Kramers–Kronig relationship between ultrasonic attenuation and phase velocity

O’Donnell, Matthew; Jaynes, E. T.; Miller, James G.

doi:10.1121/1.385566

Cited by 436 publications

(201 citation statements)

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“…Figure 2 demonstrate the increase of the bulk modulus with the frequency increase. According to the principle of causality, presented for linear viscoelastic systems by the KramersKronig relations (O'Donnel et al 1981), the increase of moduli should correspond to attenuation increase which is consistent with our experimental data presented in Figure 3. As can be seen, the barrel shape of a sample does not affect the results of the measurements.…”

Section: Measurements and Resultssupporting

confidence: 91%

A laboratory study of the “barrel shape” effect in a viscoelastic cylindrical sample at seismic frequencies

Mikhaltsevitch¹,

Lebedev²,

Gurevich³

2015

ASEG Extended Abstracts

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Section: Measurements and Resultssupporting

confidence: 91%

A laboratory study of the “barrel shape” effect in a viscoelastic cylindrical sample at seismic frequencies

Mikhaltsevitch¹,

Lebedev²,

Gurevich³

2015

ASEG Extended Abstracts

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“…5a), and we observe a general increase in Q with increasing frequency for all modal types. Dispersion and attenuation are coupled by the Kramers-Kronig relations (O'Donnell et al, 1981). The ob-served increase in Q and V p with frequency is consistent with a visco-elastic medium.…”

Section: Frequency Dependence Of Velocity and Attenuationmentioning

confidence: 71%

Monitoring the temperature-dependent elastic and anelastic properties in isotropic polycrystalline ice using resonant ultrasound spectroscopy

et al. 2016

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Abstract. The elastic and anelastic properties of ice are of interest in the study of the dynamics of sea ice, glaciers, and ice sheets. Resonant ultrasound spectroscopy allows quantitative estimates of these properties and aids calibration of active and passive seismic data gathered in the field. The elastic properties and anelastic quality factor Q in laboratorymanufactured polycrystalline isotropic ice cores decrease (reversibly) with increasing temperature, but compressionalwave speed and attenuation prove most sensitive to temperature, indicative of pre-melting of the ice. This method of resonant ultrasound spectroscopy can be deployed in the field, for those situations where shipping samples is difficult (e.g. remote locations), or where the properties of ice change rapidly after extraction (e.g. in the case of sea ice).

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“…the Kramers-Kronig relations [5,6] . Kramers-Kronig relations show the storage and loss moduli master curves should be interrelated and be able to calculate from each other.…”

Section: Master Curves Quality Assessmentsmentioning

confidence: 99%

Determining the Shear Relaxation Modulus and Constitutive Models for Polyurea and Polyurea-Based Composite Materials from Dynamic Mechanical Testing Data

Jia

Amirkhizi

Nantasetphong

et al. 2016

Conference Proceedings of the Society for Experimental Mechanics Series

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Polyurea and polyurea-based composite materials are widely used due to their excellent mechanical properties. In order to facilitate large-scale computational studies for this group of materials, a robust and standard method is needed to extract their viscoelastic constitutive parameters. In this study, frequency-domain master curves which cover a wide range of frequencies are developed using the data of dynamic mechanical analysis through time-temperature superposition (TTS). The quality of the master curves is assessed both by Kramers-Kronig relations and by comparing with the ultrasonic wave testing data. Then the time-domain relaxation modulus is obtained by the high-resolution Prony series approximated from the relaxation spectrum. To reduce computational cost, 4 to 8-term Prony series are then fitted from the time-domain relaxation modulus for a limited frequency range of interest. Both the high and low-resolution Prony series are converted back to frequency domain to compare with the master curves developed by TTS and show good agreements. This method is not limited to polyurea and polyurea-based composites and it can be applied to other similar polymer systems as well.

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Kramers–Kronig relationship between ultrasonic attenuation and phase velocity

Cited by 436 publications

References 0 publications

A laboratory study of the “barrel shape” effect in a viscoelastic cylindrical sample at seismic frequencies

A laboratory study of the “barrel shape” effect in a viscoelastic cylindrical sample at seismic frequencies

Monitoring the temperature-dependent elastic and anelastic properties in isotropic polycrystalline ice using resonant ultrasound spectroscopy

Determining the Shear Relaxation Modulus and Constitutive Models for Polyurea and Polyurea-Based Composite Materials from Dynamic Mechanical Testing Data

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