ABOUT HEAD WAVES AND UNDER-SURFACE LONGITUDINAL WAVES, RADIATED BY THE NORMAL PROBE WHICH IS TAKING PLACE ON A FREE FLAT SURFACE OF THE ELASTIC ENVIRONMENT

2021 ◽  
pp. 4-19
Author(s):  
V. N. Danilov
Keyword(s):  
Longitudinal Wave ◽  
Flat Surface ◽  
Wave Number ◽  
Head Wave ◽  
Directivity Characteristic ◽  
Longitudinal Waves ◽  
Local Maxima ◽  
Normal Probe ◽  
Geometrical Acoustics ◽  
Head Waves

On the basis of integrated representations Fourier–Bessel a component of displacement of elastic waves, radiating by the normal converter which is taking place on a free flat surface of the elastic environment, receives analytical estimations of displacement a under-surface longitudinal and head (it is surface-longitudinal) waves. Components of displacement a under-surface longitudinal wave are the sum a component in approximation of geometrical acoustics (GA), the diffraction amendments to this approximation and the amendments which are taking into account influence of feature when the parameter of integrated representation is equal to wave number of a longitudinal wave. Components of displacement of a head wave are defined as the sum appropriate diffraction amendments for a component of displacement of a volumetric longitudinal wave in approximation GA and a component of displacement of a lateral wave. The maximum of amplitude of displacement a under-surface longitudinal wave in angular area of a direction of distribution near to a free surface of environment is caused by one of local maxima of the directivity characteristic of the normal probe. Thus dependence of change of amplitude of this wave of distance wave from the centre of the probe practically corresponds to similar dependence for displacement of a volumetric longitudinal wave in GA approximation. Quantitative estimations of maxima of amplitude of displacement under-surface longitudinal and head waves concerning the greatest amplitude, radiated by the normal probe of a volumetric longitudinal wave.

Analysis and Interpretation of Longitudinal Waves in Periodic Multiphase Rods Using the Method of Reverberation-Ray Matrix Combined With the Floquet-Bloch Theorem

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Y. Q. Guo ◽  
D. N. Fang
Keyword(s):  
Phase Velocity ◽  
Longitudinal Wave ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Wave Number ◽  
Wave Band ◽  
Frequency Wave ◽  
Longitudinal Waves ◽  
Bloch Theorem ◽  
Velocity Spectra

The method of reverberation-ray matrix (MRRM) combined with the Floquet–Bloch theorem, which serves as an alternative method, is presented for accurately analyzing longitudinal waves in general periodic multiphase rods. Closed-form dispersion relation of periodic quaternary rods is derived. Based on this relation, the functions of constituent-rod parameters in the formation of longitudinal-wave band structures are analytically revealed. Numerical examples validate the proposed method and indicate the characteristics/applications of all kinds of dispersion curves that include the frequency-wave number spectra, the frequency-wavelength spectra, the frequency-phase velocity spectra, the wave number-phase velocity spectra and the wavelength-phase velocity spectra. The effect of unit-cell layout on the frequency band properties and the functions of constituent-rod parameters in the band structure formation are also illustrated numerically. The analysis and interpretation of longitudinal waves in periodic multiphase rods given in this paper will push forward the design of periodic structures for longitudinal wave filtering/guiding and vibration isolation/control applications.

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

Dynamic properties of reflected and head waves near the critical point

1979 ◽  
Vol 16 (7) ◽  
pp. 1388-1401 ◽  
Author(s):  
Larry W. Marks ◽  
F. Hron
Keyword(s):  
Exact Solution ◽  
High Frequency ◽  
Classical Problem ◽  
Plane Boundary ◽  
Head Wave ◽  
Disk File ◽  
Ray Theory ◽  
Computational Point ◽  
Spherical Waves ◽  
Head Waves

The classical problem of the incidence of spherical waves on a plane boundary has been reformulated from the computational point of view by providing a high frequency approximation to the exact solution applicable to any seismic body wave, regardless of the number of conversions or reflections from the bottoming interface. In our final expressions the ray amplitude of the interference reflected-head wave is cast in terms of a Weber function, the numerical values of which can be conveniently stored on a computer disk file and retrieved via direct access during an actual run. Our formulation also accounts for the increase of energy carried by multiple head waves arising during multiple reflections of the reflected wave from the bottoming interface. In this form our high frequency expression for the ray amplitude of the interference reflected-head wave can represent a complementary technique to asymptotic ray theory in the vicinity of critical regions where the latter cannot be used. Since numerical tests indicate that our method produces results very close to those obtained by the numerical integration of the exact solution, its combination with asymptotic ray theory yields a powerful technique for the speedy computation of synthetic seismograms for plane homogeneous layers.

Exact seismograms for a point force using generalized ray theory

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1421-1427 ◽  
Author(s):  
E. R. Kanasewich ◽  
P. G. Kelamis ◽  
F. Abramovici
Keyword(s):  
Half Space ◽  
Near Field ◽  
Sedimentary Basins ◽  
Transverse Component ◽  
Point Force ◽  
Seismic Exploration ◽  
Head Wave ◽  
Vertical Force ◽  
Low Velocity ◽  
Head Waves

Exact synthetic seismograms are obtained for a simple layered elastic half‐space due to a buried point force and a point torque. Two models, similar to those encountered in seismic exploration of sedimentary basins, are examined in detail. The seismograms are complete to any specified time and make use of a Cagniard‐Pekeris method and a decomposition into generalized rays. The weathered layer is modeled as a thin low‐velocity layer over a half‐space. For a horizontal force in an arbitrary direction, the transverse component, in the near‐field, shows detectable first arrivals traveling with a compressional wave velocity. The radial and vertical components, at all distances, show a surface head wave (sP*) which is not generated when the source is compressive. A buried vertical force produces the same surface head wave prominently on the radial component. An example is given for a simple “Alberta” model as an aid to the interpretation of wide angle seismic reflections and head waves.

scholarly journals Microseismic hydraulic fracture imaging in the Marcellus Shale using head waves

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. KS1-KS10 ◽  
Author(s):  
Zhishuai Zhang ◽  
James W. Rector ◽  
Michael J. Nava
Keyword(s):  
Marcellus Shale ◽  
P Wave ◽  
Head Wave ◽  
Wave Polarization ◽  
Horizontal Section ◽  
Location Accuracy ◽  
Arrival Times ◽  
Microseismic Data ◽  
Head Waves ◽  
Event Location

We have studied microseismic data acquired from a geophone array deployed in the horizontal section of a well drilled in the Marcellus Shale near Susquehanna County, Pennsylvania. Head waves were used to improve event location accuracy as a substitution for the traditional P-wave polarization method. We identified that resonances due to poor geophone-to-borehole coupling hinder arrival-time picking and contaminate the microseismic data spectrum. The traditional method had substantially greater uncertainty in our data due to the large uncertainty in P-wave polarization direction estimation. We also identified the existence of prominent head waves in some of the data. These head waves are refractions from the interface between the Marcellus Shale and the underlying Onondaga Formation. The source location accuracy of the microseismic events can be significantly improved by using the P-, S-wave direct arrival times and the head wave arrival times. Based on the improvement, we have developed a new acquisition geometry and strategy that uses head waves to improve event location accuracy and reduce acquisition cost in situations such as the one encountered in our study.

Experiments and Computations for KCS Added Resistance for Variable Heading

2015 ◽  
Author(s):  
Hamid Sadat-Hosseini ◽  
Serge Toxopeus ◽  
Dong Hwan Kim ◽  
Teresa Castiglione ◽  
Yugo Sanada ◽  
...  
Keyword(s):  
Surface Profile ◽  
Engine Performance ◽  
Head Wave ◽  
Added Resistance ◽  
Local Flow ◽  
Wake Field ◽  
Head Waves ◽  
Calm Water ◽  
Free Surface Profile ◽  
Peak Location

Experiments, CFD and PF studies are performed for the KCS containership advancing at Froude number 0.26 in calm water and regular waves. The validation studies are conducted for variable wavelength and wave headings with wave slope of H/λ=1/60. CFD computations are conducted using two solvers CFDShip-Iowa and STAR-CCM+. PF studies are conducted using FATIMA. For CFD computations, calm water and head wave simulations are performed by towing the ship fixed in surge, sway, roll and yaw, but free to heave and pitch. For variable wave heading simulations, the roll motion is also free. For PF, the ship model moves at a given speed and the oscillations around 6DOF motions are computed for variable wave heading while the surge motion for head waves is restrained by adding a very large surge damping. For calm water, computations showed E<4%D for the resistance,<8%D for the sinkage, and <40%D for the trim. In head waves with variable wavelength, the errors for first harmonic variables for CFD and PF computations were small, <5%DR for amplitudes and <4%2π for phases. The errors for zeroth harmonics of motions and added resistance were large. For the added resistance, the largest error was for the peak location at λ/L=1.15 where the data also show large scatter. For variable wave heading at λ/L=1.0, the errors for first harmonic amplitudes were <17%DR for CFD and <26%DR for PF. The comparison errors for first harmonic phases were E<24%2π. The errors for the zeroth harmonic of motions and added resistance were again large. PF studies for variable wave headings were also conducted for more wavelength condition, showing good predictions for the heave and pitch motions for all cases while the surge and roll motions and added resistance were often not well predicted. Local flow studies were conducted for λ/L=1.37 to investigate the free surface profile and wake field predicted by CFD. The results showed a significant fluctuation in the wake field which can affect the propeller/engine performance. Additionally it was found that the average propeller inflow to the propeller is significantly higher in waves.

Longitudinal Waves in a Submerged Cylindrical Rod 1

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
G. Iosilevskii
Keyword(s):  
Boundary Layer ◽  
Wave Number ◽  
Analytical Relation ◽  
Velocity Of Sound ◽  
Longitudinal Displacement ◽  
Wave Propagation Velocity ◽  
Longitudinal Waves ◽  
Short Waves ◽  
The Waves ◽  
Surrounding Fluid

This study is concerned with longitudinal displacement waves propagating in an elastic cylindrical rod submerged in a viscous fluid. Provided that the wave propagation velocity in the rod is small compared with the velocity of sound in the surrounding fluid and the wavelength is large compared with the thickness of the boundary layer around the rod, an analytical relation is obtained between the wave number and the frequency. The presence of the fluid makes the waves disperse—the short waves become faster than the long ones.

Numerical simulation of internal defect imaging with the longitudinal wave generated by laser induced ultrasonic array

2020 ◽  
pp. 2150103
Author(s):  
Hao Sui ◽  
Kesi Li ◽  
Zhenyu Zhu ◽  
Le Cheng ◽  
Xiaorong Gao ◽  
...  
Keyword(s):  
Longitudinal Wave ◽  
Phased Arrays ◽  
Synthetic Aperture ◽  
Wave Component ◽  
The Finite Element Method ◽  
Internal Defect ◽  
Longitudinal Waves ◽  
Synthetic Aperture Focusing ◽  
Synthetic Aperture Focusing Technique ◽  
Defect Imaging

To verify the performance of longitudinal waves induced by laser phased arrays (LPA) for detection and quantitative evaluation in internal defects, the finite element method (FEM) is utilized to establish the models of LPA scanning processing. The interaction of longitudinal wave and internal defect is analyzed. Besides, the two components of the reflected longitudinal waves (the longitudinal wave component [Formula: see text] and the shear wave component [Formula: see text] are focused on the imaging of defects with the synthetic aperture focusing technique (SAFT) and total focusing method (TFM) algorithms. It shows that the imaging of internal sub-millimeter defect is obtained using the LPA. The defect size and location are simultaneously calculated, with the relative error being 6.7% and 2.9%, respectively. The proposed longitudinal wave-based LPA is a promising method for the imaging and evaluation of internal micro defects.

scholarly journals A Study on Fatigue State Evaluation of Rail by the Use of Ultrasonic Nonlinearity

Materials ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 2698
Author(s):  
Bo Zhu ◽  
Jaesun Lee
Keyword(s):  
Longitudinal Wave ◽  
Second Harmonic ◽  
Early Stage ◽  
Wave Mixing ◽  
Third Harmonic ◽  
Longitudinal Waves ◽  
Testing Method ◽  
State Evaluation ◽  
Stress Fatigue ◽  
Train Safety

Nonlinear ultrasonic testing has been accepted as a promising manner for evaluating material integrity in an early stage. Stress fatigue is the main threats to train safety, railways examinations for stress fatigue are more significant and necessary. A series of ultrasonic nonlinear wave experiments are conducted for rail specimens extracted from railhead with different degree of fatigue produced by three-point bent loading condition. The nonlinear parameter is the indicator of nonlinear waves for expressing the degree the fatigue. The experimental results show that the sensitivity of a third harmonic longitudinal wave is higher than second harmonic longitudinal wave testing. As the same time, collinear wave mixing shows strong relative with fatigue damages than a second longitudinal wave nondestructive testing (NDT) method and provides more reliable results than third harmonic longitudinal waves nonlinear testing method.

Compressional head waves in attenuative formations: Forward modeling and inversion

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1908-1920 ◽  
Author(s):  
Qing‐Huo Liu ◽  
Chung Chang
Keyword(s):  
Radiation Condition ◽  
Forward Modeling ◽  
Head Wave ◽  
Transmission Measurement ◽  
Processing Scheme ◽  
Straightforward Application ◽  
Head Waves ◽  
Simple Processing ◽  
The Individual ◽  
Branch Cut

We develop a method of forward modeling and inverting formation attenuation data from sonic compressional head waves in a fluid‐filled borehole using a branch‐cut integration (BCI) technique to calculate individual acoustic arrivals. We validate this approach with a real‐ axis integration (RAI) method that does not separate the individual arrivals. We show that the straightforward application of the original BCI method for lossless media gives erroneous results for attenuative formations. With a choice of the Riemann sheets satisfying the radiation condition, the new BCI method gives correct results for most lossy and lossless formations. However, modeling very slow formations needs to include the contribution of a leaky pole near the vertical branch cut. With a constant‐Q assumption, we develop a simple processing scheme to extract the formation compressional Q factor from the P head‐wave arrivals. We used experimental data from laboratory‐scale borehole measurements to invert for the compressional Q value of a Lucite block. The inverted results agree within 4.5% of an independent ultrasonic transmission measurement of Q.

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