Perturbation Analysis on Guided Waves in a Fluid-Filled Borehole Surrounded by a Cubic Crystal Anisotropic Medium

The perturbation method is employed to analyse the guided waves in a borehole surrounded by a cubic crystal medium for the first time. The cubic crystal medium is regarded as a reference unperturbed isotropic state added to the perturbation. The dispersion characteristics of Stoneley wave, pseudo-Rayleigh wave, flexural wave, and screw wave are investigated in detail. It is found that dispersion of the guided waves excited by monopole and dipole sources does not depend on the azimuth of the source, whereas the dispersion of screw wave excited by quadrupole source is significantly related to the azimuth of the source. Screw waves propagated along different azimuth in the borehole can be split. This is different from screw waves in transversely isotropic media （hexagonal crystal）, which have been widely studied.     

Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

We investigate the guided waves in a multi-layered cylindrical elastic solid medium. The dispersion function of guided waves is usually complex and the dispersion curves of all modes are not conveniently obtained. Here we present an effective method to obtain the dispersion curves of all modes. First, the dispersion function of the guided waves is transformed into a real function. The dispersion curves are then calculated for all the modes of the guided waves by the bisection method. The modes with the orders n = 0, 1, and 2 are analysed in two- and three-layer media. The existence condition of Stoneley wave is discussed. The modes of the guided waves are also investigated in a two-layer medium, in which the velocity of shear wave in the outer layer is less than that in the inner layer.     

Laser Generation of Surface Waves on Cylinder with a Slow Coating

An analytical model of acoustic field excited by a pulsed-laser line source on a coated cylinder is presented. Surface wave dispersive behaviours for a cylinder with a slow coating are analysed and compared with that of a bare cylinder. Based on this analysis, the laser-generated transient response of the perturbed Rayleigh wave and the higher modes of steel cylinder with a zinc coating are calculated from the model using residue theory and FFT technique. The theoretical result from the superposed waveform of the perturbed Rayleigh wave and higher modes agree well with the waveform obtained in experiment. The results show that the model and numerical method provide a useful technique for quantitatively characterizing coating parameters of coated cylinder by the laser generated surface waves.     

Phononic band structure in a two-dimensional hybrid triangular graphite lattice

The propagation of acoustic wave in a two-dimensional phononic crystal of a hybrid triangular graphite array is investigated by the plane wave expansion (PWE) method. Our numerical results show that the location and width of the band gaps can be tuned by altering the radii of scatters at different positions.     

Ultrasonic field modeling for immersed components using Gaussian beam superposition

The Gaussian beam (GB) superposition approach can be applied to model ultrasound propagation in complex-structured materials and components. In this article, progress made in extending and applying the Gaussian beam superposition technique to model the beam fields generated by transducers with flat and focused rectangular apertures as well as with circular focused apertures is addressed. The refraction of transducer beam fields through curved surfaces is illustrated by calculation results for beam fields generated in curved components during immersion testing. In particular, the following developments are put forward: (i) the use of individually determined sets of GBs to model transducer beam fields with a number of less than ten beams; (ii) the application of the GB representation of rectangular transducers to focusing probes, as well as to the problem of transmission through interfaces; and (iii) computationally efficient transient modeling by superposition of ‘temporally limited’ GBs.     

Coupling of Acoustical Plane p-Wave to a Cased Borehole

Theoretical and numerical study on the coupling acoustic field of the plane p-wave to a cased borehole is carried out. The medium outside the cased borehole is modeled as the porous medium. The scattering field characteristics in the cased borehole are investigated when a plane fast p-wave is incident in tilt to the cased borehole from the porous medium. The scattering fields inside and outside the cased borehole are analyzed and deduced by Biot＇s theory under the boundary conditions on each interface, and they are numerically studied. It is found that the scattering field has strong resonant characteristics and there exists a series of resonant frequencies and peaks. The effects of the frequency, radii of each interface, incident angle, porosity, and other parameters on the resonant acoustic field have been investigated in detail in the fast and slow formations respectively. The resonant characteristics of the scattering field are also analyzed from the physical sense.     

Extraordinary Resonant Scattering in Imperfect Acoustic Cloak

We present a systematic study on the extraordinary resonant scattering in imperfect acoustic cloak by means of acoustic scattering theory. Analysis results demonstrate that the resonances are inevitable due to the perturbation to the ideal clo~k, and specific resonance modes are excited by specific order waves. The strength of resonance is determined by the magnitude of perturbation and each order wave＇s sensitivity to the perturbation. Further studies reveal the unique scattering characters of different resonance modes.     

Coupling of cavity modes and guiding modes in two-dimensional phononic crystals

Cavity modes for the single-cavity and the double-cavities in two-dimensional phononic crystal are studied by using a plane waves expansion supercell method. We show that the single-cavity behaves like an atom while the double-cavities behave like a molecule. Couplings of cavity modes with the waveguide modes are investigated for typical configurations. Suitably designed waveguides with introduced cavities might be used as acoustic filter in waveguide applications.     

The influence of the micro-topology on the phononic band gaps in 2D porous phononic crystals

The phononic band structures of two-dimensional metal porous phononic crystals consisting of different lattices (the lattice structures transformed from square to triangle), and pores of various shapes (circle, square, and triangle) and sizes are studied numerically by using Finite Difference Time Domain (FDTD) scheme. It is found that for x-y mode waves, the absolute phononic band gaps (PBGs) rely more on the pore shapes. For triangular pores, the PBG is opening in the whole process of the lattice transformation, and for circular ones, the PBG is closed after a certain lattice structure. No PBG forms in the crystals with square pores. The PBG can be varied by adjusting the size of the pores. But a critical porosity exists for the opening of the PBG.     

Impedance-Matched Reduced Acoustic Cloaking with Realizable Mass and Its Layered Design

We present an impedance-matched reduced version of acoustic cloaking whose mass is in a reasonable range. A layered cloak design with isotropic material is also proposed for the reduced cloak. Numerical calculations from the transfer matrix methods show that the present layered cloak can reduce the scattering of an air cylinder substantially.     

Transmission Frequency Properties of Elastic Waves along a Hetero-Phononic Crystal Waveguide

We investigate the propagation properties of hetero-phononic crystal waveguides by the improved eigen-mode matching theory, which can be used at same time to calculate both the transmission （reflection） coefficient and band structure. The numerical results show that the transmission frequency range is the same as the common range for two uniform waveguides composing the hereto-system, and the gap of any composite waveguide is also the gap of the hetero-phononic crystals waveguide.     

Tri-component phononic crystals for underwater anechoic coatings

Localized resonance in phononic crystal, composed of three-dimensional arrays of composite units, has been discovered recently. The composite unit is a high-density sphere coated by soft silicon rubber. In this Letter, the absorptive properties induced by the localized resonance are systemically investigated. The mode conversions during the Mie scattering of a single coated lead sphere in unbounded epoxy are analyzed by referring the elements of the scattering matrix. Then the anechoic properties of a slab containing a plane of such composite scatterers are investigated with the multiple-scattering method by accounting the effects of the multiple scattering and the viscous dissipation. The results show that the longitudinal to transverse mode conversion nearby the locally resonant region is an effective way to enhance the anechoic performance of the finite slab of phononic crystal. Then, the influences of the viscoelasticity of the silicon rubber and the coating thickness on the acoustic properties of the finite slab are investigated for anechoic optimization. Finally, we synthetically consider the destructive scattering in the finite slab of phononic crystal and the backing, and design an anechoic slab composed of bi-layer coated spheres. The results show that the most of the incident energy is absorbed at the desired frequency band.     

Homogenization of Three-Dimensional Periodic Solid-Solid Elastic Composites

We develop an approach to homogenize three-dimensional periodic solid-solid elastic composites with cubic lattice at low frequencies, by using plane wave expansion and perturbation theory with respect to the long wavelength limit. Based on the fact that the two shear waves propagating along lattice axis are degenerated, we derive formulae for effective velocities parallel and normal to the lattice axis, from which three independent effective elastic moduli are calculated, respectively. Theoretical results, which take into account the multiple scattering and the structure of the periodic medium, are in good agreement with the previous isotropic theory at high-symmetry directions.     

Directional Propagation Characteristics of Flexural Waves in Two-Dimensional Thin-Plate Phononic Crystals

The propagation characteristics of flexural waves in two-dimensional thin-plate phononic crystals （PCs） are analysed with the plane wave expansion （PWE） method to yield phase constant surfaces, which predict high directivity of flexural wave propagation for certain frequencies outside the band gap. The prediction is validated through the computation of the harmonic responses of a finite structure with 9 × 9 unit cells. The results indicate that directional propagation of flexural waves is an while specific effects of the directional propagation in inherent characteristic of two-dimensional thin-plate PCs a finite structure vary with the positions of excitations.     

Phononic crystals containing piezoelectric material

The elastic band structure of a two-dimensional phononic crystal containing piezoelectric material is investigated by the plane-wave-expansion method. Numerical results show that for large filling fraction, the full band gap of this kind of system is enlarged by considering the piezoelectric effect, but for small filling fraction, the influence of the piezoelectric effect is so small that it can be neglected.     

Vibro-acoustography imaging of permanent prostate brachytherapy seeds in an excised human prostate - Preliminary results and technical feasibility

Objective:

The objective in this work is to investigate the feasibility of using a new imaging tool called vibro-acoustography (VA) as a means of permanent prostate brachytherapy (PPB) seed localization to facilitate post-implant dosimetry (PID).

Methods and materials:

Twelve OncoSeed (standard) and eleven EchoSeed (echogenic) dummy seeds were implanted in a human cadaver prostate. Seventeen seeds remained after radical retropubic prostatectomy. VA imaging was conducted on the prostate that was cast in a gel phantom and placed in a tank of degassed water. 2-D magnitude and phase VA image slices were obtained at different depths within the prostate showing location and orientation of the seeds.

Results:

VA demonstrates that twelve of seventeen (71%) seeds implanted were visible in the VA image, and the remainder were obscured by intra-prostatic calcifications. Moreover, it is shown here that VA is capable of imaging and locating PPB seeds within the prostate independent of seed orientation, and the resulting images are speckle free.

Conclusion:

The results presented in this research show that VA allows seed detection within a human prostate regardless of their orientation, as well as imaging intra-prostatic calcifications.     

In vitro comparative study of vibro-acoustography versus pulse-echo ultrasound in imaging permanent prostate brachytherapy seeds

Background

Permanent prostate brachytherapy (PPB) is a common treatment for early stage prostate cancer. While the modern approach using trans-rectal ultrasound guidance has demonstrated excellent outcome, the efficacy of PPB depends on achieving complete radiation dose coverage of the prostate by obtaining a proper radiation source (seed) distribution. Currently, brachytherapy seed placement is guided by trans-rectal ultrasound imaging and fluoroscopy. A significant percentage of seeds are not detected by trans-rectal ultrasound because certain seed orientations are invisible making accurate intra-operative feedback of radiation dosimetry very difficult, if not impossible. Therefore, intra-operative correction of suboptimal seed distributions cannot easily be done with current methods. Vibro-acoustography (VA) is an imaging modality that is capable of imaging solids at any orientation, and the resulting images are speckle free.

Objective and methods

The purpose of this study is to compare the capabilities of VA and pulse-echo ultrasound in imaging PPB seeds at various angles and show the sensitivity of detection to seed orientation. In the VA experiment, two intersecting ultrasound beams driven at f₁ = 3.00 MHz and f₂ = 3.020 MHz respectively were focused on the seeds attached to a latex membrane while the amplitude of the acoustic emission produced at the difference frequency 20 kHz was detected by a low frequency hydrophone.

Results

Finite element simulations and results of experiments conducted under well-controlled conditions in a water tank on a series of seeds indicate that the seeds can be detected at any orientation with VA, whereas pulse-echo ultrasound is very sensitive to the seed orientation.

Conclusion

It is concluded that vibro-acoustography is superior to pulse-echo ultrasound for detection of PPB seeds.     

Thickness Determination for a Two-Layered Composite of a Film and a Plate by Low-Frequency Ultrasound

We present an ultrasonic method for determining the thickness of a composite consisting of a soft thin film attached to a hard plate substrate, by resonance spectra in the low frequency region, The interrogating waves can be incident only to the two-layered composite from the substrate side. The reflection spectra are obtained by FFT analysis of the compressive pulsed echoes from the composite, and the thicknesses of the film and the substrate are simultaneously inversed by the simulated annealing method from the resonant frequencies knowing other acoustical parameters in prior. The sensitivity of the method to individual thickness, its convergence and stability against experimental noises are studied, Experiment with interrogating wavelength 4 times larger than the film thickness in a sample of a polymer film （0.054mm） on an aluminium plate （6.24mm） verifies the validity of the method. The average relative errors in the measurement of the thicknesses of the film and the substrate are found to be -4.1% and -0.62%, respectively.     

Defect imaging with elastic waves in inhomogeneous-anisotropic materials with composite geometries

Imaging of defects in composite structures plays an important role in non-destructive testing (NDT) with elastic waves, i.e., ultrasound. Traditionally the imaging of such defects is performed using the synthetic aperture focusing technique (SAFT) algorithm assuming homogeneous isotropic materials. However, if parts of the structure are inhomogeneous and/or anisotropic, this algorithm fail to produce correct results that are needed in order to asses the lifetime of the part under test. Here we present a modification of this algorithm which enables a correct imaging of defects in inhomogeneous and/or anisotropic composite structures, whence it is termed InASAFT. The InASAFT is based on the exact modelling of the structure in order to account for the true nature of the elastic wave propagation using travel time ray tracing techniques. The algorithm is validated upon several numerical and real life examples yielding satisfactory results for imaging of cracks. The modified algorithm suffers, though, from the same difficulties encountered in the SAFT algorithm, namely “ghost” images and eventual lack of clear focused images. However, these artifacts can be identified using a forward wave propagation analysis of the structure.     

Numerical predictions and experiments for optimizing hidden corrosion detection in aircraft structures using Lamb modes

To increase the sensitivity of Lamb waves to hidden corrosion in aircraft structures, a preliminary step is to understand the phenomena governing this interaction. A hybrid model combining a finite element approach and a modal decomposition method is used to investigate the interaction of Lamb modes with corrosion pits. The finite element mesh is used to describe the region surrounding the corrosion pits while the modal decomposition method permits to determine the waves reflected and transmitted by the damaged area. Simulations make easier the interpretation of some parts of the measured waveform corresponding to superposition of waves diffracted by the corroded area. Numerical results permit to extract significant information from the transmitted waveform and thus to optimize the signal processing for the detection of corrosion at an early stage. Now, we are able to detect corrosion pits down to 80-μm depth distributed randomly on a square centimeter of an aluminum plate. Moreover, thickness variations present on aircraft structures can be discriminated from a slightly corroded area. Finally, using this experimental setup, aircraft structures have been tested.