Volume 57, Issue 3, March 1975
Index of content:
57(1975); http://dx.doi.org/10.1121/1.380481View Description Hide Description
The exact theory for the radiation of a small loudspeaker in the surface of a rigid circular disk of elliptic profile is presented. Numerical results are included for a monopole at the center of the disk and on its surface. The solution for the loudspeaker in the center of a free circular baffle is then formulated by superimposing the solution of a positive source on one side of the baffle with that for a negative source on the other side. For wavelengths greater than the circumference of the baffle, the resulting field turns out to be very similar to that of a dipole of finite dipole axis. However, for wavelengths smaller than the diameter of the baffle, the diffraction field is shown to be dominated by edge effects. In particular, the total field may also be represented by a simple ring−point source combination, i.e., the edge of the baffle is essentially replaced by a ring source. It is shown that in the vicinity of the axis of the baffle, the shape of the frequency response curve depends little on how much volume flow is generated on the opposite side of the baffle. In other words, it makes little difference (except in absolute level) whether a loudspeaker is enclosed in a box or is permitted to radiate from the rear.
Subject Classification: 20.15, 20.30, 20.55.
57(1975); http://dx.doi.org/10.1121/1.380482View Description Hide Description
The paper deals with the diffraction of time−harmonic axisymmetric low−frequency acoustic waves by two concentric coaxial rigid spherical caps. An integral equation technique is used to solve this boundary value problem. Formulas are derived for the farfield amplitude as well as the scattering cross section when the incident wave is a low−frequency plane wave traveling along the common axis of the two caps. By taking an appropriate limit, the solution for the corresponding problem for a rigid spherical cap is also presented.
Subject Classification: 20.30.
57(1975); http://dx.doi.org/10.1121/1.380483View Description Hide Description
The monostatic reflection from a lucite sphere in water is measured and compared with the exact classical scattering theory. Experimental results do not agree with theory which neglects absorption, in direct contrast to the excellent agreement found when metal spheres are used as targets. The theory is modified to include the effects of absorption of shear and compressional waves in lucite, and agreement between experiment and the modified theory is demonstrated.
Subject Classification: 20.30, 20.15.
57(1975); http://dx.doi.org/10.1121/1.380484View Description Hide Description
An experimental investigation of the parametric array in air was conducted using a circular piston transducer which produced spherically spreading, collinear, primary beams at frequencies of 18.6 and 23.6 kHz. Since source levels were not strong (about 110 dB r e 0.0002 μbar at 1 ft), the 5−kHz difference frequency signal generated by the parametric array was relatively weak. Because of space limitations, all measurements were made in the nearfield of the array. Spurious difference frequency signals resulting from intermodulation distortion in the receiving system were suppressed by judicious choice of electronic components and by the addition of an acoustical filter in front of the microphone. The classic properties of the parametric array were observed. The 5−kHz beam was narrow, and no minor lobes were evident. The propagation curve first increased with increasing range, reached a broad maximum, and then gradually decreased. Theoretical predictions were based on a perturbationsolution of Burgers’ equation and on the integral solution of the inhomogeneous wave equation. Comparison of measured results with these predictions conclusively demonstrated the existence of the parametric array in air. Beam patterns and propagation data obtained for the second−harmonic and sum−frequency signals also confirmed theoretical predictions.
Subject Classification: 25.35.
57(1975); http://dx.doi.org/10.1121/1.380485View Description Hide Description
SOFAR ray geometry, travel time, and spreading loss are considered for a still−ocean region in which the sound speed is a bilinear function of depth. A sound source is placed above and a receiver below the SOFAR axis at depths corresponding to the same sound speed. Next, an assumed Rossby wave is introduced, and its effect on the phase of the total acoustic field is determined. It is found that the amplitude of phase variation can vary by a factor of three as the source and receiver depths are altered. Our theory is applied to sound transmission in the Sargasso Sea area, and phase variation values are determined which are in general agreement with experimental results.
Subject Classification: 30.20.
57(1975); http://dx.doi.org/10.1121/1.380486View Description Hide Description
A method for determining the acoustic properties of thin plates is described. Existing theoretical expressions are used to calculate transmission and reflection coefficients for sound waves striking the plates at arbitrary angles of incidence. Theory is substantiated by experimental data, and refined values for absorption coefficient and shear velocity are obtained by combining theory and experiment. Materials tested were Absonic−A, plexiglass, and polyethylene.
Subject Classification: 30.30, 30.50, 20.30.
57(1975); http://dx.doi.org/10.1121/1.380487View Description Hide Description
In many applications of underwater acoustics, the ocean bottom is adequately characterized by a critical angle and a density. An estimate of the sound speed in the bottom is obtained by seismic refraction measurements (i.e., measurements of arrival time) or bottom−reflection measurements. In this paper, the theoretical basis is presented for an alternate technique that, it is hoped, will simplify the determination of the critical angle(s) associated with high−speed bottom layers. The technique requires the measurement of the normal component of the specific acoustic impedance at the ocean−bottom interface. As a function of incidence angle, this impedance function displays a strong peak near the critical angle. The precise location depends in a predictable manner on the location of the source, the source frequency, and the sound speed in the bottom. This technique exploits this dependence to obtain an estimate of the sound speed in the bottom.
Subject Classification: 30.25, 30.20.
57(1975); http://dx.doi.org/10.1121/1.380474View Description Hide Description
A series of simulated acoustic emission experiments in thin plates and bars conducted to assess the effects of structural geometry on the detection of emission is described. It is shown that the structure introduces peaks in the received signal spectra corresponding to thickness resonances that may be estimated from Lamb wave theory. Spectra of acoustic emission signals from a thin−walled pressure vessel show a peak at the frequency corresponding to the lowest symmetric plate mode. It is concluded that a significant portion of the energy detected by a surface contact transducer on a thin−walled structure is concentrated at these resonances and should be accounted for in choosing a detection system.
Subject Classification: 35.10, 35.80.
57(1975); http://dx.doi.org/10.1121/1.380475View Description Hide Description
In this paper a theoretical model is presented that can be used to evaluate analytically ultrasonic transducer longitudinal wave−generation characteristics in homogeneous isotropic solids. Comparisons with fluid−type solutions are also outlined. A continuous wave solution is determined first, from which particle displacement, particle velocity, and stress solutions for arbitrary pulse shapes are obtained. The ultrasonic field distributions resulting from several basic pulse shapes are presented along with the results of an experimentally obtained distribution. Nearfield and beam angle of divergence for pulse output transducers are also discussed. In addition to developing data for ultrasonic field analysis in solids, the equations developed can be used for obtaining solutions to many other ultrasonics problems. For example, it now becomes possible to develop equations that can analyze the resulting stress and particle velocity distribution in a multilayer structure for materials subjected to either normal beam incidence or angle beam incidence. The work may also be extended to include many aspects of ultrasonic field measurement analysis for flaw characterization work.
Subject Classification: 35.65; 20.50.
57(1975); http://dx.doi.org/10.1121/1.380476View Description Hide Description
57(1975); http://dx.doi.org/10.1121/1.380477View Description Hide Description
The general problem of the response of a cantilever beam to flow over its surface is considered experimentally and theoretically. The model response of a beam in flowing water is shown normalized on the dynamic head of the inflow, the total mass of the beam, and the modal loss factors. Results are presented for a series of beams of varying length and chord. The magnitude of hydrodynamically induced damping is also characterized experimentally. It is shown that results agree favorably with an approximate expression based on finite aspect−ratio, unsteady airfoil theory. Loss factors, based on entrained mass, are found to be inversely proportional to a reduced frequency based on the width of the strut and inflow speed.
Subject Classification: 40.35, 40.22; 30.50.
57(1975); http://dx.doi.org/10.1121/1.380478View Description Hide Description
A method for obtaining the signatures (waveforms) of certain acoustic emission events has been developed. The waveform is that at the source, free of contamination by ringing of the specimen, apparatus, and transducer. The technique is based on the comparison of two signals at the transducer, one from the event in question and one from an artificial event of known waveform. The apparatus is also adapted to the calibration of transducers in a certain sense. The configurations of source (real or simulated acoustic−emission event) and receiving transducer correspond to those of some special cases of Lamb’s problem. As a byproduct, the results may be of some interest to seismologists.
Subject Classification: 40.42; 35.54, 35.80, 35.68; 40.50; 85.44.
57(1975); http://dx.doi.org/10.1121/1.380479View Description Hide Description
Wave propagation and thickness vibrations in two−layered piezoelectric plates are investigated by the three−dimensional theory of piezoelectricity and approximate theories. Piezoelectric materials of hexagonal symmetry are considered. The sixfold axes of the materials are assumed to be parallel or perpendicular to the plate. Dispersion curves and frequencies for thickness vibrations are presented. The electromechanical coupling effect is examined and
57(1975); http://dx.doi.org/10.1121/1.380480View Description Hide Description
A method for the quantitative measurements of the acoustic emission is worked out. Its performance is analyzed with regard to the transducer loss and the ultrasonic attenuation in the specimen. This method is actually applied to the tension tests of pure aluminium specimens. The power spectrum of the acoustic emission is obtained over a wide range of 100 kHz to 4 MHz. The total power attains a peak of 5 pW at the beginning of the plastic deformation and decreases to 0.3 pW with the increase of the deformation. The autocorrelation function for the acoustic emission is given as a monotonically decreasing function. This result reveals that the elastic energy of the acoustic emission is radiated not oscillatorily but in the form of random pulses. Mean value of the pulse widths is estimated to change from 0.6 to 0.2 μsec in the early stages of the deformation. This change is shown to be attributable to the increase of the density of dislocations in the material.
Subject Classification: 35.10.
Vibration of simply supported rectangular and square plates to which lumped masses and dynamic vibration absorbers are attached57(1975); http://dx.doi.org/10.1121/1.380488View Description Hide Description
The forced vibration of internally damped rectangular and square plates with simply supported boundaries is described theoretically. Calculations that illustrate the frequency dependence of the force transmissibility and driving−point impedance of the plates are presented. Both central and noncentral driving forces are considered, and the reduction in plate vibration that results from the attachment of central loading masses and dynamic vibration absorbers is demonstrated. The way in which the natural frequencies of the plates are moved to progressively lower frequencies as the loading mass is increased is explained and illustrated. Conditions of optimum tuning and damping for the dynamic absorbers are described and design data are tabulated. The resilient mounting of massive vibrating items on the plates is also considered. The vibrating items are supported via four damped springs that are symmetrically, but otherwise arbitrarily, located with respect to the plate centers. Advantageous reductions in force transmissibility are shown to result from judicious choice of spring locations that enable the excitation of several modes of plate vibration to be avoided.
Subject Classification: 40.24, 40.70.
57(1975); http://dx.doi.org/10.1121/1.380489View Description Hide Description
The author has previously derived an effective stiffness, velocity−corrected theory of laminated composite plates based upon a microstructure plate theory developed by C. T. Sun. This theory is now used to study the flexural and extensional vibrations of simply supported rectangular plates; comparisons will be made to similar results obtained from a reduced effective modulus or transversely isotropic plate theory. Free vibration frequency equations for simply supported edges are developed by passing solutions harmonic in both length and width through the differential equations while at the same time automatically satisfying the boundary conditions for simple supports. The variation of dimensionless frequency for such dimensionless variables is discussed and comparisons of the effective stiffness and effective modulus frequency results are made.
Subject Classification: 40.24.
57(1975); http://dx.doi.org/10.1121/1.380490View Description Hide Description
The nonlinear differential equations and boundary conditions containing terms up to cubic in the small field variables are obtained from general rotationally invariant nonlinear electroelasticequations derived previously. The electroelasticequations cubic in the small field variables are considerably more tractable than the general electroelasticequations and are applicable in the description of such phenomena as the dependence of wave velocities on wave amplitudes and resonant frequencies on vibration amplitudes in addition to a host of other nonlinear phenomena. The nonlinear constitutive equations for an isotropic purely elastic solid containing terms up to cubic in the small mechanical displacement gradients are presented. The nonlinear equations for the extensional motion of thin isotropic plates containing terms up to cubic in the small mechanical displacement gradients in the plane of the plate are obtained and the influence of the vertical inertia is included, in addition to the extensional stiffness and inertia, when the plating is attached to an electroelastic solid.
Subject Classification: 40.24.
57(1975); http://dx.doi.org/10.1121/1.380491View Description Hide Description
Electroelastic equations containing terms up to cubic in the small mechanical displacement field, but no higher than linear in the electric variables, are applied in the analysis of intermodulation in rotated Y−cut quartz oscillators. Both pure thickness−shear vibrators and essentially thickness−shear trapped energy resonators are treated. In the linear part of the analysis of the trapped energy resonator, a closed−form asymptotic expression for the frequency wavenumber dispersion relation for the fundamental and odd overtone thickness−shear branches near cutoff is obtained from the three−dimensional linear equations. Lumped parameter representations of the solutions, which are valid in the vicinity of a resonance, are presented for the linear and nonlinear portions of both the pure thickness−shear and trapped energy thickness−shear problems. The influence of the driving and detecting circuitry is included and, in particular, in each case the relation between the intermodulation and driving voltage is obtained. Application of this relation to a number of A T−cut quartz fundamental and third overtone trapped energy resonators yields good agreement with experiment and an estimate of the fourth−order elastic constant c E 46666 for the A T−cut.
Subject Classification: 40.24, 40.20, 40.65; 85.32.
57(1975); http://dx.doi.org/10.1121/1.380492View Description Hide Description
If the sound power of a source is obtained by forming the surface integral of the normal component of the sound intensity vector, the shape of the surface of measurement is unimportant and projection error only occurs as a result of nonideal polar response of the composite microphone. Furthermore, the sound power of the source may be determined selectively in the presence of background noise originating outside the closed surface. If a sufficient number of points of measurement are taken, the error depends mainly on the signal−to−noise ratio at each point and on the accuracy of the measuring system.
Subject Classification: 50.25, 50.85.
57(1975); http://dx.doi.org/10.1121/1.380493View Description Hide Description
With the concept of mutual information about a coherent signal in additive noise, where signal and noise are assumed jointly Gaussian, it is shown that information is preserved, in a trivial way, by block diagonal matrix filters of full rank and by weighting and summing matrix filters of rank 1 which are identical, within a multiplicative scalar, with the following matrix estimator filters: (1) maximum signal−to−noise ratio estimator, (2) best linear unbiased estimator, (3) minimum mean−square error estimator, (4) maximum liklihood estimator, and (5) maximum a p o s t e r i o r i estimator.
Subject Classification: 60.XX.