Calculation Of Sound Field Research Articles

Design and experiment of 256-element ultrasound phased array for noninvasive focused ultrasound surgery

A 256-element phased array high intensity focused ultrasound system has been designed and constructed in our laboratory. The 256-element spherical-section ultrasound phased array made from piezocomposite material operates at 1.1 MHz with 11-cm radius of curvature, 14-cm outer diameter, and 3.4-cm diameter central hole for mounting diagnostic ultrasound imaging probe. First, the explicit sound field calculation approach for the spherical-section phased array and the genetic optimal algorithm are briefly introduced as the optimal focus pattern control methods. Then, the design guidelines of 256-element spherical-section focused ultrasound phased array and 256-channel driver system are given. The results of single on and off axial focus, multiple on and off axial foci, half sub-array focus pattern provide further evidence for the 3D focus steering and sub-array mode for avoiding obstacles in focused ultrasound surgery. The multi-foci pattern can enlarge the treatment volume to 22 times larger than that of a single focus in one sonication. Finally, in vitro and transparent tissue-mimicking phantom experiment results confirm the ability of 256-element spherical-section phased array system to induce thermal lesions for noninvasive ultrasound surgery.

Comparison of an analytic horn equation approach and a boundary element method for the calculation of sound fields in the human ear canal

The sound field inside a model human ear canal has been computed, to show both longitudinal variations along the canal length and transverse variations through cross-sectional slices. Two methods of computation were used. A modified horn equation approach parametrizes the sound field with a single coordinate, the position along a curved center axis-this approach can accommodate the curvature and varying cross-sectional area of the ear canal but cannot compute transverse variations of the sound field. A boundary element method (BEM) was also implemented to compute the full three-dimensional sound field. Over 2000 triangular mesh elements were used to represent the ear canal geometry. For a plane piston source at the entrance plane, the pressure along the curved center axis predicted by the two methods is in good agreement, for frequencies up to 15 kHz, for four different ear canals. The BEM approach, though, reveals spatial variations of sound pressure within each canal cross section. These variations are small below 4 kHz, but increase with frequency, reaching 1.5 dB at 8 kHz and 4.5 dB at 15 kHz. For source configurations that are more realistic than a simple piston, large transverse variations in sound pressure are anticipated in the vicinity of the source.

Focused beam control for ultrasound surgery with spherical-section phased array: sound field calculation and genetic optimization algorithm

This study aims at a sound field calculation for the spherical-section phased array and an optimization algorithm for the focus patterns of phased array ultrasound surgery. An efficient field calculation formula represented as an explicit expression is derived by the strategies of projection and binomial expansion. An optimization algorithm based on genetic algorithm is constructed by the suitable fitness function and the selection strategies. The simulation results of 256-element spherical-section phased array show the capability of controlling focus accurately and effectively with the combined method made up of the explicit expression method and the genetic optimization algorithm. The simulation results of single focus, multiple foci, on-axial focus, and off-axial focus further convince the feasibility of three-dimensional (3-D) focus steering with excellent acoustic performances. A single focus with the focus dimension of 1.25 mm x 1.25 mm x 7 mm and with the intensity of 6080 W/cm2 is formed. The multiple-focus pattern can enlarge the treatment volume 22 times larger than that of single focus with a sonication. In addition, a comparison between the explicit expression approach and the point source approach testifies to the applicability of the explicit expression approach. The experiment and simulation results of 16-element array actually confirm the feasibility of the combined method.

Auralization studies to develop a classroom questionnaire

Modern, computer-based room acoustic modeling software allows apart from the calculation and visualization of sound fields also the auralization of room acoustic conditions. By these means the listening conditions in (virtual) class rooms can easily be modeled and modified. Furthermore, for each listening position a full set of room acoustical parameters is available. Corresponding measurements in real class rooms would require much effort; well-defined changes could only be reached by interior works in the building. So, computer modeling offers a larger variety of well-defined acoustic conditions. This contribution reports on the auralizations carried out for the development of a questionnaire for subjective evaluations in real class rooms. For this purpose six different virtual class rooms have been modeled. In each of the six situations auralizations at two different listening positions for male and female speakers have been deduced. The auralizations have been presented to 80 test persons. The objective room acoustic parameters have been correlated with the subjective judgements. The questionnaire has been used by Meis et al. in real life experiments on the subjective evaluation of listening conditions. Results of these experiments will be presented in another contribution to this session by M. Meis (2pAAa1).

Noise generation by a supersonic leading edge. Part 1: general theory

This paper concerns the calculation of the sound fields which are generated when a vortical gust, convected in a supersonic mean flow, strikes the leading edge of a fan blade or aerofoil. Inviscid linear theory is applied, with the blade modelled as an infinite-span flat rigid plate, and a gust of arbitrary form is considered. By application of Fourier transforms the boundary value problem for the velocity potential is solved, leading to an integral expression for the generated sound field. This expression is applicable everywhere inside a Mach wedge. For gusts localized in the span direction, a farfield approximation is derived which is valid inside a Mach cone, and which is of simple enough form to be evaluated analytically for specified gust shapes. The new feature of this analysis is the consideration of an arbitrary gust form: previous authors have only ever considered the properties of specific gusts, focusing principally on harmonic gusts and jets.

Performance Analysis of Acoustic Receiving Devices Functioning in a Car Cabin Based on Computer Modeling of a Sound Field

A model for speech and noise sound fields in a car cabin is proposed. The model takes into account a complicated geometry of the cabin, frequency dependence of sound absorption on its surfaces and spatial correlation of distributed noises. The sound field computation is based on the wave approach for the range of low frequencies (below 1000 Hz) and on the ray approximation for higher frequencies. The software is developed, which provides simulation of speech and noise fields in the cabin during the car motion. This software may be utilized as an simulator of the sound field for the development of speech coding and recognition devices intended for car cabins. To check the model adequacy the spectra of simulated noise of the engine and results of natural measurements are compared. The effectiveness of microphone arrays as speech enhancement tools is investigated on the base of the developed model for different signal processing algorithms and noise conditions.

拡散音場計算と波動音場計算の差に関する検討 : 拡散度法による重量床衝撃音の予測計算法に関する研究 その2

拡散音場計算と波動音場計算の差に関する検討 : 拡散度法による重量床衝撃音の予測計算法に関する研究 その2

Stability analysis of an acoustically levitated disk.

In this paper, a model is developed for the stability analysis of an acoustically levitated disk on the basis of analyzing eddy acoustic streaming and acoustic viscous stress. In the model, the effect of the acoustic streaming outside the boundary layer that is on the surface of the levitated disk is properly taken into account. Also, the calculation of sound field and acoustic viscous stress is limited to the range that has a dominant effect on the stability. By this method, we obtain a quite accurate solution of the stability coefficient. For the small horizontal shift of a large levitated disk, the model is verified by the good agreement between the experimental and theoretical results. By means of this model and relevant experiments, some factors that affect the stability of the levitated disk are investigated, and useful guidelines for design and application are obtained. It is found that the range from the edge to the outermost nodal circle of the disk-shaped vibrator has a large effect on the stability of the levitated disk. To stabilize the levitated disk by acoustic viscous force, the distance between the edge and the outermost nodal circle of the vibrator must be larger than a critical value, which is determined by the driving frequency and the sound velocity of the fluid between the levitated disk and the vibrator. When this condition is satisfied, increasing the distance between the edge and the outermost nodal circle leads to a decrease in the stability. It is also found that the property of the fluid between the levitated disk and the vibrator has a large effect on the stability. It is easier to stabilize the levitated disk in steam than in air, but more difficult to do so in carbon dioxide and hydrogen. In addition, theoretical results show that increasing the weight per unit area of the levitated object increases the stability for a given vibrator velocity. The distribution of the acoustic viscous stress and the dependence of the stability coefficient and the holding force on the horizontal shift of the levitated disk, which are obtained by this study, also are useful to a better understanding of the stability of the levitated disk.

Sound Field Calculations of Elliptical Pistons by theSuperposition of Two-Dimensional Gaussian Beams

We present an alternative approach to calculate the sound field ofultrasonic transducers. The distribution function of sources isexpanded into the superposition of a series of two-dimensional Gaussianfunctions. The corresponding radiated sound field is expressed as thesuperposition of these two-dimensional Gaussian beams and is thenreduced to the computation of these simple functions. This treatmentdoes not require the condition that the shape of the source is of circularaxial symmetry. A numerical example is presented for the uniformelliptical piston transducer and this is in good agreement with the resultsgiven by complicated computation.

Solving the diffusion equation with a finite element solver: Calculation of diffuse sound field in room acoustics

Over the last years, some publications [e.g., Picaut, Simon, and Hardy, J. Acoust. Soc. Am. 106, 2638–2645 (1999)] showed that the acoustic energy density in closed or semiclosed spaces is the solution of a diffusion equation. This approach allows the nonuniform repartition of energy, and is especially relevant in room acoustics for complex spaces or long rooms. In this work, the 3-D diffusion equation is solved directly by using a finite element solver, for a set of long rooms and absorbing rooms. The stationary equation is first solved. A constant-power acoustic source is modelized by setting appropriate boundary conditions. The time-dependent problem is also solved to simulate the sound decay, with an impulse source defined in a subregion with relevant initial conditions. Results concerning sound attenuation and reverberation times match satisfactorily with other theoretical and numerical models. An application is also given for two coupled rooms.

A comparison of radiosity with current methods of sound level prediction in commercial spaces

The ray tracing and image methods (and variations thereof) are widely used for the computation of sound fields in architectural spaces. The ray tracing and image methods are best suited for spaces with mostly specular reflecting surfaces. The radiosity method, a method based on solving a system of energy balance equations, is best applied to spaces with mainly diffusely reflective surfaces. Because very few spaces are either purely specular or purely diffuse, all methods must deal with both types of reflecting surfaces. A comparison of the radiosity method to other methods for the prediction of sound levels in commercial environments is presented. [Work supported by NSF.]

Acoustic radiosity for computation of sound fields in diffuse environments

The use of image and ray tracing methods (and variations thereof) for the computation of sound fields in rooms is relatively well developed. In their regime of validity, both methods work well for prediction in rooms with small amounts of diffraction and mostly specular reflection at the walls. While extensions to the method to include diffuse reflections and diffraction have been made, they are limited at best. In the fields of illumination and computer graphics the ray tracing and image methods are joined by another method called luminous radiative transfer or radiosity. In radiosity, an energy balance between surfaces is computed assuming diffuse reflection at the reflective surfaces. Because the interaction between surfaces is constant, much of the computation required for sound field prediction with multiple or moving source and receiver positions can be reduced. In acoustics the radiosity method has had little attention because of the problems of diffraction and specular reflection. The utility of radiosity in acoustics and an approach to a useful development of the method for acoustics will be presented. The method looks especially useful for sound level prediction in industrial and office environments. [Work supported by NSF.]

Analysis of interior and exterior sound fields using iterative boundary element solvers

The boundary element method (BEM) is an efficient tool for the calculation of interior and exterior sound fields. However, the discretization of the Helmholtz integral equation often leads to large, unsymmetrical, and fully populated systems of linear equations. Such systems can be solved by means of various iterative solvers. Three examples are considered: First, a preconditioned version of the generalized minimum residual method (GMRES) is used for calculating the high-frequency acoustic scattering from cylinderlike structures. Second, the sound field in a passenger compartment is analyzed by using five different iterative solvers: GMRES, the conjugate gradient squared algorithm (CGS), the quasiminimal residual approximation (QMR), the biconjugate gradient stabilized algorithm (BICGSTAB), and the conjugate gradient iteration on the normal equations (CGNR). These methods and a Gaussian elimination are compared with respect to their numerical performance and speed of convergence. Third, scattering and radiation of a nonconvex structure is investigated. This structure—called ‘‘cat’s eye’’—consists of a sphere, where the positive octant is cut out. The efficiency and accuracy of the above mentioned five iterative methods are studied for the vibrating cat’s eye. By means of the preconditioned GMRES, scattering cat’s eyes of several thousand boundary elements can be treated on personal computers.

Enhanced Ray Theory

The numerical problems of SWAM'99 workshop are quite challenging for any method of sound field calculation. This report presents a detailed description of the enhanced ray theory approach briefly outlined in Ref. 2. It contains a new method of phase and amplitude computation along the ray, a new method of calculation of eigenrays, and a new method of analytic approximation of sound-speed and density. An application of these methods is presented.

ENHANCED RAY THEORY

The numerical problems of SWAM'99 workshop are quite challenging for any method of sound field calculation. This report presents a detailed description of the enhanced ray theory approach briefly outlined in Ref. 2. It contains a new method of phase and amplitude computation along the ray, a new method of calculation of eigenrays, and a new method of analytic approximation of sound-speed and density. An application of these methods is presented.

Spatial structure of the coherence parameter of the sound field in an irregular arctic waveguide

Results of numerical simulation of the total and coherent sound fields and the coherence parameter for a multimode acoustic signal excited by a monochromatic sound source and propagating in an irregular arctic waveguide are presented. Expressions used as the basis for the algorithm of the sound field calculation by the method of coupled normal modes are given. Both regular and stochastic sound scattering by horizontal inhomogeneities of the bottom, water medium, and ice cover are taken into account. It is found that, in the course of sound propagation in an arctic waveguide, an anomalous variation of the energy coherence parameter of the sound field as a function of distance is observed. This variation manifests itself in the form of local peaks of the field coherence parameter. This fact should be taken into account in both the measurements of the ice cover characteristics by acoustic methods and the evaluation of the efficiency of the operation of receiving arrays.

Low-frequency horizontal acoustic refraction caused by internal wave solitons in a shallow sea

The effect of internal wave solitons on the sound field generated by a point source in a shallow sea is considered. In the framework of the theory of “horizontal rays and vertical modes,” the sound field pattern governed by the aforementioned hydrodynamic effect is investigated. It is shown that solitons can induce time-periodic focusing and defocusing of horizontal rays propagating at shallow angles to the internal wave front. This may result in the formation of “dynamical” horizontal sound channels, which, in its turn, results in considerable temporal fluctuations of the field along the acoustic track oriented along the internal wave front. For the sound field calculations, an approach is developed on the basis of the parabolic approximation in the horizontal plane and the mode representation in the vertical direction. The results obtained can be used for remote monitoring of internal wave packets in a shallow sea.

Physical modeling of individual head-related transfer functions (HRTFs)

A model of HRTFs was developed based on the Ph.D. thesis of Genuit. The two basic ideas are (1) HRTFs can be described by the influence of a few acoustically relevant objects; first the head was modeled by a sphere and the pinna with cavum conchae by two elliptical disks with an eccentric cylindrical cave (ear canal). (2) Individual variations of HRTFs correspond to variations of geometrical parameters (diameter of sphere, dimensions of disks and cave,...); the position of the ear canal entrance point is the most important parameter. Simulation results were compared to HRTFs measured with an artificial head of well-known geometry. In general, a good correspondence between calculated and measured HRTFs was found. The correlation is significantly higher if the influence of shoulder/torso is considered, too, modeled by an additional rigid sphere. Second, the shape of head and shoulder/torso was approximated with oblate respective prolate spheroids in order to get even better results. Sound field calculation were performed using numerical methods (boundary element method, source simulation technique) and analytical methods (solution of the wave equation, use of Huygens’ integral formula). The interaction between the different reflecting and diffracting bodies was analyzed to validate a simplified model.

A simulation package for room acoustics with an open interface

The solution of complex acoustic problems of the low-frequency sound field presupposes the numeric implementation of the wave equation. Especially for the calculation of sound fields in a finite volume (interior problem), the method of the finite elements (FEM) can be applied. The software market gives the acoustic engineer many different commercial simulation packages, which have no or only a limited user interface for user extensions. This was the reason to create the simulation module called WaveSolve3D. Due to its high portable structure WaveSolve3D can be used on all current and future computer generations, and thereby permits the running of the application on the hardware with the best computing power. In the context of this paper some simulation results computed by WaveSolve3D will be presented. Verification can be achieved by comparison with analytical results in simple enclosures or with measurement results for more complex rooms. The work is part of a project which intends to extend the frequency range in room acoustical computer simulation.

Two surface element formulations in the time domain for the calculation of sound fields in cavities with varying boundary conditions

Two different surface element formulations are presented which apply the equivalent source method in the time domain. The first method uses planar surface elements. The boundary condition of the cavity surface in the form of a prescribed impedance is fulfilled by using monopole elements (i.e., layers of free-field radiating monopoles with a uniform signal over the element). The second method is based on the Kirchhoff–Helmholtz integral. While the traditional boundary element technique uses the free-field Green’s functions, here a set of specialized Green’s functions is applied which is adapted to the cavity geometry. This set of functions fulfills the boundary conditions for the cavity with rigid walls. In this way the Kirchhoff–Helmholtz integral is simplified substantially and only areas of the surface with nonrigid boundary conditions have to be included in the calculations. Advantages and disadvantages of both formulations are highlighted, and results from both methods are compared for rooms of different complexity.