Incident Plane Acoustic Wave Research Articles

Generating reconfigurable acoustic orbital angular momentum with double-layer acoustic metasurface

In this paper, a double-layer acoustic metasurface (DAM) composed of a fixed lower acoustic metasurface (LAM) and a rotatable upper acoustic metasurface (UAM) is proposed for the generation of mode-reconfigurable acoustic orbital angular momentum (OAM). The UAM and LAM are divided into multiple sections, in which the hybrid structures combining cascaded Helmholtz resonators and a straight pipe are adopted to achieve specific phase compensation. By rotating the UAM, the incident acoustic plane wave can be efficiently converted into the vortex acoustic waves of reconfigurable topological charges ranging from −5 to +5 with distinguishable purity. Furthermore, the influences of the parameters on the purity of the generated topological charges have been investigated and discussed, such as the distance between LAM and UAM, rotatable angle error, and operating frequency. With the capability of reconfigurable OAM modes, the proposed DAM can be used to efficiently increase capacity or to conveniently switch between different channels in underwater vortex acoustic communications.

Simulating the acoustic response of cavities to improve microphone array measurements in closed test section wind tunnels.

Cavities placed along wind tunnel walls can attenuate the turbulent boundary layer (TBL) fluctuations as they propagate into the cavity. Placing microphones within the cavities can thus improve the signal-to-noise ratio of acoustic data. However, standing waves form within these cavities distorting the acoustic measurements. This work uses a finite element (FE) solver to evaluate how cavity geometry (depth, diameter, and wall angle) and wall material (hard-walled and melamine foam) affect the amplitude and eigenfrequency of standing waves when excited by an incident acoustic plane wave. Good agreement between predicted and measured acoustic transfer functions is shown. Compared to cylindrical cavities, countersunk and conical cavities improve the overall response, i.e., reducing the quality factor quantifying the resonance and damping characteristics. Stainless steel coverings also reduce the quality factor. A finding is that the shape of the external foam holder rather than the cavity shape drives the standing wave characteristics for the melamine foam cavities. The optimization problem of minimizing the acoustic response while also attenuating the TBL is thus decoupled by using the melamine foam. Consequently, these considerations can be addressed independently by optimizing the outer cavity shape for acoustics and the melamine foam insert for TBL attenuation.

Approximate Solutions for Surface Reflection Loss Inclusive of a Practical Model of Refraction in the Wind-Driven Bubbly Layer

The authors previously prepared a model of coherent acoustic reflection loss at the ocean surface by combining a model of surface roughness loss with determination of surface incidence angle that accounted for the refractive effects of a uniformly stratified distribution of wind-driven bubbles. Originally, the surface roughness loss was based on a second-order small-slope approximation and the surface incidence angle was obtained using an exact solution for propagation of the incident acoustic plane wave in a layer of particular sound-speed variation. In this paper, the previous solution for surface incidence angle is simplified with the assumption that the grazing angle at the bottom of the layer is small. An approximate solution for the surface grazing angle is found in terms of grazing angle below the layer and a polynomial series in a derived parameter, which in turn is a function of wind speed and acoustic frequency. This determination of surface angle is combined with a simplified model of surface roughness loss to produce a complete model suitable for use with ray-type transmission calculations or hand calculations. The resulting model permits the prediction of the coherent surface reflection loss with only wind speed and frequency as input parameters. Results from the use of this approximated model with a Gaussian beam acoustic propagation code are compared with predictions based on Monte Carlo parabolic equation transmission calculations for surface ducted scenarios including various levels of roughness. The zones of validity of the model are considered at length.

Acoustic response in a one-dimensional layered pseudo-Hermitian metamaterial containing defects

Using transfer-matrix methods, we investigate the response of a multilayered metamaterial system containing defects to an incident acoustic plane wave at normal or oblique incidence. The transmission response is composed of pass-bands with oscillatory behaviour, separated by band gaps, and covers a wide frequency range. The presence of gain and loss in the layers leads to the emergence of symmetry breaking and re-entrant phases. In the general case, a system containing defects will display a more general property, pseudo-Hermiticity (PH), of which PT systems are a subset. In the PH-symmetric phase, unidirectional responses of the reflection, accomplished by reversing the parity P, can be found, but the response sometimes deviates from the predictions of simple scattering theory which call for a pseudo-unitarity relation relating the transmission and the two directions of reflections to hold. The converse of reversing the parity and reversing the time operator T in a spatially asymmetric system within the PH-symmetric regime can lead to different transmissions: a pass-band versus a stop-band. As regions of stable PH-symmetric pass-band transmission oscillations occur over a wide spectral range, there is a large flexibility in system parameters such as layer thicknesses, for leading to the desired unidirectional traits. In addition, we find that while defects in general lead to a near or complete loss of PH symmetry at all frequencies, they can be exploited to produce highly sensitive responses, making such systems good candidates for sensor applications.

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

Viscous effects on the attenuation of a plane wave by an acoustic lining in shear flow.

The attenuation of a plane acoustic wave incident on a flat impedance surface in a sheared and viscous fluid is investigated numerically and asymptotically. Predictions of various boundary models of impedance surfaces in shear flow are tested by comparing their predicted reflection coefficient. It is found that viscosity has a significant effect, reducing the reflection of upstream propagating sound while increasing the reflection of cross-stream propagating sound. The classical Ingard-Myers boundary condition is shown to incorrectly predict the damping rate of sound in many cases, and in some cases viscous effects are shown to be comparable to shear effects.

High-frequency diffraction by a narrow hyperboloid of revolution

High-frequency diffraction of a plane acoustic wave incident at a small angle to the axis of a narrow hyperboloid of revolution is considered. By the parabolic equation method in spheroidal coordinates, the leading term of field asymptotics in the near-surface boundary layer is constructed in the form of an integral involving Whittaker functions. Difficulties associated with its calculation are considered. Results obtained for the field at the surface of a perfectly rigid hyperboloid are presented. They reproduce the predicted high-frequency diffraction effects.

Localized acoustic surface modes

We introduce the concept of localized acoustic surface modes. We demonstrate that they are induced on a two-dimensional cylindrical rigid surface with subwavelength corrugations under excitation by an incident acoustic plane wave. Our results show that the corrugated rigid surface is acoustically equivalent to a cylindrical scatterer with uniform mass density that can be represented using a Drude-like model. This, indeed, suggests that plasmonic-like acoustic materials can be engineered with potential applications in various areas including sensing, imaging, and cloaking.

Experimental verification of acoustic trace wavelength enhancement.

Directivity is essentially a measure of a sonar array's beamwidth that can be obtained in a spherically isotropic ambient noise field; narrow array mainbeam widths are more directive than broader mainbeam widths. For common sonar systems, the directivity factor (or directivity index) is directly proportional to the ratio of an incident acoustic trace wavelength to the sonar array's physical length (which is always constrained). Increasing this ratio, by creating additional trace wavelengths for a fixed array length, will increase array directivity. Embedding periodic structures within an array generates Bragg scattering of the incident acoustic plane wave along the array's surface. The Bragg scattered propagating waves are shifted in a precise manner and create shorter wavelength replicas of the original acoustic trace wavelength. These replicated trace wavelengths (which contain identical signal arrival information) increase an array's wavelength to length ratio and thus directivity. Therefore, a smaller array, in theory, can have the equivalent directivity of a much larger array. Measurements completed in January 2015 at the Naval Undersea Warfare Center's Acoustic Test Facility, in Newport, RI, verified, near perfectly, these replicated, shorter, trace wavelengths.

Reflection of acoustic wave at the interface of a fluid-loaded dipolargradient elastic half-space

This paper is about the reflection of a plane acoustic wave incident on a material modeled as a dipolar gradient solid. The dipolar gradient model has been used in order to account for the micro-structure present in multi-scale materials (e.g. biological issues, composites, meta-materials). The influence of the internal lengths of the gradient model on the reflection coefficient is described and discussed. A dispersive behavior is observed at high frequency, when the wavelength of the disturbance approaches the characteristic size of the material. This topic is of major interest for understanding the role played by the micro-structure in the reflection phenomena occurring at fluid–solid interfaces and find its application to material properties characterization by means of ultrasound waves.

VIBROACOUSTIC ANALYSIS OF STIFFENED PLATES WITH NONUNIFORM BOUNDARY CONDITIONS

This paper deals with vibroacoustic analysis of bidirectional stiffened thin plates with nonuniform discrete elastic edge restraints. The displacement-like governing equation of motion of the stiffened plate is derived by applying energy approach. A series of simple polynomials satisfying the Rayleigh–Ritz convergence criteria as well as the edge boundary conditions are then applied to discretize the governing equation, and the transverse displacements of the plate are solved considering the excitation of an incident acoustic plane wave. The commonly-adopted vibroacoustic indicators of elastic plane surface, i.e., mean square velocity (MSV), radiation efficiency (σ) and sound transmission loss (STL), are calculated for the stiffened plate with uniform and nonuniform discrete boundary conditions (BCs). Numerical studies are performed and results are discussed in detail for the vibroacoustic performance of the plate with different edge elastic restraints.

Acoustic Radiation Force on a Spherical Contrast Agent Shell Near a Vessel Porous Wall – Theory

Contrast agent microshells (CAMSs) are under intensive investigation for their wide applications in biomedical imaging and drug delivery. In drug delivery applications, CAMSs are guided to the targeted site before fragmentation by high-intensity ultrasound waves leading to the drug release. Prediction of the acoustic radiation force used to nondestructively guide a CAMS to the suspected site is becoming increasingly important and gaining attention particularly because it increases the system efficiency. The goal of this work is to present a theoretical model for the time-averaged (static) acoustic radiation force experienced by a CAMS near a blood vessel wall. An exact solution for the scattering of normal incident plane acoustic waves on an air-filled elastic spherical shell immersed in a nonviscous fluid near a porous and nonrigid boundary is employed to evaluate the radiation force function (which is the radiation force per unit energy density per unit cross-sectional surface). A particular example is chosen to illustrate the behavior of the time-averaged (static) radiation force on an elastic polyethylene spherical shell near a porous wall, with particular emphasis on the relative thickness of the shell and the distance from its center to the wall. This proposed model allows obtaining a priori information on the static radiation force that may be used to advantage in related as drug delivery and contrast agent imaging. This study should assist in the development of improved models for the evaluation of the time-averaged acoustic radiation force on a cluster of CAMSs in viscous and heat-conducting fluids. (E-mail: mitri@lanl.gov)

Multiple scattering of an obliquely incident plane acoustic wave from a grating of immersed cylindrical shells

The study of the interaction of acoustic waves with cylindrical structures has numerous applications including the ultrasonic nondestructive testing of materials. In this paper, using a new mathematical model presented for the scattering of obliquely incident plane acoustic waves from a grating of immersed cylindrical shells, a detailed study of the resonant interaction of A-wave resonances originating from the shells is conducted. The nature of A-wave resonances and the effect of center-to-center distance of the shells on these resonances are examined. It is observed that this resonant interaction not only results in the splitting of A-wave resonances, but also causes an increase in resonance amplitudes. This interaction phenomenon is not seen in Rayleigh, whispering gallery and guided wave resonances. It is also shown that increasing the angle of wave incidence to the grating weakens the A-wave resonant interactions. The numerical results obtained from the mathematical model are compared to experimental results available in the literature for gratings composed of two and three aluminum shells. The numerical results are in very good agreement with their experimental counterparts.

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675–682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka ⩽ 0.1 . The incidence angle α c at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka ⩽ 0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.

Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

Background and objective The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0° to 40°, revealed the existence of an anomalous “pseudo-Rayleigh” mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole ( n = 1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40° for various elastic and viscoelastic cylinder materials. Method Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0° ⩽ α < 90°. The “pure” resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified. Results and conclusion The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka ≲ 0.1 at a critical angle α c bounded by the longitudinal and shear waves coupling angles θ L = sin - 1 ( c / c L ) and θ S = sin - 1 ( c / c S ) such that θ L < α c < θ S (where c L and c S are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle θ L < α c < θ S result from the excitation of the monopole ( n = 0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 ≲ ka ≲ 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle θ R = sin - 1 ( c / c R ) (where c R is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole ( n = 1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder’s surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.

The far field asymptotics in the problem of diffraction of an acoustic plane wave by an impedance cone

The work deals with the far field asymptotics of the classical solution for the problem of diffraction by an impedance cone. The incident acoustic plane wave completely illuminates the semi-infinite conical surface. The scattered field contains different components in the asymptotics, namely, the spherical wave from the vertex of the cone, the reflected waves, and, under some conditions, also the surface waves of Rayleigh type. We give integral representations for the scattering diagram of the spherical wave. The uniform (with respect to the observation direction) asymptotic expression for the wave field is also addressed and described by the parabolic cylinder ansatz.

Acoustic wave scattering from infinite cylinders made from functionally graded materials

Functionally graded materials (FGM's) are superheat-resistive materials which show attractive properties in many applications including furnace liners. FGM's consist of two distinct materials, for example a ceramic and a metal alloy. These two materials are mixed such that the composition of each material changes continuously along a specific direction resulting in a continuous change of microstructure along that direction. The change in microstructure induces chemical, material, and microstructural gradients, and makes functionally graded materials different in behavior from homogeneous materials and traditional composites. In this paper, the scattering of an incident plane acoustic wave from an infinite solid cylinder made from functionally graded materials is studied. Expressions are derived for the far-field scattered pressure generated by illumination of the infinite FGM cylinder by an infinite plane acoustic wave. The propagation direction of the incident wave can make an arbitrary angle with the normal to the cylinder axis. The mathematical equations are derived and numerical results for cylinders made from specific functionally graded materials are presented at different incidence angles.

Diffraction on a semi-infinite screen of a plane nonstationary wave the amplitude of which increases linearly along the front set

An exact analytic solution of the two-variables nonstationary problem of diffraction on an ideal half-infinite screen is obtained by the Smirnov-Sobolev method. The source of the field is an incident plane acoustic wave with a δ-function profile. The wave amplitude is a linear function increasing along the front set. Bibliography: 6 titles.

Complete transmission through a periodically perforated rigid slab

The propagation of a normally incident plane acoustic wave through a three-dimensional rigid slab with periodically placed holes is modeled and analyzed. The spacing of the holes A and B, the wavelength lambda, and the thickness of the slab L are order one parameters compared to the characteristic size D of the holes, which is a small quantity. Scattering matrix techniques are used to derive expressions for the transmission and reflection coefficients of the lowest mode. These expressions depend only on the transmission coefficient, tau(0), of an infinitely long slab with the same configuration. The determination of tau(0) requires the solution of an infinite set of algebraic equations. These equations are approximately solved by exploiting the small parameter D/square root(AB). Remarkably, this structure is transparent at certain frequencies and opaque for all others. Such a structure may be useful in constructing narrow-band filters and resonators.

Scattering of plane acoustic waves by a transversely isotropic cylindrical shell—application to material characterization

Scattering of obliquely incident plane acoustic wave by an air-filled, transversely isotropic cylindrical shell immersed in water is investigated theoretically and experimentally. The normal mode expansion technique is employed for analyzing the scattering field, and then resonance modes of the shell appearing in modal scattering form functions are identified performing the resonance scattering analysis. Dispersion curves for Sholte–Stoneley, SH and Lamb waves are obtained and their characteristics are interpreted. Calculated backscattering and resonance spectra as well as dispersion curves are compared with those from ultrasonic experiments for two composite samples having the same nominal composition but fabricated under different conditions. Sensitive change of the dispersion curves is observed for both normal and oblique incidences, which demonstrates the feasibility of systematic inverse evaluation of damage or elastic constants of the composite shell using data from the acoustic scattering measurements.