Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

http://ieeexplore.ieee.org/iel5/5/31047/01444179.pdf

Fundamentals of acoustics

Spherical microphone arrays have been recently studied for sound-field recordings, beamforming, and sound-field analysis which use spherical harmonics in the design. Although the microphone arrays and the associated algorithms were presented, no comprehensive theoretical analysis of performance was provided. This work presents a spherical-harmonics-based design and analysis framework for spherical microphone arrays. In particular, alternative spatial sampling schemes for the positioning of microphones on a sphere are presented, and the errors introduced by finite number of microphones, spatial aliasing, inaccuracies in microphone positioning, and measurement noise are investigated both theoretically and by using simulations. The analysis framework can also provide a useful guide for the design and analysis of more general spherical microphone arrays which do not use spherical harmonics explicitly.

Analysis and design of spherical microphone arrays

We present a study of 33 {\it Kepler} planet-candidate host stars for which asteroseismic observations have sufficiently high signal-to-noise ratio to allow extraction of individual pulsation frequencies. We implement a new Bayesian scheme that is flexible in its input to process individual oscillation frequencies, combinations of them, and average asteroseismic parameters, and derive robust fundamental properties for these targets. Applying this scheme to grids of evolutionary models yields stellar properties with median statistical uncertainties of 1.2\% (radius), 1.7\% (density), 3.3\% (mass), 4.4\% (distance), and 14\% (age), making this the exoplanet host-star sample with the most precise and uniformly determined fundamental parameters to date. We assess the systematics from changes in the solar abundances and mixing-length parameter, showing that they are smaller than the statistical errors. We also determine the stellar properties with three other fitting algorithms and explore the systematics arising from using different evolution and pulsation codes, resulting in 1\% in density and radius, and 2\% and 7\% in mass and age, respectively. We confirm previous findings of the initial helium abundance being a source of systematics comparable to our statistical uncertainties, and discuss future prospects for constraining this parameter by combining asteroseismology and data from space missions. Finally we compare our derived properties with those obtained using the global average asteroseismic observables along with effective temperature and metallicity, finding an excellent level of agreement. Owing to selection effects, our results show that the majority of the high signal-to-noise ratio asteroseismic {\it Kepler} host stars are older than the Sun.

/pdf/ages-and-fundamental-properties-of-kepler-exoplanet-host-3lmy52z0a4.pdf

Ages and fundamental properties of Kepler exoplanet host stars from asteroseismology

Reproduction of a sound field is a fundamental problem in acoustic signal processing. In this paper, we use a spherical harmonics analysis to derive performance bounds on how well an array of loudspeakers can recreate a three-dimensional (3-D) plane-wave sound field within a spherical region of space. Specifically, we develop a relationship between the number of loudspeakers, the size of the reproduction sphere, the frequency range, and the desired accuracy. We also provide analogous results for the special case of reproduction of a two-dimensional (2-D) sound field. Results are verified through computer simulations.

/pdf/reproduction-of-a-plane-wave-sound-field-using-an-array-of-a2b6tt8xjb.pdf

Reproduction of a plane-wave sound field using an array of loudspeakers

Preface. Fourier Transforms & Special Functions. Plane Waves. The Inverse Problem: Planar NAH. Cylindrical Waves. The Inverse Problem: Cylindrical NAH. Spherical Waves. Spherical NAH. Green Functions & the Helmholtz Integral. Index.

Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography

The reconstruction of the pressure and normal surface velocity provided by near-field acoustical holography (NAH) from pressure measurements made near a vibrating structure is a linear, ill-posed inverse problem due to the existence of strongly decaying, evanescentlike waves. Regularization provides a technique of overcoming the ill-posedness and generates a solution to the linear problem in an automated way. We present four robust methods for regularization; the standard Tikhonov procedure along with a novel improved version, Landweber iteration, and the conjugate gradient approach. Each of these approaches can be applied to all forms of interior or exterior NAH problems; planar, cylindrical, spherical, and conformal. We also study two parameter selection procedures, the Morozov discrepancy principle and the generalized cross validation, which are crucial to any regularization theory. In particular, we concentrate here on planar and cylindrical holography. These forms of NAH which rely on the discrete Fourier transform are important due to their popularity and to their tremendous computational speed. In order to use regularization theory for the separable geometry problems we reformulate the equations of planar, cylindrical, and spherical NAH into an eigenvalue problem. The resulting eigenvalues and eigenvectors couple easily to regularization theory, which can be incorporated into the NAH software with little sacrifice in computational speed. The resulting complete automation of the NAH algorithm for both separable and nonseparable geometries overcomes the last significant hurdle for NAH.

Regularization methods for near-field acoustical holography

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.

Sound source reconstructions using a microphone array

From the measurement of the acoustic pressure on a cylindrical, two‐dimensional contour located close to the surface of an underwater, vibrating cylinder, the complete three‐dimensional sound field can be reproduced (reconstructed) with the aid of a computer. This reconstruction technique, called GENAH (generalized nearfield acoustical holography), is unlike conventional holography because it provides a super resolution image of the sound‐pressure field from the surface of the cylinder to the farfield. At the same time, GENAH reconstructs, from this two‐dimensional measurement, the vector velocity and the vector intensity fields (energy flow) in the nearfield of the source, and identifies modes of surface vibration of the cylinder. Experimental results are provided and the accuracy of GENAH is demonstrated by comparison with the two‐hydrophone technique.

Generalized nearfield acoustical holography for cylindrical geometry : theory and experiment

Nearfield acoustical holography (NAH) requires the measurement of the pressure field over a complete surface in order to recover the normal velocity on a nearby concentric surface, the latter generally coincident with a vibrator. Patch NAH provides a major simplification by eliminating the need for complete surface pressure scans-only a small area needs to be scanned to determine the normal velocity on the corresponding (small area) concentric patch on the vibrator. The theory of patch NAH is based on (1) an analytic continuation of the patch pressure which provides a spatially tapered aperture extension of the field and (2) a decomposition of the transfer function (pressure to velocity and/or pressure to pressure) between the two surfaces using the singular value decomposition (SVD) for general shapes and the fast Fourier transform (FFT) for planar surfaces. Inversion of the transfer function is stabilized using Tikhonov regularization and the Morozov discrepancy principle. Experimental results show that root mean square errors of the normal velocity reconstruction for a point-driven vibrator over 200-2700 Hz average less than 20% for two small, concentric patch surfaces 0.4 cm apart. Reconstruction of the active normal acoustic intensity was also successful, with less than 30% error over the frequency band.

Earl G. Williams

Papers

Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography

Regularization methods for near-field acoustical holography

Sound source reconstructions using a microphone array

Generalized nearfield acoustical holography for cylindrical geometry : theory and experiment

Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography