A. Cummings

Prediction of the bulk acoustic properties of fibrous materials at low frequencies

Abstract In many acoustical modelling applications, it is necessary to be able to predict the bulk acoustic properties of sound absorbing porous media at frequencies below the range of the usual measurement methods for these properties. A semi-empirical prediction method for fibrous media is described here, which not only yields physically reasonable predictions for the bulk properties at arbitrarily low frequencies, but also is in good agreement with measured data at higher frequencies. In this it represents an improvement over previously published low frequency models.

The effects of a resonator array on the sound field in a cavity

Abstract A multi-mode theoretical analysis, of the scattering of a reverberant sound field in a cavity by an array of resonators, is described; the sound field is driven by an arbitrary distribution of sources. Comparisons are made between computed data based on the present analysis and published measurements, and generally favourable agreement is noted. A selection of computed data is also presented, illustrating various aspects of the use of resonators to reduce the resonant response of a cavity to a source distribution.

Impedance tube measurements on porous media: The effects of air-gaps around the sample

Abstract The effects, on the measured impedance, of air-gaps around the edge of a sound-absorbing test sample in an impedance tube are examined both theoretically and experimentally, for a rigid-framed anisotropic porous medium. The results show that media of high flow resistivity tend to be more susceptible to measurement errors incurred by air-gaps than those with low resistivities. Experimental and predicted data concerning the effects of air-gaps on the impedances of both isotropic and anisotropic materials are presented, and are in reasonable agreement. Errors in the bulk acoustic properties, infered from normal surface impedance data on two different thicknesses of an isotropic material against a rigid backing, are also examined in an illustrative numerical study.

Behavior of rigid-porous layers at high levels of continuous acoustic excitation: Theory and experiment

A model for the propagation of high amplitude continuous sound through hard-backed rigid-porous layers has been developed which allows for Forchheimers correction to Darcys law. The nonlinearity associated with this is shown to be particularly important in the range of frequencies around layer resonance. The model is based on the introduction of particle velocity dependent flow resistivity into the equivalent fluid model expression for complex tortuosity. Thermal effects are accounted for by means of a linear complex compressibility function. The model has been used to derive analytical expressions for surface impedance and reflection coefficient as a function of incident pressure amplitude. Depending on the material parameters, sample thickness, and frequency range the model predicts either growth or decrease of reflection coefficient with sound amplitude. Good agreement between model predictions and data for three rigid-porous materials is demonstrated.

Response of multiple rigid porous layers to high levels of continuous acoustic excitation

A model has been developed for the response of a rigid-porous hard-backed medium containing an arbitrary number of layers to high amplitude sound. Nonlinearity is introduced by means of a velocity-dependent flow resistivity in Johnson’s equivalent fluid model for the complex tortuosity of each layer. Numerical solution of the resulting system of algebraic equations allows prediction of the dependence of surface impedance and reflection coefficient on the incident pressure amplitude. Measurements have been made of the surface impedance of various triple layers, made from different diameters of spherical lead shot and double layers consisting of gravel with different mean particle size, subject to high-intensity continuous sound. Good agreement between the model predictions and data for these multiple-granular layers is demonstrated. Moreover it is shown both theoretically and experimentally that the layer configuration giving optimum performance at low sound intensities may not continue to do so as the incident sound level is increased and the response becomes increasingly nonlinear. It is shown also that the nonlinear behavior depends strongly on layering and that, in some cases, the behavior is changed simply by changing the top layer thickness.

Combustion oscillations in gas fired appliances: Eigen-frequencies and stability regimes

Abstract This paper presents a one-dimensional acoustic model for prediction of the frequencies of self-excited oscillation and acoustic mode shapes in combustion systems. The impedance of the combustion system is represented in terms of a frequency response function (FRF). Impedances of the settling and combustion chambers are predicted by using the acoustic model, taking into account the temperature distribution in the combustion chamber. Reasonably good agreement between measured and predicted acoustic resonance frequencies and mode shapes was achieved. Some data on stability regimes are discussed.

Nonlinear behavior of poroelastic absorbing materials

A theory for the non‐linear acoustic behavior of porous materials with an elastic frame composed of incompressible grains or fibers has been derived. Johnson’s expression for complex flow resistivity [D. L. Johnson et al., J. Fluid. Mech. 176, 379–402 (1987)] has been combined with the dependence of dc flow resistivity on the amplitude of particle velocity (Forchheimer’s nonlinearity). The frame compressibility has been assumed to be linear. The system of coupled nonlinear equations for slow and fast planar compressional modes propagating in the material has been solved approximately by method of slow varying amplitudes. As a result of calculations the dependence of surface impedance on the amplitude of sound wave has been obtained for either fixed or moving surfaces. For all of the parameter values considered so far, it is predicted that the amplitude of the reflection coefficient increases with the incident sound intensity. This approach has been extended to allow for waves reflected from rigid backing ...