection coefficient found using the Wiener-Hopf technique. The results from studying the reflection problem gave inspiration to chapter 4, which focuses on the time dependent forcing of an infinite beaded string that is initially at rest. We again use the Fourier transform to find a time dependent solution. The z-transform is then used, after sampling the solution at the bead positions. We impose a sinusoidal loading which is switched on at a specified time. In doing this we are able to explore how the system behaves differently when excited in a stop band, a pass band and at a frequency on the edge between the two. An exact solution for the infinite beaded string is found at any point in time by expanding the branch points of the solution as a series of poles. We compare this exact solution to the long time asymptotics. The energy input into the system is studied with the results from the exact solution and long time approximation showing agreement. Interesting behaviour is discovered on the two edges between stop and pass bands. In chapter 5 the effect of a nonlinear elastic pre-stress on the wave band structure of a two dimensional phononic crystal is investigated. In this chapter we restrict ourselves to incompressible materials with the strain energy functions used being the neo-Hookean, Mooney-Rivlin and Fung. The method of small-on-large is used to derive the equation for incremental elastic waves and then the plane wave expansion method is used to find the band structure. Finally, chapter 6 focuses on the same geometry with a compressible elastic material. The strain energy function used is the one suggested by Levinson and Burgess. We use the theory of small-on-large to derive the incremental equations for coupled small amplitude pressure and shear waves in this material. In both compressible and incompressible materials we show how it is possible to control the stop bands in a material by applying a large elastic pre-stress.

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