Influence of sorption on sound propagation in granular activated carbon.

Granular activated carbon (GAC) has numerous applications due to its ability to adsorb and desorb gas molecules. Recently, it has been shown to exhibit unusually high low frequency sound absorption. This behavior is determined by both the multi-scale nature of the material, i.e., the existence of three scales of heterogeneities, and physical processes specific to micro- and nanometer-size pores, i.e., rarefaction and sorption effects. To account for these processes a model for sound propagation in GAC is developed in this work. A methodology for characterizing GAC which includes optical granulometry, flow resistivity measurements, and the derivation of the inner-particle model parameters from acoustical and non-acoustical measurements is also presented. The model agrees with measurements of normal incidence surface impedance and sound absorption coefficient on three different GAC samples.

Influence of Forchheimer's nonlinearity and transient effects on pulse propagation in air saturated rigid granular materials.

It has been shown in the earlier work of Umnova et al. [Noise Control Eng. 50, 204-210 (2002)] that interaction of a relatively long, high amplitude acoustic pulse with a rigid porous material can be accurately described accounting for the Forchheimer nonlinearity. In the present study, the goal is to determine whether the accuracy of the modeling can be improved in the case of a lower amplitude and a shorter pulse. A model that accounts for the Forchheimer's nonlinearity and the transient effects is developed. It is assumed that all the contributions to the viscous force are additive in the time domain. The governing equations are solved numerically using finite difference time domain scheme. The results are compared with the data for two granular materials. The latter are obtained in an impedance tube and in a shock tube experiments, where acoustic pulses with various amplitudes and durations are generated.

Analytical approximations for low frequency band gaps in periodic arrays of elastic shells.

This paper presents and compares three analytical methods for calculating low frequency band gap boundaries in doubly periodic arrays of resonating thin elastic shells. It is shown that both Foldy-type equations (derived with lattice sum expansions in the vicinity of its poles) and a self-consistent scheme could be used to predict boundaries of low-frequency (below the first Bragg band gap) band gaps due to axisymmetric (n=0) and dipolar (n=1) shell resonances. The accuracy of the former method is limited to low filling fraction arrays, however, as the filling fraction increases the application of the matched asymptotic expansions could significantly improve approximations of the upper boundary of band gap related to axisymmetric resonance. The self-consistent scheme is shown to be very robust and gives reliable results even for dense arrays with filling fractions around 70%. The estimates of band gap boundaries can be used in analyzing the performance of periodic arrays (in terms of the band gap width) without using full semi-analytical and numerical models. The results are used to predict the dependence of the position and width of the low frequency band gap on the properties of shells and their periodic arrays.

Comparisons of two effective medium approaches for predicting sound scattering by periodic arrays of elastic shells.

Two effective medium models are presented and used to predict complex reflection and transmission coefficients of finite periodic arrays of resonant elastic shells as well as their effective density and bulk modulus at low frequencies. Comparisons with full multiple scattering theory and measurements show that the self-consistent model fails to correctly predict the shape of the transmission/reflection curves when scatterer resonances are close to the first Bragg bandgap. The low frequency grating model, which neglects the evanescent modes and considers scattered wave propagation only in the same direction as the incident one, gives a much better agreement with both measurements and the full multiple scattering theory. Moreover, because it does not require the wavelength to strongly exceed the size of scatterers, the model gives reliable predictions even at frequencies around the first periodicity related bandgap. In contrast to the self-consistent model, the low frequency grating model is applicable when the resonant scatterers have more than two low frequency resonances.

Mathematics summer schools for acoustics research training.

Mathematical methods are important for research in many aspects of acoustics. Most researchers in acoustics in the United Kingdom do not have access to master level courses to broaden their postgraduate study, so they advance their fundamental mathematical methodologies taught at undergraduate level through independent learning. They develop their mathematical skills as appropriate rather than being made aware of the potential of advanced mathematical tools at the onset of their research career. Attempts to improve this situation were made through summer schools held in 2003 and 2005 at Southampton University and in 2007 at Salford University. The background to these Summer Schools, their content and structure, recruitment figures and student feedback are reported together with conclusions about their performance and role particularly in respect of PhD completion.

Acoustical properties of double porosity granular materials.

Granular materials have been conventionally used for acoustic treatment due to their sound absorptive and sound insulating properties. An emerging field is the study of the acoustical properties of multiscale porous materials. An example of these is a granular material in which the particles are porous. In this paper, analytical and hybrid analytical-numerical models describing the acoustical properties of these materials are introduced. Image processing techniques have been employed to estimate characteristic dimensions of the materials. The model predictions are compared with measurements on expanded perlite and activated carbon showing satisfactory agreement. It is concluded that a double porosity granular material exhibits greater low-frequency sound absorption at reduced weight compared to a solid-grain granular material with similar mesoscopic characteristics.

Acoustic insertion loss due to two dimensional periodic arrays of circular cylinders parallel to a nearby surface.

The acoustical performances of regular arrays of cylindrical elements, with their axes aligned and parallel to a ground plane, have been investigated through predictions and laboratory experiments. Semi-analytical predictions based on multiple scattering theory and numerical simulations based on a boundary element formulation have been made. Measurements have been made in an anechoic chamber using arrays of (a) cylindrical acoustically-rigid scatterers (PVC pipes) and (b) thin elastic shells. Insertion loss (IL) spectra due to the arrays have been measured without and with ground planes for several receiver heights. Data and predictions have been compared. The minima in the excess attenuation spectrum i.e., attenuation maxima due to the ground alone resulting from destructive interference between direct and ground-reflected sound waves, tend to have an adverse influence on the band gaps (BG) related to a periodic array in the free field when these two effects coincide. On the other hand, the presence of rigid ground may result in an IL for an array near the ground similar to or, in the case of the first BG, greater than that resulting from a double array, equivalent to the original array plus its ground plane mirror image, in the free field.

Predictions and measurements of sound transmission through a periodic array of elastic shells in air.

Analytical and numerical approaches have been made to the problems of (a) propagation through a doubly periodic array of elastic shells in air, (b) scattering by a single elastic shell in air, and (c) scattering by a finite periodic array of elastic shells in air. Using the Rayleigh identity and the Kirchhoff-Love approximations, a relationship is found between the elastic material parameters and the size of the bandgap below the first Bragg frequency, which results from the axisymmetric resonance of the shells in an array. Predictions and laboratory data confirm that use of a suitably "soft" non-vulcanized rubber results in substantial insertion loss peaks related to the resonances of the shells. Inclusion of viscoelasticity is found to improve the correspondence between predictions and data. In addition the possible influences of inhomogeneity due to the manufacturing of the elastic shells (i.e., the effects of gluing sheet edges together) and of departures from circular cylindrical cross-sections are considered by means of numerical methods.

Volumetric diffusers: pseudorandom cylinder arrays on a periodic lattice.

Most conventional diffusers take the form of a surface based treatment, and as a result can only operate in hemispherical space. Placing a diffuser in the volume of a room might provide greater efficiency by allowing scattering into the whole space. A periodic cylinder array (or sonic crystal) produces periodicity lobes and uneven scattering. Introducing defects into an array, by removing or varying the size of some of the cylinders, can enhance their diffusing abilities. This paper applies number theoretic concepts to create cylinder arrays that have more even scattering. Predictions using a boundary element method are compared to measurements to verify the model, and suitable metrics are adopted to evaluate performance. Arrangements with good aperiodic autocorrelation properties tend to produce the best results. At low frequency power is controlled by object size and at high frequency diffusion is dominated by lattice spacing and structural similarity. Consequently the operational bandwidth is rather small. By using sparse arrays and varying cylinder sizes, a wider bandwidth can be achieved.

Time domain formulation of the equivalent fluid model for rigid porous media.

A set of equations has been derived which corresponds to the time domain formulation of the equivalent fluid model. It models the propagation of an acoustic pulse in rigid frame porous material accounting for both viscous and thermal effects. It has been shown analytically and confirmed numerically that the equations can be reduced to those published previously in the limit of long and short duration pulses. Numerical solutions have been found for different pulse durations and the results have been compared with other time domain models.

Effect of boundary slip on the acoustical properties of microfibrous materials.

A variety of new porous materials with unusually small pores have been manufactured in the past decades. To predict their acoustical properties, the conventional models need to be modified. When pore size becomes comparable to the molecular mean free path of a saturating fluid, the no-slip conditions on the pore surface are no longer accurate and hence the slip effects have to be taken into account. In this paper, sound propagation in microfibrous materials is modeled analytically, approximating the geometry by a regular array of rigid parallel cylinders. It has been shown that velocity and thermal slip on a cylinder surface significantly changes the model predictions leading to lower attenuation coefficient and higher sound speed values. The influence of material porosity, fiber orientation, and size on these effects is investigated. Finite element method is used to numerically solve the oscillatory flow and heat transfer problems in a square array of cylindrical fibres. Numerical results are compared with predictions of the analytical model and the range of its validity is identified.

Nonlinear dynamics of coupled transverse-rotational waves in granular chains.

The nonlinear dynamics of coupled waves in one-dimensional granular chains with and without a substrate is theoretically studied accounting for quadratic nonlinearity. The multiple time scale method is used to derive the nonlinear dispersion relations for infinite granular chains and to obtain the wave solutions for semi-infinite systems. It is shown that the sum frequency and difference frequency components of the coupled transverse-rotational waves are generated due to their nonlinear interactions with the longitudinal wave. Nonlinear resonances are not present in the chain with no substrate where these frequency components have low amplitudes and exhibit beating oscillations. In the chain positioned on a substrate two types of nonlinear resonances are predicted. At resonance, the fundamental frequency wave amplitudes decrease and the generated frequency component amplitudes increase along the chain, accompanied by the oscillations due to the wave number asynchronism. The results confirm the possibility of a highly efficient energy transfer between the waves of different frequencies, which could find applications in the design of acoustic devices for energy transfer and energy rectification.

Detection of Osteoporosis from Percussion Responses Using an Electronic Stethoscope and Machine Learning.

Osteoporosis is an asymptomatic bone condition that affects a large proportion of the elderly population around the world, resulting in increased bone fragility and increased risk of fracture. Previous studies had shown that the vibroacoustic response of bone can indicate the quality of the bone condition. Therefore, the aim of the authors' project is to develop a new method to exploit this phenomenon to improve detection of osteoporosis in individuals. In this paper a method is described that uses a reflex hammer to exert testing stimuli on a patient's tibia and an electronic stethoscope to acquire the impulse responses. The signals are processed as mel frequency cepstrum coefficients and passed through an artificial neural network to determine the likelihood of osteoporosis from the tibia's impulse responses. Following some discussions of the mechanism and procedure, this paper details the signal acquisition using the stethoscope and the subsequent signal processing and the statistical machine learning algorithm. Pilot testing with 12 patients achieved over 80% sensitivity with a false positive rate below 30% and accuracies in the region of 70%. An extended dataset of 110 patients achieved an error rate of 30% with some room for improvement in the algorithm. By using common clinical apparatus and strategic machine learning, this method might be suitable as a large population screening test for the early diagnosis of osteoporosis, thus avoiding secondary complications.

Effects of porous covering on sound attenuation by periodic arrays of cylinders.

The acoustic transmission loss of a finite periodic array of long rigid cylinders, without and with porous absorbent covering, is studied both theoretically and in the laboratory. A multiple scattering model is extended to allow for the covering and its acoustical properties are described by a single parameter semi-empirical model. Data from laboratory measurements and numerical results are found to be in reasonable agreement. These data and predictions show that porous covering reduces the variation of transmission loss with frequency due to the stop/pass band structure observed with an array of rigid cylinders with similar overall radius and improves the overall attenuation in the higher frequency range. The predicted sensitivities to covering thickness and effective flow resistivity are explored. It is predicted that a random covered array also gives better attenuation than a random array of rigid cylinders with the same overall radius and volume fraction.