Infinite Rigid Baffle Research Articles

Use of a nearfield array for acoustic backscattering cross‐section measurements

It is theoretically demonstrated that a large circular piston in an infinite rigid baffle operating at high frequency can be used as a nearfield array (NFA) to measure farfield backscattering (sonar) cross sections. Pulsed experiments are described which use the same piston both to insonify the object and receive the scattered wave. In transmitting, the piston produces a collimated plane wave within its Rayleigh zone. When the scatterer is placed within this zone, the scattered wave is received by the piston and integrated to reproduce a voltage response proportional to the scatterer's farfield amplitude function (NFA reciprocity principle). Measurements have been made on spheres and cylinders as well as model ships, insonified by a 4.75‐in. circular beam at a frequency of 15 MHz. The sonar cross sections (target strengths) obtained are in good agreement with those theoretically predicted by finite beam insonification scattering theory. Comparison of scaled model ship measurements with full‐scale target strength values shows reasonable agreement as well. [Work supported by NAVSEA‐034.]

Optical holography for the study of sound radiation from vibrating surfaces

Time-averaged holography has been used to quantitatively investigate sound radiation from an edge-clamped circular flat plate mounted in an infinite rigid baffle. For a particular mode of vibration, the plate response is measured using holography and the sound power radiated is measured in a reverberant room with the plate mounted in one of the room walls. From these measurements a radiation efficiency is determined. The theoretical plate responce is calculated using both classical and Mindlin–Timoshneko plate theory and is shown to agree well with experimental measurements. Radiated sound power is calculated for each mode of interest by solving the wave equation in oblate spheroidal coordinates at the plate surface. These calculations are verified by direct evaluation of the Rayleigh integral in the farfield. Good agreement is obtained between experimentally measured radiation efficiencies and theoretical predictions. Small discrepancies between theory and experiment are discussed. Subject Classification: [43]20.55, [43]40.24, [43]35.65.

Data requirements for the mapping of ultrasonic fields with conventional light diffraction

A procedure has been proposed by Cook [J. Acoust. Soc. Am. 53, 330(A) (1972)] through which a cross-sectional mapping of a progressive sound beam could be obtained by conventional light diffraction. This technique requires that a series of optical diffraction measurements be taken laterally across the field, for a large number of rotations about the sound field’s major axis. Since the number of measurements could become excessive, and investigation of the data requirements of this technique has been performed. Computer-generated data were calculated of the integrated optical effect (both magnitude and phase) produced by the pressure field of a circular plane piston in an infinite rigid baffle. From these data a cross-sectional map was obtained using an effective two-dimensional Fourier transform, as well as the two-dimensional fast Fourier transform algorithm. The cross-sectional mapping was evaluated at different axial positions, using one set of data obtained by varying the data set and comparing the results to those obtained from the diffraction integral. The data requirements were found not to be excessive. Subject Classification: 35.65.

Vibroacoustic response of turbulence excited thin rectangular finite plates in heavy and light fluid media

A comparative study is made of various methods for computing the vibroacoustic response of a turbulence excited finite rectangular plate in an infinite rigid baffle. The plate is thin, flat, flexible and isotropic, simply supported or clamped, and is immersed in either heavy or light fluid media. One of the methods—that of Maestrello—applicable to an air loaded plate is modified to introduce (a) a correction for obtaining the true pressure statistics, (b) a simple procedure for including clamped supports, (c) fluid loading, i.e., added mass, and (d) radiation damping. Numerical computations are made for the vibratory response and the radiated power of a water-loaded plate subject to turbulence excitation. The computations are shown to be valid over the low wavenumber-broad frequency range of interest. Basic tubulence-vibroacoustic relationships, useful in numerical computation are given for infinite and finite plates in light and heavy fluid media.

Data requirements for the mapping of ultrasonic fields with conventional light diffraction

A procedure has been proposed by Cook [J. Acoust. Soc. Am. 53, 330(A)(1972)] through which a cross-sectional mapping of a progressive sound beam could be obtained by conventional light diffraction. This technique requires that a series of optical diffraction measurements be taken using a parallel beam of light passing through and perpendicular to the sound beam. These measurements are taken laterally across the field, for a large number of rotations about the sound field's major axis. Since the number of measurements could become excessive, an investigation of the data requirements of this technique has been performed. Computer-generated data were calculated of the integrated optical effect (both magnitude and phase) produced by the pressure field of a circular plane piston in an infinite rigid baffle. From these data a cross-sectional map was obtained using an effective two-dimensional Fourier transform, as well as the two-dimensional fast-Fourier-transform algorithm. The cross-sectional mapping was evaluated at different axial positions, using one set of data generated at a single axial distance. Data requirements were obtained by varying the data set and comparing the results to those obtained from the diffraction integral. The data requirements were found to be not excessive.

Intermodal coupling coefficients for a fluid-loaded rectangular plate

The intermodal coupling coefficients are calculated for a thin, simply supported rectangular plate in an infinite rigid baffle. The coefficients describe the modal auto- and cross-resistive and reactive coupling induced by a dense fluid-filled half-space above the plate.

Impulse response and radiation impedance of an annular piston

An approach is presented to evaluate the impulse response of an annular piston, which is mounted in an infinite planar rigid baffle. Since the impulse response is defined to be the time-dependent force on the ring, which results from an impulsive velocity of the ring, the impulse response and radiation impedance of the ring are a Fourier transform pair. A closed-form expression for the impulse response of a ring of any size is developed from the well-known double surface integral representation of the radiation impedance. Various integral and asymptotic expressions for the radiation impedance of the ring are derived from the impulse response, and the results are shown to be in agreement with those of earlier investigators. Several numerical results are also presented to show the effect of changing the ring size on the impulse response, and on the radiation resistance and reactance of the ring.

Radiation from arbitrarily positioned circular pistons in an infinite baffle

An arbitrarily positioned array of circular pistons in an infinite rigid baffle having an acoustic fluid on one side is analyzed to determine the velocity of each piston and the total radiated pressure, both near- and farfield, when the acoustic-pressure interaction between all the pistons taken into account. The diameter of the pistons and the phase relations between each of the harmonically varying driving forces on the pistons are arbitrary as are the masses of the pistons and the mechanical parameters characterizing the piston assembly. The solution is obtained using oblate spheroidal coordinates and the principle of superposition to reduce the array problem to a collection of simpler problems. The expressions derived appear to have a computational advantage for computing both the velocity of the pistons and the nearfield and farfield pressures. The method can also be extended to two arbitrarily positioned circular elastic plates in an infinite baffle. Numerical results for the series solutions describing the pressure field and the mutual impedances are not given.

The Stability of Simply Supported Rectangular Surfaces in Uniform Subsonic Flow

A study is made of the stability of a simply supported flat plate set in an infinite rigid baffle when an inviscid fluid flows uniformly at subsonic speed past one side of the surface. The generalized pressures are derived for low frequencies with two and three-dimensional flows. The three-dimensional generalized pressures are expanded asymptotically for high and low aspect ratios, and analytic forms derived for the critical flow velocity at instability. The asymptotic expansions enable the effect of aspect ratio on stability to be determined. It is shown that the incompressible limit, for two-dimensional flows, is singular but the stability criterion is associated with first-mode divergence and is identical with the three-dimensional high aspect ratio stability result, although there are certain detailed differences in the nature of the instability.

Acoustic radiation from a long solid rod into a semiinfinite liquid medium

An approximate numerical technique is presented whereby the pressure-radiation patterns in a liquid half-space produced by radiation from the end face of a circular cylindrical, semiinfinite, solid rod set flush in an infinite rigid baffle at the boundary of the half-space can be calculated as a function of the elastic properties of the solid rod. The method is restricted to the low-frequency range such that the lowest numbered mode in the solid rod is the only propagating mode. Axisymmetric longitudinal modes are the only ones assumed to exist in the rod. The velocity distribution of the rod end face does not have to be known or assumed. The radiation impedance of the rod end is calculated and compared with that of the rigid piston, as are the pressure radiation fields. The work here presents farfield radiation only, though the method can easily be extended to study the nearfield radiation patterns in the liquid half-space.

Sound Field of a Pulsed, Planar, Straight-Edged Radiator

Assuming pulsed or CW conditions, theoretical expressions are derived for the farfield of an arbitrary plane straight-edged radiator, vibrating with spatially uniform velocity within an infinite plane rigid baffle. The results are then specialized to radiators whose shapes are regular polygons. The farfield is made up of components, termed “transmission replica pulses,” which are shown to act, in general, as if they originated at the corners of the radiators. Examples of pulsed field structure and of CW directivity curves of polygonal radiators are presented.

Tables of Rectangular Piston Radiation Impedance Functions, with Application to Sound Transmission Loss through Deep Apertures

Extensive and highly accurate tables have been calculated for the radiation impedance functions of a rigid rectangular piston mounted in a rigid infinite baffle radiating into a half-space. This was accomplished by developing a numerical technique of general applicability which yields a highly efficient computer algorithm. The latter computed 3792 highly oscillatory integrals containing branch point singularities, each to 7D accuracy, in a total of 74 sec on a CDC 6400 computer.

Numerical computation of the radiation impedance of a rigid annular ring vibrating in an infinite plane rigid baffle

An expression for the radiation impedance of a rigid annular ring vibrating with uniform amplitude in a close-fitting infinite plane rigid baffle is presented. An algorithm for the numerical evaluation of this expression by electronic computer is included in the form of an Algol 60 procedure. A selection of numerical results obtained is included.

Transient Radiation from Pistons in an Infinite Planar Baffle

An approach is presented to compute the near- and farfield transient radiation resulting from a specified velocity motion of a piston or array of pistons in a rigid infinite baffle. The approach, which is based on a Green's function development, utilizes a transformation of coordinates to simplify the evaluation of the resultant surface integrals. A simple expression is developed for an impulse response function, which is the time-dependent velocity potential at a spatial point resulting from an impulse velocity of a piston of any shape. The time-dependent velocity potential and pressure for any piston velocity motion may then be computed by a convolution of the piston velocity with the appropriate impulse response. The response of an array may be computed using superposition. Several examples illustrating the usefulness of the approach are presented. The farfield time-dependent radiation from a rectangular piston is discussed for both continuous and pulsed velocity conditions. For a pulsed velocity of time duration T it is shown that the pressure at several of the field points can consist of two separate pulses of the same duration, when T is less than the travel time across the piston.

Radiation from the Forced Harmonic Vibrations of a Clamped Circular Plate in an Acoustic Fluid

The forced harmonic vibrations of a solid circular plate clamped to a rigid infinite baffle and bounded on one side of an inviscid fluid of infinite extent is considered. The motion in the plate is described by the Mindlin-Timoshenko theory, which includes the effects of transverse shear and rotatory inertia. The external force, which is applied from the in vacuo side of the plate, can have any spatial distribution. The solution is obtained with the use of orthogonal functions which result from transforming the polar cylindrical coordinates describing the fluid motion into oblate spheroidal coordinates and the solution to the in vacuo vibrations of the clamped plate. This method of solution removes all previous restrictions regarding the solution of this problem, namely, boundary conditions of the plate, symmetry of loading, applicable frequency range, and extensive numerical calculations for the determination of the complete nearfield pressure. Expressions are obtained for the near- and farfield pressure in the fluid and the radiated power from the plate-fluid surface. A numerical case for a concentrated load at the center of the plate is presented.

Variational Finite-Element Calculation of the Acoustic Response of a Rectangular Panel

The problem of the acoustic response of a structure falls into three parts. (1) The response of the structure to given acoustic excitation, when the effect on the vibration of the resultant acoustic radiation is ignored. This part of the problem is usually solved by using a normal-mode approach, and has usually therefore been carried out only for simply supported plates, for which the normal modes are simple functions. (2) The determination of the acoustic radiation from a given structural vibration. Numerous workers have calculated the total radiated energy and/or the radiation-intensity-distribution pattern for different vibrating surfaces. (3) The effect of the radiation on the response of the plate. This aspect is usually ignored, and when the acoustic medium is air, it is in any case, an effect that is usually negligible. When it is included, the problem is closed (in the sense that it has a feedback loop) and its theoretical analysis involves the use of integral equations. Morse has recently solved the complete problem for the case of a circular membrane set in an infinite plane rigid baffle. In this paper, a variational principle derived in an earlier paper [J. Sound Vibration 4, 233 (1966)] is used in conjunction with a finite element method to calculate the response of a rectangular panel set in an infinite plane rigid baffle. The method can be applied with equal ease to plates with different boundary conditions, and the effect of the acoustic radiation on the plate vibration is considered in full.

Transient Radiation from Pistons in an Infinite Planar Baffle

An approach is presented to compute the near- and farfield transient radiation resulting from a specified velocity motion of a piston in a rigid infinite baffle. The approach, which is based on a Green's function development, utilizes a transformation of coordinates to simplify the evaluation of the resultant surface integral. A simple expression is developed for an impulse response function, which is the time-dependent velocity potential at a spatial point resulting from an impulsive velocity of a piston of any shape. The time-dependent velocity potential and pressure for any piston velocity motion may then be computed by a convolution of the piston velocity with the impulse response. Several examples illustrating the usefulness of the approach are then presented. The familiar steady-state nearfield on-axis pressure fluctuations resulting from the sinusoidal velocity of a circular piston is derived from the impulse-response data. The farfield time-dependent radiation from a rectangular piston is also discussed for both continuous- and pulsed-velocity conditions. For a pulsed velocity of time duration T, it is shown that the pressure at several of the field points can consist of two separate pulses of the same time duration.

Transmission of reverberant sound through a single-leaf partition surrounded by an infinite rigid baffle

A solution is found by classical methods. For resonance transmission, the results agree with those found by statistical energy methods. For forced vibration transmission, a formula is found which does not require the arbitrary assumption usually made in estimating this type of transmission from the solution for an infinite partition, but is in at least as good agreement with experiment. Differences from the solution for a partition in a waveguide are noted.

Two-dimensional solution for transmission of reverberant sound through a double partition

The problem is solved for a partition consisting of similar simply-supported leaves each mounted in an infinite rigid baffle. It is assumed that sound passing through the open reveals into the region between the baffles is never returned. The solution is applied to real three-dimensional partitions by using rules derived from the solutions for single partitions, and numerical examples are given.

Acoustic radiation impedance of a rigid annular ring vibrating in an infinite rigid baffle

A theoretical investigation of the acoustic radiation impedance of a rigid annular ring vibrating with uniform amplitude in a close-fitting infinite rigid baffle is presented. The analysis involves the use of Besse], Struve and hypergeometric functions and formulae are derived by means of which the real and imaginary components of the radiation impedance can be computed.