Proof that plane wave attenuation at low frequencies is proportional to square of frequency

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.

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Study of wave attenuation in concrete

Journal of Materials Research ◽

10.1557/jmr.1993.2344 ◽

1993 ◽

Vol 8 (9) ◽

pp. 2344-2353 ◽

Cited By ~ 8

Author(s):

J-M. Berthelot ◽

Souda M. Ben ◽

J.L. Robert

Keyword(s):

Experimental Study ◽

Plane Wave ◽

Wave Attenuation ◽

Plane Waves ◽

Propagation Distance ◽

Experimental Results ◽

The Other ◽

Wave Frequency ◽

Concrete Composition ◽

Analytical Expression

The experimental study of wave attenuation in concrete has been achieved in the case of the propagation of plane waves in concrete rods. Different mortars and concretes have been investigated. A transmitter transducer coupled to one of the ends of the concrete rod generates the propagation of a plane wave in the rod. The receiver transducer, similar to the previous one, is coupled to the other end of the rod. The experimental results lead to an analytical expression for wave attenuation as function of the concrete composition, the propagation distance, and the wave frequency.

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Elastic wave propagation in metamaterial rods with periodic shunted piezo-patches

INTER-NOISE and NOISE-CON Congress and Conference Proceedings ◽

10.3397/in-2021-2657 ◽

2021 ◽

Vol 263 (2) ◽

pp. 4303-4311

Author(s):

Edson J.P. de Miranda ◽

Edilson D. Nobrega ◽

Leopoldo P.R. de Oliveira ◽

José M.C. Dos Santos

Keyword(s):

Wave Propagation ◽

Elastic Wave ◽

Wave Attenuation ◽

Periodic Structures ◽

Band Gaps ◽

Low Frequencies ◽

Periodic Arrays ◽

Extended Plane ◽

Elastic Metamaterials ◽

Piezoelectric Structures

The wave propagation attenuation in low frequencies by using piezoelectric elastic metamaterials has been developed in recent years. These piezoelectric structures exhibit abnormal properties, different from those found in nature, through the artificial design of the topology or exploring the shunt circuit parameters. In this study, the wave propagation in a 1-D elastic metamaterial rod with periodic arrays of shunted piezo-patches is investigated. This piezoelectric metamaterial rod is capable of filtering the propagation of longitudinal elastic waves over a specified range of frequency, called band gaps. The complex dispersion diagrams are obtained by the extended plane wave expansion (EPWE) and wave finite element (WFE) approaches. The comparison between these methods shows good agreement. The Bragg-type and locally resonant band gaps are opened up. The shunt circuits influence significantly the propagating and the evanescent modes. The results can be used for elastic wave attenuation using piezoelectric periodic structures.

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Spatio-temporal variation of Anaelastic and Scattering Seismic Attenuation during the 2016-2017 Central Italy Seismic Sequence

10.5194/egusphere-egu21-8802 ◽

2021 ◽

Author(s):

Simona Gabrielli ◽

Aybige Akinci ◽

Ferdinando Napolitano ◽

Luca De Siena ◽

Edoardo Del Pezzo ◽

...

Keyword(s):

Wave Attenuation ◽

Central Italy ◽

Temporal Variations ◽

Seismic Attenuation ◽

Coda Wave ◽

Seismic Sequence ◽

Rock Fracturing ◽

Low Frequencies ◽

Main Shocks ◽

Stress Changes

Between August and October 2016, the Central Apennines in Italy have been struck by a long-lasting seismic sequence, known as the Amatrice (Mw 6.0) - Visso (Mw 5.9) - Norcia (Mw 6.5) sequence. The cascading ruptures occurred in this sequence have been considered connected to the fluid migration in the fault network, as suggested by previous studies. The behaviour of fluids in the crust is crucial to understand earthquakes occurrence and stress changes since fluids reduce fault stability. It has long been understood that the seismic attenuation is strongly controlled by the structural irregularity and heterogeneities; micro-cracks and cavities, either fluid-filled or dry, temperature and pressure variations cause a decrease in seismic wave amplitude and pulse broadening. Hence seismic attenuation imagining is a powerful tool to be a relevant provenance of information about the influence and abundance of fluids in a seismic sequence.The aim of this work is to separate scattering and absorption contributions to the total attenuation of coda waves and to provide their spatial and temporal variations at different frequency bands of these quantities using two datasets: the first one comprising 592 earthquakes occurred before the sequence (March 2013-August 2016) and the second one comprising 763 events (ML > 2.8) from the Amatrice-Visso-Norcia sequence. Scattering and absorption have been measured through peak-delay and coda-wave attenuation parameters (the latter inverted using frequency-dependent sensitivity kernels).The preliminary results show a clear difference between the pre-sequence and sequence images, mainly at low frequencies (1.5 Hz), where we can define a spatial increase of scattering with time attributed to rock fracturing and fluid circulation. The coda attenuation tomography also demonstrates a clear variation between the pre-sequence and the sequence over series of time windows being before and after the largest main shocks of the seismic sequence, with an increase of the attenuation in space with decreasing time. The peak delay indicates a high scattering area corresponding to the Gran Sasso massif and L&#8217;Aquila zone, where an important seismic sequence (Mw 6.3) occurred in 2009.

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SCALAR DIFFRACTION BY A PROLATE SPHEROID AT LOW FREQUENCIES

Canadian Journal of Physics ◽

10.1139/p60-166 ◽

1960 ◽

Vol 38 (12) ◽

pp. 1632-1641 ◽

Cited By ~ 16

Author(s):

T. B. A. Senior

Keyword(s):

Exact Solution ◽

Plane Wave ◽

Oblate Spheroid ◽

Prolate Spheroid ◽

Wave Number ◽

Scalar Problem ◽

Low Frequencies ◽

Scalar Diffraction

For the scalar problem of the diffraction of a plane wave by a prolate spheroid the exact solution is known, and by expanding this in ascending powers of ka, where k is the wave number and 2a is the interfocal distance, the Rayleigh series for both the "soft" and "hard" bodies are obtained up to and including terms in (ka)6. The corresponding results for an oblate spheroid can be deduced by a trivial change of parameters. Some particular cases are examined.

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A theory of compressional wave attenuation in noncohesive sediments

Geophysics ◽

10.1190/1.1442002 ◽

1985 ◽

Vol 50 (8) ◽

pp. 1311-1317 ◽

Cited By ~ 18

Author(s):

C. McCann ◽

D. M. McCann

Keyword(s):

Wave Attenuation ◽

Compressional Wave ◽

Solid Particles ◽

Biot’S Theory ◽

Attenuation Coefficients ◽

Low Frequencies ◽

Biot's Theory ◽

Compressional Waves ◽

High Frequencies ◽

Water Saturated

Published reviews indicate that attenuation coefficients of compressional waves in noncohesive, water‐saturated sediments vary linearly with frequency. Biot’s theory, which accounts for attenuation in terms of the viscous interaction between the solid particles and pore fluid, predicts in its presently published form variation proportional to [Formula: see text] at low frequencies and [Formula: see text] at high frequencies. A modification of Biot’s theory which incorporates a distribution of pore sizes is presented and shown to give excellent agreement with new and published attenuation data in the frequency range 10 kHz to 2.25 MHz. In particular, a linear variation of attenuation with frequency is predicted in that range.

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