REFRACTION ARRIVALS THROUGH THIN HIGH‐VELOCITY LAYERS

Geophysics ◽  
1965 ◽  
Vol 30 (2) ◽  
pp. 204-212 ◽  
Author(s):  
J. H. Rosenbaum
Keyword(s):  
Exponential Decay ◽  
High Velocity ◽  
Elastic Layer ◽  
Approximate Formula ◽  
Asymptotic Theory ◽  
Surrounding Medium ◽  
Low Frequency ◽  
Horizontal Distance ◽  
Symmetric Mode ◽  
Elastic Parameters

The first significant refraction arrival through a thin high‐velocity elastic layer in an elastic medium has been investigated theoretically by means of an asymptotic theory. This first low‐frequency arrival is closely connected with the longitudinal plate wave in the thin layer. When the medium surrounding the layer is a fluid, the signal does not decay exponentially with horizontal distance; when the surrounding medium is a solid, the signal does decay exponentially. A very simple approximate formula for this exponential decay is presented and compared with numerical results of the more rigorous theory. The decay as well as the shape of the signal is dependent upon the contrast in elastic parameters between the plate and the surrounding medium. Higher‐frequency early arrivals, associated with the second symmetric mode, have also been investigated. They exhibit greater exponential decay with horizontal distance than the low‐frequency first arrivals.

Transmission of explosive sound through a fluid layer over an infinitely deep elastic bottom

1965 ◽  
Vol 55 (5) ◽  
pp. 879-901 ◽  
Author(s):  
J. H. Rosenbaum
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
High Velocity ◽  
Asymptotic Theory ◽  
Fluid Layer ◽  
Standing Waves ◽  
Horizontal Distance ◽  
Elastic Bottom ◽  
Rayleigh Mode

abstract The transmission of explosive sound through a thin fluid layer above an infinitely deep elastic bottom is described by means of an asymptotic theory. Special attention is paid to early oscillatory arrivals at large horizontal distances for the case of a high-velocity bottom, and it is found that these arrivals do not decay exponentially with horizontal distance. When the shear wave velocity in the bottom is low, the over-all response is very similar to the case of a fluid bottom, except for the Rayleigh mode, which becomes an important feature of the late signal. The response at long times may involve standing waves of finite horizontal wavelengths.

scholarly journals Strong Waves from Pulsars and Morphologies in SNRs

1983 ◽  
Vol 101 ◽  
pp. 499-501
Author(s):  
Gregory Benford ◽  
Attilio Ferrari ◽  
Silvano Massaglia
Keyword(s):  
Large Amplitude ◽  
Crab Nebula ◽  
Surrounding Medium ◽  
Low Frequency ◽  
Optical Emission ◽  
Amplitude Wave ◽  
Surface Magnetic Field ◽  
Plasma Absorption ◽  
The Crab Nebula ◽  
Large Amplitude Wave

Canonical models for pulsars predict the emission of low–frequency waves of large amplitudes, produced by the rotation of a neutron star possessing a strong surface magnetic field. Pacini (1968) proposed this as the basic drain which yields to the pulsar slowing–down rate. The main relevance of the large amplitude wave (LAW) is the energetic link it provides between the pulsar and the surrounding medium. This role has been differently emphasized (Rees and Gunn, 1974; Ferrari, 1974), referring to absorption effects by relativistic particle acceleration and thermal heating, either close to the pulsar magnetosphere or in the nebula. It has been analyzed in the special case of the Crab Nebula, where observations are especially rich (Rees, 1971). As the Crab Nebula displays a cavity around the pulsar of dimension ∼1017cm, the function of the wave in sweeping dense gas away from the circumpulsar region is widely accepted. Absorption probably occurs at the inner edges of the nebula; i.e., where the wave pressure and the nebular pressure come into balance. Ferrari (1974) interpreted the wisps of the Crab Nebula as the region where plasma absorption occurs, damping the large amplitude wave and driving “parametric” plasma turbulence, thus trasferring energy to optical radiation powering the nebula. The mechanism has been extended to interpret the specific features of the “wisps” emission (Benford et al., 1978). Possibly the wave fills the nebula completely, permeating the space outside filaments with electromagnetic energy, continuously accelerating electrons for the extended radio and optical emission (Rees, 1971).

An Analytical Model for the Interaction of Mass Inclusions in Heterogeneous (HG) Blankets

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
A. Wagner ◽  
M. E. Johnson ◽  
K. Idrisi ◽  
D. P. Bartylla
Keyword(s):  
Elastic Layer ◽  
Analytical Approach ◽  
Low Frequency ◽  
Control Device ◽  
Effective Stiffness ◽  
Special Focus ◽  
Dynamic Vibration Absorber ◽  
Low Frequencies ◽  
Dynamic Vibration ◽  
The Masses

The heterogeneous (HG) blanket is a passive treatment used to reduce the low frequency transmission of sound through partitions. HG blankets, glued onto a structure, consist of an elastic medium with embedded mass inhomogeneities that mechanically replicate a mass-spring-damper system to reduce efficient radiating structural modes at low frequencies. The elastic layer typically used has sound absorption properties to create a noise control device with a wide bandwidth of performance. The natural frequency of an embedded dynamic vibration absorber is determined by the mass of the inhomogeneity as well as by its effective stiffness due to the interaction of the mass inclusion with the elastic layer. A novel analytical approach has been developed to describe in detail the interaction of the mass inclusions with the elastic layer and the interaction between the masses by evaluating special elastomechanical concepts. The effective stiffness is predicted by the analytical approach based on the shape of the mass inclusions as well as on the thickness and material properties of the layer. The experimental validation is included and a simplified direct equation to calculate the effective stiffness of a HG blanket is proposed. Furthermore, the stress field inside the elastic material will be evaluated with focus on the stresses at the base to assess the modeling of one or more masses placed on top of the elastic layer as dynamic vibration absorbers. Finally, the interaction between two (or more) masses placed onto the same layer is studied with special focus on the coupling of the masses at low distances between them.

scholarly journals Thermal radio absorption as a tracer of the interaction of SNRs with their environments

2021 ◽  
Vol 653 ◽  
pp. A62
Author(s):  
G. Castelletti ◽  
L. Supan ◽  
W. M. Peters ◽  
N. E. Kassim
Keyword(s):  
Spectral Index ◽  
Supernova Remnants ◽  
Surrounding Medium ◽  
Low Frequency ◽  
Power Laws ◽  
Line Of Sight ◽  
Pulsar Wind Nebulae ◽  
Very Large Array ◽  
Murchison Widefield Array ◽  
Thermal Absorption

We present new images and continuum spectral analysis for 14 resolved Galactic supernova remnants (SNRs) selected from the 74 MHz Very Large Array Low-Frequency Sky Survey Redux (VLSSr). We combine new integrated measurements from the VLSSr with, when available, flux densities extracted from the Galactic and Extragalactic All-Sky Murchison Widefield Array Survey and measurements from the literature to generate improved integrated continuum spectra sampled from ~15 MHz to ~217 GHz. We present the VLSSr images. When possible we combine them with publicly available images at 1.4 GHz, to analyse the resolved morphology and spectral index distribution across each SNR. We interpret the results and look for evidence of thermal absorption caused by ionised gas either proximate to the SNR itself, or along its line of sight. Three of the SNRs, G4.5+6.8 (Kepler), G28.6−0.1, and G120.1+1.4 (Tycho), have integrated spectra which can be adequately fit with simple power laws. The resolved spectral index map for Tycho confirms internal absorption which was previously detected by the Low Frequency Array, but it is insufficient to affect the fit to the integrated spectrum. Two of the SNRs are pulsar wind nebulae, G21.5−0.9 and G130.7+3.1 (3C 58). For those we identify high-frequency spectral breaks at 38 and 12 GHz, respectively. For the integrated spectra of the remaining nine SNRs, a low frequency spectral turnover is necessary to adequately fit the data. In all cases we are able to explain the turnover by extrinsic thermal absorption. For G18.8+0.3 (Kes 67), G21.8−0.6 (Kes 69), G29.7−0.3 (Kes 75), and G41.1−0.3 (3C 397), we attribute the absorption to ionised gas along the line of sight, possibly from extended H II region envelopes. For G23.3−0.3 (W41) the absorption can be attributed to H II regions located in its immediate proximity. Thermal absorption from interactions at the ionised interface between SNR forward shocks and the surrounding medium were previously identified as responsible for the low frequency turnover in SNR G31.9+0.0 (3C 391); our integrated spectrum is consistent with the previous results. We present evidence for the same phenomenon in three additional SNRs G27.4+0.0 (Kes 73), G39.2–0.3 (3C 396), and G43.3–0.2 (W49B), and derive constraints on the physical properties of the interaction. This result indicates that interactions between SNRs and their environs should be readily detectable through thermal absorption by future low frequency observations of SNRs with improved sensitivity and resolution.

Combustion Instability and Emission Control by Pulsating Fuel Injection

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Christian Oliver Paschereit ◽  
Ephraim Gutmark
Keyword(s):  
High Frequency ◽  
Fuel Injection ◽  
Low Frequency ◽  
Nox Emissions ◽  
Modulation Amplitude ◽  
Pulsation Frequency ◽  
Symmetric Mode ◽  
Instability Mode ◽  
Secondary Fuel ◽  
Symmetric Instability

Open-loop control methodologies were used to suppress symmetric and helical thermoacoustic instabilities in an experimental low-emission swirl-stabilized gas-turbine combustor. The controllers were based on fuel (or equivalence ratio) modulations in the main premixed combustion (premixed fuel injection (PMI)) or, alternatively, in the secondary pilot fuel. PMI included symmetric and asymmetric fuel injection. The symmetric instability mode responded to symmetric excitation only when the two frequencies matched. The helical fuel injection affected the symmetric mode only at frequencies that were much higher than that of the instability mode. The asymmetric excitation required more power to obtain the same amount of reduction as that required by symmetric excitation. Unlike the symmetric excitation, which destabilized the combustion when the modulation amplitude was excessive, the asymmetric excitation yielded additional suppression as the modulation level increased. The NOx emissions were reduced to a greater extent by the asymmetric modulation. The second part of the investigation dealt with the control of low frequency symmetric instability and high frequency helical instability by the secondary fuel injection in a pilot flame. Adding a continuous flow of fuel into the pilot flame controlled both instabilities. However, modulating the fuel injection significantly decreased the amount of necessary fuel. The reduced secondary fuel resulted in a reduced heat generation by the pilot diffusion flame and therefore yielded lower NOx emissions. The secondary fuel pulsation frequency was chosen to match the time scales typical to the central flow recirculation zone, which stabilizes the flame in the burner. Suppression of the symmetric mode pressure oscillations by up to 20dB was recorded. High frequency instabilities were suppressed by 38dB, and CO emissions reduced by using low frequency modulations with 10% duty cycle.

Mapping of induced polarization using natural fields

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Erika Gasperikova ◽  
H. Frank Morrison
Keyword(s):  
Electric Field ◽  
Surrounding Medium ◽  
Low Frequency ◽  
Induced Polarization ◽  
The Body ◽  
Electromagnetic Response ◽  
Frequency Dependent ◽  
Finite Body ◽  
Electric Field Profile ◽  
Measured Response

The observed electromagnetic response of a finite body is caused by induction and polarization currents in the body and by the distortion of the induction currents in the surrounding medium. At a sufficiently low frequency, there is negligible induction and the measured response is that of the body distorting the background currents just as it would distort a direct current (dc). Because this dc response is not inherently frequency dependent, any observed change in response of the body for frequencies low enough to be in this dc limit must result from frequency‐dependent conductivity. Profiles of low‐frequency natural electric (telluric) fields have spatial anomalies over finite bodies of fixed conductivity that are independent of frequency and have no associated phase anomaly. If the body is polarizable, the electric field profile over the body becomes frequency dependent and phase shifted with respect to a reference field. The technique was tested on data acquired in a standard continuous profiling magnetotelluric (MT) survey over a strong induced polarization (IP) anomaly previously mapped with a conventional pole‐dipole IP survey. The extracted IP response appears in both the apparent resistivity and the normalized electric field profiles.

The Stability of a Two-Layer Inviscid Flow Between an Elastic Layer and a Rigid Boundary

1999 ◽  
Vol 66 (1) ◽  
pp. 197-203 ◽  
Author(s):  
P. J. Schall ◽  
J. P. McHugh
Keyword(s):  
Elastic Layer ◽  
Inviscid Flow ◽  
Elastic Parameters ◽  
Rigid Boundary ◽  
Two Fluids ◽  
Coating Flow ◽  
Fluid Layers ◽  
Mode 2 ◽  
Layer Flow ◽  
The Stability

The linear stability of two-layer flow over an infinite elastic substraw is considered. The problem is motivated by coating flow in a printing press. The flow is assumed to be inviscid and irrotational. Surface tension between the fluid layers is included, but gravity is neglected. The results show two unstable modes: one mode associated with the interface between the elastic layer and the fluid (mode 1), and the other concentrated on the interface between the two fluids (mode 2). The behavior of the unstable modes is examined while varying the elastic parameters, and it is found that mode 1 can be made stable, but mode 2 remains unstable at small wavenumber, similar to the classic Kelvin—Helmholtz mode.

Low-frequency laboratory measurements of the elastic properties of sandstone flooded with supercritical CO2

2013 ◽  
Vol 53 (2) ◽  
pp. 484
Author(s):  
Vassili Mikhaltsevitch ◽  
Maxim Lebedev ◽  
Boris Gurevich
Keyword(s):  
Supercritical Co2 ◽  
Low Frequency ◽  
Bedding Plane ◽  
Residual Water ◽  
Laboratory Measurements ◽  
Elastic Parameters ◽  
Sandstone Sample ◽  
Confining Pressures ◽  
The Difference ◽  
Set Up

This extended abstract presents the results of the first low-frequency experiments conducted on a sandstone sample (Donnybrook, WA) flooded with supercritical CO2 (scCO2). The experiments investigated the effects of scCO2 injection on the elastic and anelastic properties of the rock. The sandstone sample (porosity—11.4%, permeability—0.28 mD) was cut in the direction orthogonal to a formation-bedding plane and tested in a Hoek's triaxial pressure cell equipped with the means for independent control of pore and confining pressures. The pore and confining pressures were set up at 10 and 31 MPa correspondingly. The low-frequency system and the pump comprising of scCO2 were held at a temperature of 42°C. Supercritical CO2 was injected into the sample preliminary saturated with distilled water. The amount of the residual water in the sample after the scCO2 injection was about 40% of pore volume. The elastic parameters obtained for the sample with scCO2 at frequencies from 0.1–100 Hz are very close to those for the dry sample. Some discrepancy in calculated acoustic velocities are caused by the difference in water and scCO2 densities. The measured extensional attenuation is larger when the sample is saturated with scCO2. The applicability of Gassmann's fluid substitution theory for the interpretation of obtained results was also tested during the experiments.

Transient Compressional Waves in an Infinite Elastic Plate or Elastic Layer Overlying a Rigid Half-Space

1962 ◽  
Vol 29 (1) ◽  
pp. 53-60 ◽  
Author(s):  
Julius Miklowitz
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Integral Transform ◽  
Formal Solution ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Frequency Equation ◽  
Point Load ◽  
Phase Method ◽  
Stationary Phase Method

The problem treated is that of an infinite free plate excited symmetrically by two equal and normally opposed step point-loads on its faces. The problem is equivalent to that of the surface normal point-load excitation of an infinite elastic layer, half the thickness of the plate, overlying a rigid half-space with lubricated contact. The formal solution is obtained from the equations of motion in linear elasticity with the aid of a double integral transform technique and residue theory. The stationary phase method, and known characteristics of the governing Rayleigh-Lamb frequency equation, are used to analyze and evaluate numerically the far field displacements. It is shown that the head of the disturbance is composed predominantly of the low-frequency long waves from the lowest mode of wave transmission.

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