Infinite Rigid Plane Research Articles

The imaginary part of the diffuse field forced normalized radiation impedance of a rectangular panel

This paper modifies previous approximate formulae for calculating the imaginary part of the azimuthally averaged forced normalized radiation impedance experienced on one side of a rectangular panel mounted in an infinite rigid plane baffle by a forced travelling wave on the rectangular panel which is excited by an infinite plane sound wave incident at an angle to the normal to the rectangular panel on one side of the rectangular panel. This modification is made so that the formulae can be analytically integrated over all possible solid angles of incidence on one side to obtain formulae for the imaginary part of the diffuse sound field forced normalized radiation impedance of the rectangular panel. The paper also gives existing formulae for the real part of this diffuse sound field forced normalized radiation impedance. The reason for developing approximate formulae for the imaginary part of this diffuse sound field forced normalized radiation impedance is so that they can be used when approximating the equation for the diffuse field sound transmission coefficient of a limp single leaf wall.

Acoustic time-dependent energy and instantaneous power from planar radiators via a generalized radiation impulse response approach.

The radiation impulse response, which is the temporal Fourier transform of the radiation impedance, provides the basis for a convolution approach to evaluate the time-dependent force, instantaneous power, and energy transfer into the fluid resulting from a separable space-time normal velocity of a fluid loaded surface. After a brief review of the radiation impulse response approach to address such problems for planar radiators, several specific examples for planar radiators are addressed. General results for the temporal evolution of the energy from a baffled planar source of arbitrary shape with a specified space-time separable normal velocity distribution are developed. The case of a circular piston in an infinite rigid plane is then addressed to illustrate the time-dependent force, instantaneous power, and energy transfer into the fluid for pulsed velocity excitations. In particular, the energy exchange between the incompressible near field and the acoustic far field is addressed for the pulsed excitations.

Application of the method of fundamental solutions to predict the acoustic performance of T-shaped thin barriers

A frequency-domain formulation based on Method of Fundamental Solutions (MFS) is used to simulate the sound field generated by a point source in the presence of a T-shaped thin noise barrier. The MFS formulation is here developed by making use of adequate Green's functions, defined by using the image-source technique, that satisfy specific boundary conditions, allowing decreasing the number of discretized surfaces and consequently reducing the computational cost of the numerical model. Both the ground and the building are modeled as infinite rigid plane surfaces, and the barrier is assumed to be absorptive. The surface treatment of the barrier is characterized by a porous material. The Zwikker and Kosten model is here used for predicting the acoustic properties of the porous material. To validate the numerical implementation of the proposed method, the results are compared with solutions of the Dual-BEM formulation. Numerical simulations are carried out in order to demonstrate the efficiency of the proposed method and the performance of the T-shaped thin noise barriers in typical cases of traffic noise.

A Fast Method to Calculate the Spatial Impulse Response for 1-D Linear Ultrasonic Phased Array Transducers.

A method is developed to accurately determine the spatial impulse response at the specifically discretized observation points in the radiated field of 1-D linear ultrasonic phased array transducers with great efficiency. In contrast, the previously adopted solutions only optimize the calculation procedure for a single rectangular transducer and required approximation considerations or nonlinear calculation. In this research, an algorithm that follows an alternative approach to expedite the calculation of the spatial impulse response of a rectangular linear array is presented. The key assumption for this algorithm is that the transducer apertures are identical and linearly distributed on an infinite rigid plane baffled with the same pitch. Two points in the observation field, which have the same position relative to two transducer apertures, share the same spatial impulse response that contributed from corresponding transducer, respectively. The observation field is discretized specifically to meet the relationship of equality. The analytical expressions of the proposed algorithm, based on the specific selection of the observation points, are derived to remove redundant calculations. In order to measure the proposed methodology, the simulation results obtained from the proposed method and the classical summation method are compared. The outcomes demonstrate that the proposed strategy can speed up the calculation procedure since it accelerates the speed-up ratio which relies upon the number of discrete points and the number of the array transducers. This development will be valuable in the development of advanced and faster linear ultrasonic phased array systems.

Acoustic radiation from a point excited multi-layered finite plate

The acoustic radiation from a finite rectangular composite plate is evaluated using eigenfunctions obtained through the use of three-dimensional equations of elasticity. The composite plate is made of perfectly bonded finite plates of identical lateral dimensions and of different thicknesses. The plate is free of shear stresses and is pinned on the in-plane displacements on all its boundaries and is baffled by an infinite rigid plane. The multi-layered plate is in contact with a different fluid medium on each of its two surfaces. The solution for the vibration response due to normal and shear surface forces is found in terms of the composite plate eigenfunctions that include heavy acoustic loading. The displacement vector field throughout the thickness of the plate is computed as well as the resultant near- and far-field radiated acoustic pressures for various ratios of thickness to plate dimensions over a broad frequency range. Initial results focus on a bilaminar plate. [Work supported by the ASEE Summer Faculty Research Program.]

Acoustic radiation from finite bilaminar submerged plates: Three-dimensional elasticity solution

The vibration and radiation of a submerged baffled finite rectangular bilaminar plate is obtained analytically using the three-dimensional equations of elasticity. The plate is composed of two perfectly bonded finite layers of identical size. The boundary conditions on the perimeter of the plate are free of shear stresses and pinned on the in-plane displacements. The plate is coupled to acoustic media on both sides and is baffled by an infinite rigid plane. The solution for the vibration response due to normal surface forces is found in terms of the bilaminar plate eigenmodes. The vibratory response and the associated near- and far-field radiated acoustic pressures are computed for various ratios of thickness to plate dimensions over a broad frequency range. [Work supported by the ASEE Summer Faculty Research Program.]

Self- and mutual-radiation impedances for flexible sound sources in an infinite rigid plane baffle

Self- and mutual-radiation impedances for flexible sound sources in an infinite rigid plane baffle

Vortex sound under the influence of a piecewise porous material on an infinite rigid plane

The vortex dynamics and the sound generation by an inviscid vortex in the presence of a finite length porous material on an otherwise rigid plane are studied numerically in the present study in an attempt to understand the sound generation near the surface of a wall lining in a lined duct. The combined effects of the effective fluid density and flow resistance inside the porous material, and the length and thickness of the porous material on the sound generation process are examined in detail. Results obtained demonstrate the sound pressure is longitudinal dipole and show how seriously the above-mentioned parameters are affecting the vortex sound pressure under the influence of the porous material.

A TECHNIQUE FOR PLANE-SYMMETRIC SOUND FIELD ANALYSIS IN THE FAST MULTIPOLE BOUNDARY ELEMENT METHOD

The fast multipole boundary element method (FMBEM) is an advanced BEM, with which both the operation count and the memory requirements are O(Na log b N) for large-scale problems, where N is the degree of freedom (DOF), a ≥ 1 and b ≥ 0. In this paper, an efficient technique for analyses of plane-symmetric sound fields in the acoustic FMBEM is proposed. Half-space sound fields where an infinite rigid plane exists are typical cases of these fields. When one plane of symmetry is assumed, the number of elements and cells required for the FMBEM with this technique are half of those for the FMBEM used in a naive manner. In consequence, this technique reduces both the computational complexity and the memory requirements for the FMBEM almost by half. The technique is validated with respect to accuracy and efficiency through numerical study.

Sound propagation around rigid barriers laterally confined by tall buildings

This paper focuses on the propagation of sound waves in the presence of acoustic barriers placed close to very tall buildings. The boundary element method (BEM) is used to model the acoustic barrier, while the presence of the tall buildings is taken into account by using the image source method. Different geometries are analyzed, representing the cases of a single building, two buildings forming a corner and three buildings defining a laterally confined space. The acoustic barrier is assumed to be non-absorbing, and all the buildings and the ground are modeled as infinite rigid plane surfaces. Calculations are performed in the frequency domain and time signals are then obtained by means of Inverse Fourier Transforms. The sound pressure loss provided by the acoustic barrier is computed, illustrating the importance of the lateral confinements.

Effect of Radiation Impedance of Arrayed Transducers in Water on Radiated Sound Field

The effect of the radiation impedance of arrayed transducers in water on radiation sound power is discussed. The mutual radiation impedance is calculated for two identical square piston transducers vibrating in an infinite rigid plane. Using the numerical values of the radiation impedance, radiated power response curves are given for arrays with 12 transducers operating in various modes. In low frequency regions below coincidence frequency, sound absorption caused by acoustic interaction effects between transducers is confirmed both theoretically and experimentally.

Relation between Active Sound Absorption and Mutual Radiation Resistance of an Array of Piston Transducers in Water

Sound absorption due to acoustic interaction between transducers arranged in water, that is, an active sound absorption is described. The mutual radiation resistance is calculated for two identical square piston transducers vibrating in an infinite rigid plane, and its effect on sound absorption is made clear. The calculated reduction in radiation power is about -16 dB in a three-transducer system with relative velocities 1, -1.7, and 1. Acoustic intensity field maps are drawn to visualize the behavior of active sound absorption. The negative intensity vector was observed experimentally.

Acoustic interaction effects in unbaffled transducer arrays

To calculate the transmitting characteristics of a transducer array, it is often necessary to take into account the acoustic interaction effects. For an array of pistonlike transducers set on planar surfaces, the model most commonly used is to assume the pistons set in an infinite rigid plane. This is not adequate when the array is not baffled, and when its dimensions are comparable to the wavelength. A theoretical model, using the combined Helmoltz integral equation method, is developed to calculate the mutual impedance matrix, the transmitting characteristics, and farfield directivities for arbitrary antenna geometries. Some results are compared to analytical models and to experiments. It is shown that the unbaffled condition produces important effects on the directivity functions and that the acoustic interactions modify the pressure distribution on the surface of the array.

Design of an experiment to measure the acoustic mutual impedances of a resonant, close-packed sonar array

Knowledge of the acoustic mutual impedance coefficients for a sonar array is necessary to achieve an accurate analytical description of the performance of the array. In the early stages of a design, analytical approximations, e.g., of an array in an infinite rigid plane baffle, provide adequate estimates. When prototype hardware is available, it may be appropriate to derive refined estimates of the impedance coefficients. This allows more accurate prediction of the effects of design changes on performance, and also provides an analytical baseline for a design that is entering production. The measurement of the mutual impedance coefficients in a resonant, close-packed array is difficult. The only previously reported attempt [Stephen C. Thompson, J. Acoust. Soc. Am. Suppl. 1 68, S34 (1980] achieved inconclusive results, due to inaccurate estimates of the element electromechanical transfer matrices and strong element interactions that occur in the vicinity of the element resonance frequency. These measurements are being repeated, with greater care given to the previously noted deficiencies. The experiment will be described, concluding with the requirements placed on the special transducer elements that were necessary for the measurement. The design of these transducer elements will be described in a companion paper in this session [M. P. Johnson, J. Acoust. Soc. Am. Suppl. 1 82, S2 (1987)].

On two-dimensional laminar flows of a particulate suspension in the presence of gravity field

Three simple two-dimensional streaming motions of a mixture of solid particles with a continuous carrier fluid, or gas, in the presence of the gravity field are considered. These include flow of a mixture over an infinite stationary rigid plane perpendicular to the direction of the gravity field, flow near an oscillating rigid plane and flow in a mixture induced by a suddenly accelerated plane. The nature of the boundary conditions at the interface between a layer of sediment settling on the rigid boundary and the mixture above it suggests an introduction of the independent variables that enable simple analytical expressions for the solutions of the first two flows and a numerical solution by means of a Laplace transform in the last case.

The acoustics of turbulence near sound-absorbent liners

Acoustic liners are often perforated screens backed by sound-absorbent material. Turbulence can interact with these screens to generate additional sound. The dynamics of the generation process is examined in this paper, where the liner is modelled as an infinite rigid plane boundary with a homogeneous array of circular orifices or rigid pistons. The acoustic properties of these boundaries are derived in the long wavelength limit. Small-scale turbulence is scattered by individual apertures into sound. Acoustically transparent surfaces support dipole scattering centres while more ‘opaque’ surfaces have monopoles at the apertures which convert turbulence into sound more effectively. It is shown that the process can be described once the response of an individual aperture in an infinite baffle is known. At low Mach numbers the screen can increase the sound radiated by adjacent turbulence by a factor equal to the inverse fourth power of the Mach number. Mean-flow effects are ignored but they are thought to increase the effects deduced in this preliminary study.

Retarded Potential Approach to the Scattering of Elastic Pulses by Rigid Obstacles of Arbitrary Shape

The scattering of elastic pulses by rigid obstacles of arbitrary shape is discussed in terms of an integrodifferential equation similar to Kirchhoff's equation. This approach has proved valuable in the treatment of acoustic scattering problems and the extension proposed is relatively straightforward. The advantage of this approach is that the problem can be formulated completely in terms of values of stress and strain on the scattering surface only thereby reducing the order of the problem by one spatial dimension. Field values can be obtained from the surface values by a direct quadrature if required. The simple problem of a P-step wave reflecting from an infinite rigid plane is discussed as an example of the procedure.

Mutual Acoustic Impedance between Flexible Disks of Different Sizes in an Infinite Rigid Plane

A direct method of analysis based on the “classical” Rayleigh formula is presented for calculating the mutual acoustic impedance between circular radiators of different sizes in an infinite rigid plane. The effects of the interactions between two radiators are considered in detail. The acoustic pressure on the plane baffle is described by a distribution of surface “sources” of known strength at the plane-fluid boundary. As the sound-pressure field produced by one radiator exerts a force on another radiator on the plane, the mutual radiation impedance can be defined by the force exerted by one radiator integrated over the surface of the other. This impedance is expressed by a series solution of products of Bessel functions. The results can be reduced to those found by Pritchard and Porter, who based their solutions of the problem as formulated by Bouwkamp. Numerical calculations for the series solutions of the pressure field and of the mutual impedance terms are not given. Attention is paid only to mathematical formulisms.

The effects of a single bubble on the sound field of a piston

The effect of a single bubble on the acoustic pressure radiated by a circular piston in an infinite rigid plane baffle is examined. Numerical calculations of the radiation impedance and the far field radiation pattern are presented for a resonant bubble on the axis of the piston. The calculations show that a bubble within a half-wavelength distance from the piston has a large effect on the sound field radiated by the piston. The resonant frequency and the damping constant of a bubble are changed by the presence of the rigid baffle.

Acoustic Radiation from a Wobbling Piston

The sound field of a circular piston in an infinite rigid plane baffle is calculated when the motion of the piston consists of the conventional uniform velocity normal to the plane of the piston plus a wobbling motion about a diameter of the circle: as an axis. There is a net resultant moment owing to the wobble; this moment is proportional to an integral of the square of the farfield pattern function over real and imaginary angles. A wobble impedance is defined as the moment divided by the angular velocity of the wobble. The real part of the wobble impedance is obtained from the integral of the square of the farfield pressure over real angles, and the imaginary part is obtained from the real part by the use of the Kramers-Kronig, or dispersion relations. Numerical results for the wobble impedance are presented. It is shown that for small pistons a merely wobbling piston is less efficient as a generator of sound than the customary uniform-velocity piston.