Volume 106, Issue 6, December 1999
 GENERAL LINEAR ACOUSTICS [20]


Improvement of sound barriers using headpieces with finite acoustic impedance
View Description Hide DescriptionThe paper deals with the reduction of the sound energy in the shadow region behind barriers by means of an attached body at the edge of the screen. The reflecting attributes of the barrier’s headpiece are described by a locally reacting impedance. Diffraction at ideal soft and hard bodies demonstrates the basic principle of tangential power transport parallel to their surface: the impedance must be chosen so that the tangential intensity near the edge is lowered, turning the incoming power in harmless directions. The differences due to finite impedances are then discussed. The physical principles are demonstrated in frozen pictures of the sound field for the different cases. Theoretical computations show considerably improved levels in the shadow zone for larger angles of diffraction. These are compared with empirical results, and practical applications are discussed.

Wideband quantitative ultrasonic imaging by timedomain diffraction tomography
View Description Hide DescriptionA quantitative ultrasonic imaging method employing timedomain scattering data is presented. This method provides tomographic images of medium properties such as the sound speed contrast; these images are equivalent to multiplefrequency filteredbackpropagation reconstructions using all frequencies within the bandwidth of the incident pulse employed. However, image synthesis is performed directly in the time domain using coherent combination of farfield scattered pressure waveforms, delayed and summed to numerically focus on the unknown medium. The timedomain method is more efficient than multiplefrequency diffraction tomography methods, and can, in some cases, be more efficient than singlefrequency diffraction tomography. Example reconstructions, obtained using synthetic data for two and threedimensional scattering of wideband pulses, show that the timedomain reconstruction method provides image quality superior to singlefrequency reconstructions for objects of size and contrast relevant to medical imaging problems such as ultrasonic mammography. The present method is closely related to existing syntheticaperture imaging methods such as those employed in clinical ultrasound scanners. Thus, the new method can be extended to incorporate available imageenhancement techniques such as timegain compensation to correct for medium absorption and aberration correction methods to reduce error associated with weak scattering approximations.

A Galerkin method for the numerical analysis of diffraction by a rectangular screen
View Description Hide DescriptionA novel numerical analysis of acoustic diffraction by a rectangular screen is described. The boundary integral model of the system is solved by a Galerkin method using as a basis the scaling functions of discrete wavelet theory. The use of scaling functions enables the quadruple integrals in the Galerkin method to be analytically reduced to double integrals, and the singular and hypersingular integrals can be found from a recurrence formula. Numerical tests show that the new method is more efficient than a boundary element method based on collocation, particularly when the screen is irradiated near grazing incidence.

Acoustic response of a periodic layer of nearly rigid spherical inclusions in an elastic solid
View Description Hide DescriptionReflection and transmission spectra of a plane longitudinal wave normally incident on a periodic (square) array of identical spherical particles in a polyester matrix are measured at wavelengths which are comparable to the particle radius and the interparticle distance. The spectra are characterized by several resonances whose frequencies are close to the cutoff frequencies for the shear wave diffraction orders. Arrays of heavy particles (lead and steel) exhibit a pronounced resonance which occurs when the lattice resonant frequency is close to the frequency of the rigidbody translation (dipole) resonance of an isolated sphere in an unbounded matrix. An approximate lowfrequency theory is developed which assumes that the inclusions are rigid, but which takes into account the multiplescattering effect. The comparison between theory and the experiment is found to be good for arrays with particle area fraction as high as 32%.

Effect on ultrasonic signals of viscous pore fluids in unconsolidated sand
View Description Hide DescriptionUltrasonic attenuationmeasurements in unconsolidated sand with pore fluids ranging in viscosity between 0.001 and 1 Pa⋅s were compared with the predictions of fluid flow and scattering theories. Laboratory experiments were performed for P waves propagating through sand samples saturated with water, castor oil and two different silicone oils. The attenuation shows a frequency squared dependence for all measurements, regardless of viscosity, in the range between 100 and 1000 kHz. The results show that for unconsolidated sand, fluid flow models which imply significant effects of the viscous pore fluids on ultrasonic waves cannot explain the laboratory measurements. The main attenuationeffects observed in the laboratory can be simulated with a threedimensional generalized dynamic composite elastic medium model, which includes scattering from the pores and grains as well as intrinsic attenuation caused by the viscous pore fluids. For the studied sand samples, scattering is the main attenuation mechanism for ultrasonicP waves.

Computation of transient radiation in semiinfinite regions based on exact nonreflecting boundary conditions and mixed time integration
View Description Hide DescriptionTransient radiation in a semiinfinite region, bounded by a planar infinite baffle with a local acoustic source is considered. The numerical simulation of the transient radiation problem requires an artificial boundary here chosen to be a hemisphere, which separates the computational region from the surrounding unbounded acoustic medium. Inside the computational region we use a semidiscrete finite element method. On we apply the exact nonreflecting boundary condition (NRBC) first derived by Grote and Keller for the freespace problem. Since the problem is symmetric about the infinite planar surface, in order to satisfy the rigid baffle condition it is sufficient to restrict the indices in the spherical harmonic expansion which defines the NRBC and scale the radial harmonics which drive auxiliary equations on the boundary. The Fourier expansion in the circumferential angle appearing in the NRBC may be used to efficiently model axisymmetric problems in two dimensions. A new mixed explicitimplicit time integration method which retains the efficiency of explicit pressure field updates without the need for diagonal matrices in the auxiliary equations on is presented. Here, the interior finite elementequations are integrated explicitly in time while the auxiliary equations are integrated implicitly. The result is a very natural and highly efficient algorithm for largescale wave propagation analysis. Numerical examples of fully transient radiation resulting from a piston transducer mounted in an infinite planar baffle are compared to analytical solutions to demonstrate the accuracy of the mixed time integration method with the NRBC for the halfspace problem.

Characterization of multiplesprung masses for wideband noise control
View Description Hide DescriptionThe design of a wide frequency band neutralizer, vibration absorber and/or structural fuzzy, in the form of multiplesprung masses, is extensively reported in the open literature. The action of the device is reported in terms of the joint point impedance of the sprung masses. This joint impedance is merely the sum over the impedances of the individual sprung masses at the common point to which the device is to be attached to a master structure. The normalized frequency bandwidth of a device composed of a singlesprung mass is proportional to the loss factor of that sprung mass. To increase this bandwidth, a device composed of more than one sprung mass, with distributed resonance frequencies, is utilized. To keep suppressed the undulations in the joint impedance of a set composed of a multiplicity of sprung masses, the loss factors are rendered larger than the normalized separations between adjacent antiresonance frequencies. This modal overlap condition, together with consideration of weight, are central to the design of the device. The analysis of the device is enriched by considering two distinct distributions of resonance frequencies for each set of sprung masses. Moreover, the ranges and parameters which specify that device are limited to reasonably moderate values; e.g., the useful frequency bandwidth of a given device is limited to onethird of its center frequency and the number of sprung masses in a device is restricted not to exceed onescore. In a set employing the first resonance frequency distribution, as the number of sprung masses is initially increased, an increase in the bandwidth is accompanied by an increase in the level of the joint impedance. As the number of sprung masses is further increased, the bandwidth and the level of the joint impedance become saturated. In a set incorporating the second resonance frequency distribution, an ongoing increase in the bandwidth, as the number of sprung masses increases, is accompanied by an ongoing decrease in the level of the joint impedance. The examination of these and other characteristics in the joint impedance of the sprung masses is provided by data obtained in computer experiments performed on a few selected sets of sprung masses.

Criteria for designing multiplesprung masses for wideband noise control
View Description Hide DescriptionIn a companion paper the characterization of a multiplesprung masses design for wideband noise control is presented. The characterization is largely conducted in terms of the point impedance of a set of sprung masses. The sprung masses in the set are collectively acting at a point. In that companion paper the dependencies of the joint impedance on the number of sprung masses, the modal overlap factors, the total mass, and the resonance frequency distribution are of particular interest. In the present paper this characterization of a set of sprung masses is utilized to define a number of design criteria that determine the potential viability of the set as a noise control device. In the final analysis, the device must be assessed in an in situ setting. In that setting the device is tested in terms of the overall gain. The determination of the overall gain requires, in addition to the joint impedance of the device, the impedance of the hosting master structure at the point of attachment. (The device is meant to control the noise in the master structure.) It is argued that although the overall gain is the final judge, the potential viability of a device may be a useful critique of the intended performance of the device. In this vein, a viability and a criterion of promise are defined to assist with the design processes of this noise control device. In assessing the viability and in satisfying the criterion of promise, the desired characteristics in a set of sprung masses can be judicially selected.

A class of expansion functions for finite elastic plates in structural acoustics
View Description Hide DescriptionProblems in structural acoustics involving finite plates can be formulated using integral equation methods. The unknown function within the integral equation must satisfy the plate edge conditions, and hence appropriate expansion functions must be used. The expansion functions developed here are aimed at treating a wide class of problems. Once such functions are found, the solution process and numerical implementation are relatively straightforward. The speed of convergence to “exact” comparison solutions is fast even in the singular limit of high frequencies and wide plates. A set of expansion functions with the required properties is constructed and some illustrative problems are treated.
