Transient Wave Propagation in a Symmetrically Layered Elastic Plate

1974 ◽  
Vol 41 (3) ◽  
pp. 684-690 ◽  
Author(s):  
D. C. Viano ◽  
J. Miklowitz
Keyword(s):  
Near Field ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Short Wave ◽  
Frequency Equation ◽  
Layered Plate ◽  
Transient Wave ◽  
Long Time ◽  
Transient Wave Propagation ◽  
Front Running

The response of a symmetrically layered plate subjected to symmetric step normal line face loads is determined. The solution, which is based on the equations of motion from linear elasticity, is obtained in the form of an infinite series of integrals with each term being the contribution from a branch of the underlying frequency equation. Through numerical analysis several of the lower branches of the frequency equation, which depend on layered plate ratios (four material and one thickness) are evaluated and used to write the transient response in the near field. Integrations based on the first five branches show the dominance of the lowest mode in the solution. Applying arguments of stationary phase to the spectrum, yields low frequency-long wave and high frequency-short wave approximations for use in obtaining the far field-long time disturbance. The former governs a front running “head of the pulse” for the layered plate, and the latter, later arriving Rayleigh and Stoneley waves.

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.

Equatorial Zonal Jet Formation through the Barotropic Instability of Low-Frequency Mixed Rossby–Gravity Waves, Equilibration by Inertial Instability, and Transition to Superrotation

2009 ◽  
Vol 66 (9) ◽  
pp. 2600-2619 ◽  
Author(s):  
Mark D. Fruman ◽  
Bach Lien Hua ◽  
Richard Schopp
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Horizontal Velocity ◽  
Barotropic Instability ◽  
Velocity Amplitude ◽  
Zonal Scale ◽  
Zonal Jets ◽  
Initial Wave ◽  
Inertial Instability ◽  
Long Time

Abstract Depth-dependent barotropic instability of short mixed Rossby–gravity (MRG) waves is proposed as a mechanism for the formation of equatorial zonal jets. High-resolution primitive equation simulations show that a single MRG wave of very short zonal wavelength and small to moderate amplitude is unstable and leads to the development of a largely barotropic, zonally symmetric flow, featuring a westward jet at the equator and extra-equatorial jets alternating in direction with latitude. At higher but still moderate amplitude, westward flow still prevails at the equator at depths of maximum horizontal velocity amplitude in the initial wave, but the long-term equilibrated state can also feature eastward “superrotating” jets at the equator near the depths of zero horizontal velocity in the initial wave. The formation of the superrotating jets in the simulations is found to be sensitive to the inclusion of the nontraditional Coriolis force in the equations of motion. A linear theory is used to demonstrate the existence of exponentially growing horizontally nondivergent perturbations with a dominant zonally symmetric zonal velocity component. An argument for the sense and positioning of the jets relative to the equator is given in terms of inertial instability and the meridional mixing of planetary vorticity by the small zonal-scale components of the linearly unstable modes. In the long time evolution of the flow, if the amplitude of the westward equatorial jet becomes too great, zonally symmetric inertial instability limits the growth of the jets, and inertial adjustment leads to the homogenization of potential vorticity in latitude and depth around the equator.

scholarly journals Reynolds averaged Navier–Stokes modelling of long waves induced by a transient wave group on a beach

2010 ◽  
Vol 467 (2129) ◽  
pp. 1215-1242 ◽  
Author(s):  
Javier L. Lara ◽  
Andrea Ruju ◽  
Inigo J. Losada
Keyword(s):  
Surf Zone ◽  
Low Frequency ◽  
Short Wave ◽  
Long Waves ◽  
Navier Stokes ◽  
Type Model ◽  
Maker Movement ◽  
Wave Group ◽  
Transient Wave ◽  
Reynolds Averaged Navier Stokes

This paper presents the numerical modelling of the cross shore propagation of infragravity waves induced by a transient focused short wave group over a sloping bottom. A dataset obtained through new laboratory experiments in the wave flume of the University of Cantabria is used to validate the Reynolds averaged Navier–Stokes type model IH-2VOF. A new boundary condition based on the wave maker movement used in the experiments is implemented in the model. Shoaling and breaking of short waves as well as the enhancement of long waves and the energy transfer to low-frequency motion are well addressed by the model, proving the high accuracy in the reproduction of surf zone hydrodynamics. Under the steep slope regime, a long wave trough is radiated offshore from the breakpoint. Numerical simulations conducted for different bottom slopes and short wave steepness suggest that this low-frequency breakpoint generated wave is controlled by both the bed slope parameter and the Iribarren number. Moreover, the numerical model is used to investigate the influence that a large flat bottom induces on the propagation pattern of long waves.

The Spread of Pollutants from Harbour Sludge Depots

1984 ◽  
Vol 16 (3-4) ◽  
pp. 623-633
Author(s):  
M Loxham ◽  
F Weststrate
Keyword(s):  
Time Scales ◽  
Molecular Diffusion ◽  
Near Field ◽  
Parameter Analysis ◽  
Migration Patterns ◽  
Long Time ◽  
Dilution Effects ◽  
Short Time ◽  
Harbour Sludge

It is generally agreed that both the landfill option, or the civil techniques option for the final disposal of contaminated harbour sludge involves the isolation of the sludge from the environment. For short time scales, engineered barriers such as a bentonite screen, plastic sheets, pumping strategies etc. can be used. However for long time scales the effectiveness of such measures cannot be counted upon. It is thus necessary to be able to predict the long term environmenttal spread of contaminants from a mature landfill. A model is presented that considers diffusion and adsorption in the landfill site and convection and adsorption in the underlaying aquifer. From a parameter analysis starting form practical values it is shown that the adsorption behaviour and the molecular diffusion coefficient of the sludge, are the key parameters involved in the near field. The dilution effects of the far field migration patterns are also illustrated.

Far field modeling of the Mamala Bay outfalls

1998 ◽  
Vol 38 (10) ◽  
pp. 323-330
Author(s):  
Philip J. W. Roberts
Keyword(s):  
Field Model ◽  
Near Field ◽  
Far Field ◽  
Field Modeling ◽  
Visitation Frequency ◽  
Statistical Variation ◽  
Long Time ◽  
Harmonic Average ◽  
Ocean Outfall ◽  
Acoustic Doppler Current Profilers

The results of far field modeling of the wastefield formed by the Sand Island, Honolulu, ocean outfall are presented. A far field model, FRFIELD, was coupled to a near field model, NRFIELD. The input data for the models were long time series of oceanographic observations over the whole water column including currents measured by Acoustic Doppler Current Profilers and density stratification measured by thermistor strings. Thousands of simulations were made to predict the statistical variation of wastefield properties around the diffuser. It was shown that the visitation frequency of the wastefield decreases rapidly with distance from the diffuser. The spatial variation of minimum and harmonic average dilutions was also predicted. Average dilution increases rapidly with distance. It is concluded that any impact of the discharge will be confined to a relatively small area around the diffuser and beach impacts are not likely to be significant.

scholarly journals Occluded Grape Cluster Detection and Vine Canopy Visualisation Using an Ultrasonic Phased Array

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2182
Author(s):  
Baden Parr ◽  
Mathew Legg ◽  
Stuart Bradley ◽  
Fakhrul Alam
Keyword(s):  
Near Field ◽  
Low Frequency ◽  
Volume Estimation ◽  
Yield Estimation ◽  
3D Scan ◽  
Management Processes ◽  
Canopy Volume ◽  
Ultrasonic Phased Array ◽  
Added Benefit ◽  
Grape Yield

Grape yield estimation has traditionally been performed using manual techniques. However, these tend to be labour intensive and can be inaccurate. Computer vision techniques have therefore been developed for automated grape yield estimation. However, errors occur when grapes are occluded by leaves, other bunches, etc. Synthetic aperture radar has been investigated to allow imaging through leaves to detect occluded grapes. However, such equipment can be expensive. This paper investigates the potential for using ultrasound to image through leaves and identify occluded grapes. A highly directional low frequency ultrasonic array composed of ultrasonic air-coupled transducers and microphones is used to image grapes through leaves. A fan is used to help differentiate between ultrasonic reflections from grapes and leaves. Improved resolution and detail are achieved with chirp excitation waveforms and near-field focusing of the array. The overestimation in grape volume estimation using ultrasound reduced from 222% to 112% compared to the 3D scan obtained using photogrammetry or from 56% to 2.5% compared to a convex hull of this 3D scan. This also has the added benefit of producing more accurate canopy volume estimations which are important for common precision viticulture management processes such as variable rate applications.

scholarly journals Electromagnetic power of lightning superbolts from Earth to space

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
J.-F. Ripoll ◽  
T. Farges ◽  
D. M. Malaspina ◽  
G. S. Cunningham ◽  
E. H. Lay ◽  
...  
Keyword(s):  
Low Frequency ◽  
Optical Emission ◽  
High Energy ◽  
Very Low Frequency ◽  
Electromagnetic Power ◽  
Power Spectral ◽  
High Energy Tail ◽  
Van Allen Probes ◽  
Long Time ◽  
Low Frequency Waves

AbstractLightning superbolts are the most powerful and rare lightning events with intense optical emission, first identified from space. Superbolt events occurred in 2010-2018 could be localized by extracting the high energy tail of the lightning stroke signals measured by the very low frequency ground stations of the World-Wide Lightning Location Network. Here, we report electromagnetic observations of superbolts from space using Van Allen Probes satellite measurements, and ground measurements, and with two events measured both from ground and space. From burst-triggered measurements, we compute electric and magnetic power spectral density for very low frequency waves driven by superbolts, both on Earth and transmitted into space, demonstrating that superbolts transmit 10-1000 times more powerful very low frequency waves into space than typical strokes and revealing that their extreme nature is observed in space. We find several properties of superbolts that notably differ from most lightning flashes; a more symmetric first ground-wave peak due to a longer rise time, larger peak current, weaker decay of electromagnetic power density in space with distance, and a power mostly confined in the very low frequency range. Their signal is absent in space during day times and is received with a long-time delay on the Van Allen Probes. These results have implications for our understanding of lightning and superbolts, for ionosphere-magnetosphere wave transmission, wave propagation in space, and remote sensing of extreme events.

Analytical Solution for Rotational Rub-Impact Plate Under Thermal Shock

2016 ◽  
Vol 32 (3) ◽  
pp. 297-311
Author(s):  
T.-Y. Zhao ◽  
H.-Q. Yuan ◽  
B.-B. Li ◽  
Z.-J. Li ◽  
L.-M. Liu
Keyword(s):  
Thermal Shock ◽  
High Frequency ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Cantilever Plate ◽  
Analysis Method ◽  
Multiple Frequency ◽  
Width Direction ◽  
Blade Tip ◽  
High Frequency Vibrations

AbstractThe analysis method is developed to obtain dynamic characteristics of the rotating cantilever plate with thermal shock and tip-rub. Based on the variational principle, equations of motion are derived considering the differences between rubbing forces in the width direction of the plate. The transverse deformation is decomposed into quasi-static deformation of the cantilever plate with thermal shock and dynamic deformation of the rubbing plate under thermal shock. Then deformations are obtained through the calculation of modal characteristics of rotating cantilever plate and temperature distribution function. Special attention is paid to the influence of tip-rub and thermal shock on the plate. The results show that tip-rub has the characteristics of multiple frequency vibrations, and high frequency vibrations are significant. On the contrary, thermal shock shows the low frequency vibrations. The thermal shock makes the rubbing plate gradually change into low frequency vibrations. Because rub-induced vibrations are more complicated than those caused by thermal shock, tip-rub is easier to result in the destruction of the blade. The increasing friction coefficient intensifies vibrations of the rubbing plate. Minimizing friction coefficients can be an effective way to reduce rub-induced damage through reducing the surface roughness between the blade tip and the inner surface of the casing.

Self-diffusion of bimodal suspensions of hydrodynamically interacting spherical particles in shearing flow

1994 ◽  
Vol 281 ◽  
pp. 51-80 ◽  
Author(s):  
Chingyi Chang ◽  
Robert L. Powell
Keyword(s):  
Diffusion Coefficients ◽  
Cluster Size ◽  
Near Field ◽  
Spherical Particles ◽  
Random Structure ◽  
Shearing Flow ◽  
Self Diffusion ◽  
Long Time ◽  
Mobility Matrix ◽  
Many Body Interactions

We study the average mobilities and long-time self-diffusion coefficients of a suspension of bimodally distributed spherical particles. Stokesian dynamics is used to calculate the particle trajectories for a monolayer of bimodal-sized spheres. Hydrodynamic forces only are considered and they are calculated using the inverse of the grand mobility matrix for far-field many-body interactions and lubrication formulae for near-field effects. We determine both the detailed microstructure (e.g. the pair-connectedness function and cluster formation) and the macroscopic properties (e.g. viscosity and self-diffusion coefficients). The flow of an ‘infinite’ suspension is simulated by considering 25, 49, 64 and 100 particles to be one ‘cell’ of a periodic array. Effects of both the size ratio and the relative fractions of the different-sized particles are examined. For the microstructures, the pair-connectedness function shows that the particles form clusters in simple shearing flow due to lubrication forces. The nearly symmetric angular structures imply the absence of normal stress differences for a suspension with purely hydrodynamic interactions between spheres. For average mobilities at infinite Péclet number, Ds0, our simulation results suggest that the reduction of Ds0 as concentration increases is directly linked to the influence of particle size distribution on the average cluster size. For long-time self-diffusion coefficients, Ds∞, we found good agreement between simulation and experiment (Leighton & Acrovos 1987 a; Phan and Leighton 1993) for monodispersed suspensions. For bimodal suspensions, the magnitude of Ds∞, and the time to reach the asymptotic diffusive behaviour depend on the cluster size formed in the system, or the viscosity of the suspension. We also consider the effect of the initial configuration by letting the spheres be both organized (size segregated) and randomly placed. We find that it takes a longer time for a suspension with an initially organized structure to achieve steady state than one with a random structure.

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