J. D. Maynard

Nearfield acoustic holography (NAH) II. Holographic reconstruction algorithms and computer implementation

The basic theory treating steady‐state acoustic radiation problems in the nearfield has been presented in several articles on nearfield acoustic holography. In this article, the approximations and assumptions necessary to reduce the infinite and continuous convolution integrals encountered in these problems to a finite and discrete form, suitable for high‐speed numerical processing, are illuminated theoretically and tested numerically. To evaluate the convolution integrals two assumptions are made: First, the boundary field may be replaced with a patchwise constant field for reasonably small patches; and, second, the field is negligible outside of a finite region. With these two assumptions, the problem reduces to one of representing the Green’s functions. Six methods of sampling or representing the Green’s functions are developed, and these are compared theoretically and numerically.

Resonant Ultrasound Spectroscopy

When a new crystalline material is discovered, one of the first fundamental properties to be determined is the atomic structure, defined by the minimum in the free energy with respect to the positions of the atoms. Another fundamental characteristic of interest is the curvature of the free energy in the vicinity of the minimum, and this would be manifest in the elastic constants for the material. As derivatives of the free energy, elastic constants are closely connected to thermodynamic properties of the material. They can be related to the specific heat, the Debye temperature and the Gruneisen parameter (which relates the thermal expansion coefficient to the specific heat at constant volume), and they can be used to check theoretical models. Extensive quantitative connections among thermodynamic properties can be made if the elastic constants are known as functions of temperature and pressure. The damping of elastic waves provides information on anharmonicity and on coupling with electrons and other rela...

Sound source reconstructions using a microphone array

A square microphone array with 256 elements has been constructed along with interfacing electronics to study low‐frequency (1–5 kHz) sound sources in air using the principles of acoustical holography. The array is used in the nearfield of a radiating object and the sound source structure of that object is reconstructed with an on‐line minicomputer. Reconstruction of the source structure of a point source and an unbaffled, free rectangular plate point excited below its coincidence frequency are presented. The latter shows clear evidence of ’’corner’’ and ’’edge’’ modes in which the respective areas of the plate are the dominant radiating sources. A new imaging process which is not limited in resolution by the wavelength of the radiated sound is introduced.

Digital holographic reconstruction of sources with arbitrarily shaped surfaces

Nearfield acoustic holography has proven to be a useful tool for studying sound radiation. However, the analytic formulation and all current implementations of the technique require that the measurement and reconstruction surfaces be level surfaces of a separable coordinate system. In this article, a holographic process is presented based on numerical methods that work for source surfaces or measurement surfaces that may have an arbitrary shape.

Numerical evaluation of the Rayleigh integral for planar radiators using the FFT

Rayleigh’s integral formula is evaluated numerically for planar radiators of any shape, with any specified velocity in the source plane using the fast Fourier transform algorithm. The major advantage of this technique is its speed of computation—over 400 times faster than a straightforward two‐dimensional numerical integration. The technique is developed for computation of the radiated pressure in the nearfield of the source and can be easily extended to provide, with little computation time, the vector intensity in the nearfield. Computations with the FFT of the nearfield pressure of baffled rectangular plates with clamped and free boundaries are compared with the ‘‘exact’’ solution to illuminate any errors. The bias errors, introduced by the FFT, are investigated and a technique is developed to significantly reduce them.

Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens

The use of mechanical resonances to determine the elastic moduli of materials of interest to condensed-matter physics, engineering, materials science and more is a steadily evolving process. With the advent of massive computing capability in an ordinary personal computer, it is now possible to find all the elastic moduli of low-symmetry solids using sophisticated analysis of a set of the lowest resonances. This process, dubbed “resonant ultrasound spectroscopy” or RUS, provides the highest absolute accuracy of any routine elastic modulus measurement technique, and it does this quickly on small samples. RUS has been reviewed extensively elsewhere, but still lacking is a complete description of how to make such measurements with hardware and software easily available to the general science community. In this article, we describe how to implement realistically a useful RUS system.

The use of piezoelectric film and ultrasound resonance to determine the complete elastic tensor in one measurement.

The ultrasonic and elastic properties of materials are conventionally measured using quartz, lithium niobate, etc., transducers and a pulse‐echo technique with the transducer driven at resonance. Problems with the technique include transducer ringing, transducer‐sample coupling, parallelism of sample faces, beam diffraction, and the necessity of remounting transducers in order to measure all of the elastic constants. Usually, these problems can be minimized, but with samples that are only a fraction of a millimeter in size, conventional ultrasound measurements become difficult if not impossible. However, nearly all of these problems may be avoided if a resonance technique is used, and all of the elastic constants may be determined with a single measurement. For the broadband response and minimum transducer loading required for a resonance measurement in a small sample, polyvinylidene flouride (PVDF) piezoelectric film (as thin as 9 μm) is ideally suitable.

Elastic constants and crystal anisotropy of titanium diboride

In this study, the elastic constants of a titanium diboride (TiB2) single crystal were measured using resonant ultrasound spectroscopy. In contrast to previous work, the current results are consistent with the measured elastic constants of TiB2 polycrystals. In addition, the crystal anisotropy of TiB2 was examined. The current data show that the elastic properties of TiB2 are much more isotropic than previously considered.

Reconciliation of ab initio theory and experimental elastic properties of Al2O3

Ab initio calculations of the basic properties of solids have advanced significantly, and it is now possible to simply access a crystal structure database, and from the given constituent atoms and their positions, calculate reasonably accurate values for elastic constants and thermomechanical properties that may be derived from them. However, progress has been impeded by a unique discrepancy involving the sign of one of the elastic constants of an important material: Al2O3. In this letter, this longstanding discrepancy is resolved with experimental measurements.

Thermal history of solid H 4 e under oscillation

We have studied the thermal history of the resonant frequency of a torsional oscillator containing solid