D.A. Bies

In situ determination of loss and coupling loss factors by the power injection method

Abstract Vibrational energy distribution between two coupled plates is considered. Inversion of the linear power balance equations is used to determine the plate loss factors and the coupling loss factors in situ. To accomplish the determinations power was injected and measured sequentially at five points chosen at random on each plate to ensure effective statistical independence of modes. In each case the response of both plates was measured at ten randomly chosen points and mean values of response and injected power were determined. Good agreement is obtained between the predicted and measured coupling loss factors and between the in situ loss factors and loss factors determined for each plate separately also in steady state from power injection measurements. Loss factors determined by transient decay methods are consistently lower than those determined by either steady state method. It is suggested that the latter result may be true because the energy distribution among decaying modes is not the same as in steady state. During reverberant decay the more lightly damped modes predominate giving rise to an apparent loss factor which is significantly less than the steady state loss factor.

Free vibration of circular cylinders of variable thickness

Abstract Flexural vibrations of finite length circular cylinders with shear diaphragm ends and symmetric circumferential wall thickness variations are described by using the Rayleigh-Ritz method. Both symmetric and asymmetric solutions are presented. Only circumferential variations in the wall radial dimension are considered; the method is amenable, however, to consideration of longitudinal variations in wall thickness as well. The cylinder wall thickness variation is described as a Fourier series and the vibration is described as a series of modes of a uniform cylinder with the same mean radius. The theory has been applied to a cylinder whose inner bore is circular but is non-concentric with the circular outer surface. The mode shapes have been investigated experimentally by using time-averaged holograms of the vibrating cylinder and the results compare well with the predictions of the theory. The frequencies of the modes agree with the theoretical predictions to within 2%.

A reactive acoustic attenuator

Abstract A reactive acoustic attenuator that combines high reflection of low frequency sound with low pressure drop coefficient is investigated experimentally and theoretically by using equations for sound propagation in straight and curved ducts. Good agreement is obtained and the theory is used to redesign the device to give a minimum transmission loss of ten decibels over a frequency range of three-quarters of an octave. Small discrepancies between theoretical and experimental results are discussed.

Sound attenuation in rectangular and circular cross-section ducts with flow and bulk-reacting liner

Abstract A generalized theory is presented for sound propagation in lined ducts of arbitrary cross-section where acoustic wave propagation in the lining is also taken into account. The effects of a mean fluid flow in the duct airway, an anisotropic bulk reacting liner and a limp, impervious membrane covering the liner are all taken into account. Simple extension of the formalism to include the effect of a perforated facing is also provided. Bulk reacting and locally reacting liners are treated as limiting cases. The general analysis is pplied to ducts of both rectangular and circular cross-section, taking into account higher order modes as well as plane wave sound propagation. Design charts for duct attenuation in octave frequency band averages and in terms of dimensionless parameters are presented.

The effects of flow on the performance of a reactive acoustic attenuator

Abstract The effects of flow on the performance of a reactive acoustic attenuator discussed in a previous paper are investigated theoretically and experimentally. The attenuator is analyzed by using recently developed curved duct equations with flow. Theoretical predictions are obtained for the pressure reflection coefficient, the power reflection and transmission coefficient and the transmission loss of the attenuator, at varying flow Mach numbers. The two cases of sound propagating with and against the flow are discussed and good agreement is obtained with experimental measurements. Small discrepancies between prediction and measurement are discussed. Convection of the propagating medium is found to significantly alter the operating characteristics of the attenuator.

Time-averaged holography for the study of three-dimensional vibrations

Abstract The general theory of time-averaged holographic interferometry has been analytically extended to take account of possible motion of the surface under investigation in three dimensions but in simple harmonic motion at a single frequency. The argument of the characteristic function is replaced with an expression which includes the effects of motion in orthogonal directions as well as the directions of illumination and observation. The amended characteristic function formula is used to calculate the radial and tangential components of a vibrating cylinder from several time-averaged holograms. The components thus calculated agree well with theoretical predictions for the cylinder Love mode. Thus the problem of the strange shift in amplitude plots previously reported [1] when holograms from different angles were taken of vibrating curved surfaces is resolved.

Circular saw aerodynamic noise

Abstract The aerodynamically induced noise of an idling circular saw turning at high speed is investigated both experimentally and analytically. The origin of the noise is shown to be fluctuating lift forces acting on the teeth. The sources at the teeth radiate incoherently as baffled dipoles and account for the generated noise. The analysis predicts that the generated sound power will scale on tooth area, and this prediction is confirmed for gullet width to tooth thickness ratios greater than about two, thus establishing tooth area as the second most important scaling parameter following that of saw rotational speed. The fluctuating lift force on a tooth is shown experimentally to increase with the square of the saw rotational speed, while the generated sound power is shown to increase with saw rotational speed to a power slightly greater than five. The analysis shows that the source radiation impedance increases with the frequency of the radiated sound, which in turn increases essentially linearly with saw rotational speed. The fifth power dependence of radiated sound power on saw speed in thus explained as being due to the source location on the teeth at the perimeter of the blade. An instrumented tooth on an artificial saw blade was used to measure the aerodynamically induced local pressure fluctuations. These pressure fluctuations were used to estimate the expected sound at 1·0 m from the saw on the axis of rotation by making use of the analysis. In the analysis it is assumed that the sources at the teeth radiate incoherently to contribute to the observed sound. Fairly good agreement is demonstrated between measurement and prediction.

Near field determination of the complex radiation efficiency and acoustic intensity distribution for a resonality vibrating surface

Abstract An experimental procedure is described which allows both the resistive and reactive parts of the acoustic radiation efficiency of a resonantly vibrating surface to be determined from measurements in the acoustic near field. In addition, the procedure allows the precise quantitative location on the vibrating surfaces of acoustic sources which radiate energy to the far field. The method described here allows far greater detailed investigation of an acoustically radiating surface than is possible with alternative experimental procedures described in the literature.

Characteristics of modal wave propagation within longitudinally curved acoustic waveguides

Abstract A computational procedure based upon the Rayleigh-Ritz method is presented for generating numerical approximations to the acoustic modes in a circularly curved waveguide. These approximations are used to calculate matrices characterizing the modal transmission and reflection properties of a section of the curved waveguide, flanked on either side by infinitely long, straight waveguides. The theory is applied to a waveguide of elliptic cross-section, and tables of eigenvalues, mode contours and matrix elements are presented for specific examples.

Matrix analysis of acoustic wave propagation within curved ducting systems

Abstract A method is presented for theoretically determining the acoustic characteristics of rigid walled ducting systems which contain one or more bends. A scattering matrix approach is utilized in the method, and it is particularly useful for analyzing ducting systems which contain bends of variable curvature. The results of numerical calculations relevant to the analysis of a section of spirally curved, rectangular duct are presented. These results exhibit favourable numerical characteristics, and compare well with those produced by an alternative analysis. The method is also used to investigate acoustic wave propagation through parabolically curved, circular duct sections.