Master of Science / Department of Mechanical and Nuclear Engineering / Liang-Wu Cai / The study on artificially created materials has much evidence of naval properties. Phononic Crystals (PCs) are new class of artificially constructed materials. They have a large number of scattering inclusions that are embedded in a homogeneous host material. These scatterers are arranged in periodic lattice structures. The scatterers and host materials are usually either solids or fluids. Phononic materials are useful due to their ability to hinder the existence of certain frequencies over which the propagation of elastic and acoustic waves are forbidden. The formation of phononic band gaps (PBGs) in PCs is determined by the material properties and the geometry of the periodic lattice structures. Some PCs have full band gaps [14, 55] while others have partial band gaps [35]. Although the study of PCs is an attractive area for many researchers, the investigations on PCs are just emerging. The aim of the thesis is to study on perform fabrication and experimental characterization of 2-D PCs having eccentrically layered scatterers. In addition, the influence of the eccentricity of the layered scatterers on the amplitude spectrums are experimentally observed. Hence, the main objective in this work is to characterize the influence of the eccentricity orientation angles on the transmitted amplitude spectra. The layered scatterers were created by inserting the paraffin-coated stainless steel rods into the cavities. Two sets of stainless steel rod diameters (2 mm and 2.5 mm) were used. The eccentricity orientation angles of scatterers were changed from 0 degree to 90 degrees at the increment of 22.5 degrees. Ultrasonic waves were introduced into the test pieces to observe the propagated waves through the material. The ultrasonic Through Transmission Test (TTT) followed by signal processing techniques was employed to produce the transmitted spectra of PCs. The frequency dependent amplitude spectrums were observed at the chosen frequency ranges with the help of MATLAB and Fast Fourier Transformation (FFT) function. The results show that the geometry and the material parameters change the attenuation of amplitudes by hindering the wave propagation. This leads PC as a good candidate for a sound barrier for controlling the wave propagation or vibrations within the chosen frequency ranges. Keywords: Phononic Crystal/s (PC or PCs); Phononic Band Gap/s (PBG or PBGs); Through Transmission Test (TTT), Fast Fourier Transformation (FFT), Square array, Triangular array, Amplitude spectrum/ Spectra, Eccentrically layered scatterers

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.

There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.

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

This thesis presents the design of a two-dimensional phononic band gap crystal simulator, and phononic crystal analysis. <br /><br /> Phononic crystals and their application to microwave acoustic filters are studied. Wave mechanics is introduced. A two-dimensional phononic crystal simulator is developed. Simulator operation is validated through comparison with published data. Design parameters for phononic crystal band gap engineering are outlined. Digital signal processing and wave mechanics are utilized to analyze fractal and circular inclusion based phononic crystals. Topics for further study are given. <br /><br /> Phononic crystal band structure is found to be sensitive to inclusion boundary geometry. Fractal inclusion based crystals provide multiple pass band characteristics. The evolution of a fractal inclusion in a phononic crystal may cause band gap widening and the formation of new band gaps. Circular inclusion based phononic crystals have piecewise-linear phase characteristics and quality factors up to 600.

The control of surface acoustic waves (SAWs) using arrays of annular holes was investigated both experimentally and through numerical modelling. Periodic elastic composites, phononic crystals (PnCs), were designed using these annular holes as constituent elements. Local resonances associated with the annular hole structure were found to induce phonon bandgaps of a highly frequency tailorable nature, at frequencies where radiation of acoustic energy into the bulk of the substrate medium is avoided. These bandgaps are numerically demonstrated to exhibit order-of-magnitude improved extinction ratios for finite numbers of PnC elements, relative to the commonly used cylindrical pillar architecture. Devices fabricated on commercially available lithium niobate SAW delay lines verify the predicted behaviour. Through laser knife-edge detector vibrometry, a bandgap attenuation of 24.5 dB at 97 MHz was measured, in excellent agreement with finite element method (FEM) simulations. The first reported experimental evidence of subwavelength confinement of propagating SAWs was realised using the same annular hole PnC concept. Defect holes of perturbed resonant frequencies are included within the PnC to define waveguides and cavities. Confinement within these defects was demonstrated to occur at subwavelength frequencies which was experimentally observed in fabricated cavities using standard SAW transducers, as measured by laser Doppler vibrometry. The success of this result was attributed to the impedance matching of hybridised modes to Rayleigh SAWs in un-patterned substrates at the defect resonance. The work here has the potential to transform the field by providing a method to enhance SAW interactions, which is a route towards the realisation of many lab-on-chip applications. Finally, the use of annular hole arrays as negative refraction metamaterials was investigated. The symmetry was broken of the unit cells by alternating either the locally resonant frequencies or the distance separating the constituent elements. Both methods, called the bi-dispersive and bi-periodic methods, were numerically demonstrated to exhibit negative group velocity bands within the first Brillouin zone. Preliminary experimental results show that the design has the potential to be used in superlensing, where a SAW spot was imaged over a subwavelength flat lens. Future research looks to demonstrate that this result can be attributed to negative refraction.

Novel wave phenomena in two- and three-dimensional (2D and 3D) phononic crystals were investigated experimentally using ultrasonic techniques. Resonant tunneling of ultrasonic waves was successfully observed for the first time by measuring the transmission of ultrasound pulses through a double barrier consisting of two 3D phononic crystals separated by a cavity. This effect is the classical analogue of resonant tunneling of a quantum mechanical particle through a double potential barrier, in which transmission reaches unity at resonant frequencies. For phononic crystals, the tunneling peak was found to be less than unity, an effect that was explained by absorption. The dynamics of resonant tunneling was explored by measuring the group velocities of the ultrasonic pulses. Very slow and very fast velocities were found at frequencies close to and at the resonance, respectively. These extreme values are less than the speed of sound in air and greater than the speed of sound in any of the crystal’s constituent materials. Negative refraction and focusing effects in 2D phononic crystals were also observed. Negative refraction of ultrasound was demonstrated unambiguously in a prism-shaped 2D crystal at frequencies in the 2nd pass band where the wave vector and group velocity are opposite. The Multiple Scattering Theory and Snell’s law allowed theoretical predictions of the refraction angles. Excellent agreement was found between theory and experiment. The negative refraction experiments revealed a mechanism that can be used to focus ultrasound using a flat phononic crystal, and experiments to demonstrate the focusing of ultrasound emitted by several point sources were successfully carried out. The importance of using phononic crystals with circular equifrequency contours, as well as matching the size of the contours inside and outside the crystal, was established. Both conditions were satisfied by a flat phononic crystal of steel rods, in which the liquid inside the crystal (methanol) was different from the outside medium (water). The possibility of achieving subwavelength resolution using this phononic crystal was investigated with a subwavelength line source (a miniature strip-shaped transducer, approximately lambda/5 wide, where lambda is sound wavelength in water). A resolution of 0.55lambda was found, which is just above the diffraction limit lambda/2. / October 2007

This thesis presents the design of a two-dimensional phononic band gap crystal simulator, and phononic crystal analysis. <br /><br /> Phononic crystals and their application to microwave acoustic filters are studied. Wave mechanics is introduced. A two-dimensional phononic crystal simulator is developed. Simulator operation is validated through comparison with published data. Design parameters for phononic crystal band gap engineering are outlined. Digital signal processing and wave mechanics are utilized to analyze fractal and circular inclusion based phononic crystals. Topics for further study are given. <br /><br /> Phononic crystal band structure is found to be sensitive to inclusion boundary geometry. Fractal inclusion based crystals provide multiple pass band characteristics. The evolution of a fractal inclusion in a phononic crystal may cause band gap widening and the formation of new band gaps. Circular inclusion based phononic crystals have piecewise-linear phase characteristics and quality factors up to 600.