Radiation impedance of resonant ultrasound spectroscopy modes in fused silica

Zhang, Hong; Sorbello, R. S.; Hucho, C.; Herro, Joseph; Feller, J. R.; Beck, D. E.; Levy, M.; Isaak, Donald G.; Carnes, J. D.; Anderson, Orson L.

doi:10.1121/1.422757

Cited by 14 publications

(13 citation statements)

References 18 publications

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“…The experimental values are from a fit of the resonant peaks and they have a pressure independent factor 1/Q o subtracted from the total. 5 Overall, there is good agreement between the theoretical and experiment results for this factor. The experimental frequency shifts reported in Table III are much larger than the theoretical shifts.…”

Section: Resultssupporting

confidence: 72%

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Rayleigh–Ritz calculation of the resonant modes of a solid parallelepiped in a pressurizing fluid

Beck

2004

The Journal of the Acoustical Society of America

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Resonant ultrasound spectroscopy relies on comparisons of experimentally determined vibrational spectra to theoretically computed spectra for the extraction of the elastic moduli of the solid samples. To determine the pressure dependence of these moduli, resonant spectra are taken for samples pressurized by a surrounding gas and knowledge of the contribution of the surface loading of the sample by the gas is needed in order to extract the intrinsic pressure dependence of the moduli. To facilitate the required comparisons, a Rayleigh-Ritz variational calculation of the vibrational spectrum is formulated which includes the loading of the solid by the pressurizing fluid. This formalism is used to compute the effect of gas loading on the vibrational spectrum of an isotropic, solid parallelepiped.

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Section: Resultssupporting

confidence: 72%

“…Zhang et al 5 have published experimental data along with a theoretical analysis for small fused silica parallelepipeds pressurized with various gases. Their theoretical calculation employs a two-dimensional model ͑TDM͒ to compute the radiation impedance.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh–Ritz calculation of the resonant modes of a solid parallelepiped in a pressurizing fluid

Beck

2004

The Journal of the Acoustical Society of America

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“…Background or parasitic damping due to sound radiation in the air is proportional to gas density and inversely proportional to specimen density. It is not considered to be significant for brass since quartz, which is less dense than brass, exhibited a cube torsion 7 background damping of about 5ϫ10…”

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confidence: 99%

Resonant ultrasound spectroscopy in shear mode

Wang

Lakes

2003

Review of Scientific Instruments

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We present an enhancement of the resonant ultrasound spectroscopy method for the determination of elastic and viscoelastic properties. By using shear transducers rather than the usual compressional ones, signal strength for the fundamental is enhanced by one to three orders of magnitude. This enables simplified determination of shear modulus and damping tan ␦ with off-the-shelf electronics.Moreover, the polarization of the shear transducers can be used to identify modes of vibration. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1535739͔Resonant ultrasound spectroscopy ͑RUS͒ involves scanning the resonance structure of a compact specimen such as a cube, parallelepiped, sphere or short cylinder 1-3 with the aim of determining mechanical properties. Typically, a sample is supported by piezoelectric ultrasonic transducers, one a transmitter, and one a receiver, at opposite corners in the case of a cube or at opposite edges for a short cylinder. Corners provide elastically weak coupling to the transducers, hence minimal perturbation to the vibration, minimal shift in resonant frequency, and minimum parasitic damping. The RUS approach has the advantage of simplicity in that no gluing, clamping, or painstaking alignment of the specimen is required since it is held by contact force. Both large and small samples are readily accommodated in RUS. RUS differs from conventional pulsed wave ultrasound as follows. Plane wave approximations are used to obtain the governing equations for pulsed ultrasound; these approximations limit the sample size and test frequency. Pulsed ultrasound attenuation measurements usually involve corrections for diffraction and transducer properties. No such corrections are needed for RUS. The complexity of the usual RUS method enters in the data reduction procedure, which makes use of fast computers to infer elastic moduli from the resonant frequencies. One can obtain all the elastic moduli C i jkl of a single specimen of an anisotropic material at ultrasonic frequency. A substantial challenge in this approach is that some of the resonant modes are missing in a typical scan.2,3 The reason is that a mode which gives rise to corner motion parallel to a compressional transducer will not be observed. If the specimen is remounted at a slightly different angle, the missing mode may appear. However such iterations detract from the elegance and simplicity of the method. Moreover, if one minimizes the contact force to improve accuracy of modulus and damping measurement, angulation is limited by the tendency of the specimen to slip. The torsion and shear modes are valuable for interpretation and verification, since an exact analytical solution is available for them. However these modes are weak or absent in a standard RUS implementation since cube corner motion for them is largely tangential to the transducer face.It is possible to determine material damping tan ␦ with RUS by measuring the width of resonance curves. Since higher modes are closely spaced, it is impractical to determine tan ␦ above 0....

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“…Bending modes are more vulnerable to such error than torsion, and slender specimens more so than compact ones such as those used for RUS. Sound radiation errors for RUS 38 are more severe for compressional modes than torsional modes. To eliminate these errors, tests on low-loss materials are done under vacuum.…”

Section: ͻ10mentioning

confidence: 99%