THE REPRESENTATION OF SEISMIC WAVES IN FREQUENCY-WAVE NUMBER SPACE

1964 ◽  
Author(s):  
Jr Kelly ◽  
E. J.
Keyword(s):  
Seismic Waves ◽  
Wave Number ◽  
Frequency Wave

A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate

2006 ◽  
Vol 128 (4) ◽  
pp. 477-488 ◽  
Author(s):  
A. Chakraborty ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Shear Deformation ◽  
Mechanical Response ◽  
Laminated Composite ◽  
Wave Number ◽  
Single Element ◽  
Element Formulation ◽  
Frequency Wave ◽  
Spectral Finite Element

A new spectral plate element (SPE) is developed to analyze wave propagation in anisotropic laminated composite media. The element is based on the first-order laminated plate theory, which takes shear deformation into consideration. The element is formulated using the recently developed methodology of spectral finite element formulation based on the solution of a polynomial eigenvalue problem. By virtue of its frequency-wave number domain formulation, single element is sufficient to model large structures, where conventional finite element method will incur heavy cost of computation. The variation of the wave numbers with frequency is shown, which illustrates the inhomogeneous nature of the wave. The element is used to demonstrate the nature of the wave propagating in laminated composite due to mechanical impact and the effect of shear deformation on the mechanical response is demonstrated. The element is also upgraded to an active spectral plate clement for modeling open and closed loop vibration control of plate structures. Further, delamination is introduced in the SPE and scattered wave is captured for both broadband and modulated pulse loading.

Investigation of X-band backscattering from wave breaking in a laboratory experiment

2021 ◽  
Author(s):  
Nikita Rusakov ◽  
Georgy Baidakov ◽  
Evgeny Poplavsky ◽  
Yuliya Troitskaya ◽  
Maksim Vdovin
Keyword(s):  
Cross Section ◽  
Wave Breaking ◽  
Spectral Characteristics ◽  
Wave Number ◽  
Scattered Signal ◽  
Channel Cross Section ◽  
Frequency Wave ◽  
First Case ◽  
X Band ◽  
Working Section

<p>The work is concerned with the study of the breaking surface wave effect on the intensity and spectral characteristics of a scattered radar signal in laboratory conditions.</p><p><span>The experiments were carried out on the reconstructed TSWiWaT wind wave flume of the IAP RAS. The channel is 12 m long, the channel cross-section varies from 0.7 x 0.7 m at the entrance to 0.7 x 0.9 m in the working section at a distance of 9 m. The airflow speed on the axis is 3-35 m/s, which corresponds to the values of the wind speed U</span><sub>10</sub><span> of 11-50 m/s.</span></p><p>The wave characteristics in the flume were measured by an array of three wave gauges positioned in the corners of an equal-side triangle with 2.5 cm side, the data sampling rate was 200 Hz. Such a system gives the opportunity to retrieve 3D frequency-wave number spectra of surface waves.</p><p>The airflow parameters were measured using the profiling method. The velocity profiles were measured in the working section using an S-shaped Pitot tube. Microwave measurements were carried out using an X-band coherent Doppler scatterometer with a wavelength of 3.2 cm with sequential reception of linear polarizations.  The absolute value of the radar cross-section (RCS) on the wavy water surface was determined by comparing the scattered signal with the signal reflected from the calibrator with a known value of the RCS - a metal ball with a diameter of 6 cm. The dimensions of the observation cross-section were 40 cm x 40 cm, the incidence angles were 30°, 40°, 50° for the upwind direction, the distance to the target was 3.15 m.</p><p>Two series of experiments were carried out. In the first case, wind waves on the surface of pure deep water, developing under the action of a fan generated wind, were studied. In the second case, a train of three waves was generated at the beginning of the channel, with the fan turned on, in order to simulate shallow water an inclined plate was placed under water in front of the measurement area. As a result, the breaking waves occurred at a fixed point and at weaker winds compared to the first case.</p><p>As a result, an increase in the scattered signal intensity during artificial wave breaking in the case of weak winds was noted. For strong winds, the effect turned out to be insignificant, despite the increased amplitude of the waves under study. The Doppler spectra analysis is also presented.</p><p>This work was supported by the RFBR projects No. 19-05-00249, 19-05-00366.  </p>

Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Plane Strain, Analytical Results

1979 ◽  
Vol 46 (1) ◽  
pp. 113-119 ◽  
Author(s):  
T. J. Delph ◽  
G. Herrmann ◽  
R. K. Kaul
Keyword(s):  
Wave Propagation ◽  
Asymptotic Behavior ◽  
Plane Strain ◽  
Elastic Body ◽  
Harmonic Wave ◽  
Wave Number ◽  
Periodic Medium ◽  
Frequency Wave ◽  
Wave Numbers ◽  
Band Characteristic

The problem of harmonic wave propagation in an unbounded, periodically layered elastic body in a state of plane strain is examined. The dispersion spectrum is shown to be governed by the roots of an 8 × 8 determinant, and represents a surface in frequency-wave number space. The spectrum exhibits the typical stopping band characteristic of wave propagation in a periodic medium. The dispersion equation is shown to uncouple along the ends of the Brillouin zones, and also in the case of wave propagation normal to the layering. The significance of this uncoupling is examined. Also, the asymptotic behavior of the spectrum for large values of the wave numbers is investigated.

In-situ microseism noise generation measured from distributed acoustic sensing on seafloor optical cable

2020 ◽  
Author(s):  
Diane Rivet ◽  
Gauthier Guérin ◽  
Daniel Mata ◽  
Itzhak Lior ◽  
Anthony Sladen ◽  
...  
Keyword(s):  
Solid Earth ◽  
Gravity Waves ◽  
Ambient Noise ◽  
Wave Number ◽  
Apparent Velocity ◽  
Noise Generation ◽  
Linear Interaction ◽  
Frequency Wave ◽  
Acoustic Sensing ◽  
Scholte Waves

<p>Measuring seismic and acoustic signals on seafloor telecom cables has proven recently its very high potential for earthquake monitoring but also for beter understanding the interaction between the oceans and the solid earth. A consequence of these interactions is the generation of the primary and secondary microseismic noise on coastal regions and in the deep ocean respectively. These seismic noises that propagate across continents are central to a large fraction of todays' seismic imagery and monitoring campaigns. Compared to previous studies and instrumentation setups, acoustic sensing over oceanic telecom cables offer the unique ability to measure in a very dense manner waves that are generated on the seafloor. We analyse a week long record of ambient noise measurements on the 41.5 km-long seafloor telecom cable offshore Toulon, south of France. At shallow depth, close to the coast, we measure the pressure changes caused by the oceanic gravity waves. The bottom pressure is then compared to an oceanographic buoy located a few kilometers away from the cable. The amplitude and frequency of the pressure are modulated by the gravity waves height and dominant periods. This observation opens the way for a distributed measurement of the oceanic waves characteristics over several kilometers. At depth larger than a 1km, we observe Scholte waves at the ocean-solid earth interface produced by the non-linear interaction of gravity waves. These waves have the double frequency of the gravity waves seen at the coast. We find that the amplitude and frequency change over time, as do the gravity waves observed near the coast. The frequency-wave number decomposition of the signal reveals that the apparent velocity of the Scholte waves does not depend of the azimuth of the fiber. These observations confirm that these deep Scholte waves are secondary microseismic noise, generated locally from the interaction of landward gravity waves with oceanward gravity wave reflected on the coast. Spatially distributed monitoring of the ambient noise wave field at the ocean-solid earth interface provides a better understanding of the noise generation and therefore will allow a better modeling of the ambient noise in the future.</p>

scholarly journals Acoustic oscillations in a field-free cavity under solar small-scale bipolar magnetic canopy

2008 ◽  
Vol 26 (10) ◽  
pp. 2983-2989 ◽  
Author(s):  
D. Kuridze ◽  
T. V. Zaqarashvili ◽  
B. M. Shergelashvili ◽  
S. Poedts
Keyword(s):  
Magnetic Field ◽  
Acoustic Waves ◽  
Canopy Structure ◽  
Active Regions ◽  
Acoustic Power ◽  
Lower Atmosphere ◽  
Wave Number ◽  
Small Scale ◽  
Acoustic Oscillations ◽  
Frequency Wave

Abstract. Observations show the increase of high-frequency wave power near magnetic network cores and active regions in the solar lower atmosphere. This phenomenon can be explained by the interaction of acoustic waves with a magnetic field. We consider small-scale, bipolar, magnetic field canopy structure near the network cores and active regions overlying field-free cylindrical cavities of the photosphere. Solving the plasma equations we get the analytical dispersion relation of acoustic oscillations in the field-free cavity area. We found that the m=1 mode, where m is azimuthal wave number, cannot be trapped under the canopy due to energy leakage upwards. However, higher (m≥2) harmonics can be easily trapped leading to the observed acoustic power halos under the canopy.

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