scholarly journals Scattering of Surface Waves by a Three-Dimensional Cavity of Arbitrary Shape: Analytical and Experimental Studies

2019 ◽  
Vol 9 (24) ◽  
pp. 5459 ◽  
Author(s):  
Jaesun Lee ◽  
VanTrung Ngo ◽  
Haidang Phan ◽  
TruongGiang Nguyen ◽  
Duy Kien Dao ◽  
...  
Keyword(s):  
Surface Waves ◽  
Cylindrical Cavity ◽  
Arbitrary Shape ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Scattered Wave ◽  
Ultrasonic Pulse ◽  
Elastic Half Space ◽  
Cavity Surface ◽  
Vertical Displacements

The scattering of surface waves by a three-dimensional shallow cavity of arbitrary shape at the surface of a homogenous, isotropic, linearly elastic half-space is theoretically investigated. A novel analytical approach based on a reciprocity consideration is introduced in this article to determine the particle displacements of the scattered wave field generated by the interaction between the surface waves and the cavity. In the usual manner, the scattered field was shown to be equivalent to the radiation from the distribution of tractions, calculated from the incident wave, on the surface of the cavity. The radiation of surface waves subjected to the computed tractions applied at a single location was found using reciprocity theorems. The field scattered by the cavity was subsequently obtained from the superposition of displacements due to all the forces applied on the cavity surface. Solutions for the scattering of surface waves by a spherical, a circular cylindrical (coin-shaped) and a square cylindrical cavity are presented in detail. We here derive the closed-form expressions of the displacement amplitudes, which represent the far-field scattered waves produced by each of the cavities. An experimental setup using the ultrasonic pulse-echo technique was then carried out to record the scattered echoes of surface waves from these cavities in order to provide practical validation of the analytical findings. The vertical displacements measured at a significant distance of about twenty-five wavelengths from the cavities of the same width and different depth were compared with the corresponding theoretical predictions. The comparisons show excellent agreement for the case of a spherical cavity and good agreement in the cases of a circular and a cylindrical cavity in terms of trends and magnitudes. It is followed by a discussion on the results of the comparison and the limitations of the proposed approach regarding the degree of smoothness and the size of cavity.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

ISOCHRONS FOR A THREE‐DIMENSIONAL SEISMIC SYSTEM

Geophysics ◽  
1971 ◽  
Vol 36 (6) ◽  
pp. 1099-1137 ◽  
Author(s):  
J. W. Dunkin ◽  
F. K. Levin
Keyword(s):  
Surface Waves ◽  
Arbitrary Shape ◽  
Average Velocity ◽  
Three Dimensional ◽  
Dimensional System ◽  
Ray Geometry ◽  
Three Dimensional System ◽  
Seismic System

The three‐dimensional seismic system discussed by Walton (1970–1971) explores seismically a column of earth extending from the surface to deep reflectors. Interpretation of data from the system is done directly from displays on a grid of the detected signals. In this paper we derive expressions for the patterns expected on three‐dimensional system displays when energy returning to the detectors consists of reflections from planes, diffractions from faults or point scatterers, reflections from reflectors of arbitrary shape, refractions and reflected‐refractions from planes, or direct or surface waves. Examples of typical patterns are shown. Our derivations are limited to ray geometry and shed no light on amplitude variations. Also, an average velocity from the surface to a reflector, refractor, or diffractor is assumed.

Elementary solutions to Lamb's problem for a point source and their relevance to three-dimensional studies of spontaneous crack propagation

1979 ◽  
Vol 69 (4) ◽  
pp. 947-956
Author(s):  
Paul G. Richards
Keyword(s):  
Free Surface ◽  
Arbitrary Shape ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
P Wave ◽  
Displacement Discontinuity ◽  
Shear Cracks ◽  
Lamb’S Problem ◽  
Square Roots ◽  
Tension Cracks

abstract Certain exact solutions to Lamb's problem (the transient response of an elastic half-space to a force applied at a point) involve the computation merely of three square roots, and about ten arithmetic operations (+, −, ×, /). They arise when both source and receiver lie on the free surface. It is just these solutions which are needed in a method due to Hamano for obtaining the slip function (displacement discontinuity), as a function of space and time, for planar tension cracks and shear cracks which grow spontaneously with arbitrary shape. The solutions are described here in detail, for an elastic medium with general Poisson's ratio. They include perhaps the simplest-possible example of the P-wave.

Three-dimensional flow structures in laminar falling liquid films

2014 ◽  
Vol 743 ◽  
pp. 75-123 ◽  
Author(s):  
Georg F. Dietze ◽  
W. Rohlfs ◽  
K. Nährich ◽  
R. Kneer ◽  
B. Scheid
Keyword(s):  
Surface Waves ◽  
Stokes Equations ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Liquid Films ◽  
Capillary Waves ◽  
Flow Structures ◽  
Two Dimensional ◽  
Viscous Forces ◽  
Falling Liquid Films

AbstractFull numerical simulations of the Navier–Stokes equations for four cases of vertically falling liquid films with three-dimensional surface waves have been performed. Flow conditions are based on several previous experimental studies where the streamwise and spanwise wavelengths were imposed, which we exploit by simulating periodic wave segments. The considered flows are laminar but approach conditions at which intermittent wave-induced turbulence has been observed elsewhere. Working liquids range from water to silicone oil and cover a large interval of the Kapitza number ($\textit {Ka}=18\mbox{--}3923$), which relates capillary to viscous forces. Simulations were performed on a supercomputer, using a finite-volume code and the volume of fluid and continuum surface force methods to account for the multiphase nature of the flow. Our results show that surface waves, consisting of large horseshoe-shaped wave humps concentrating most of the liquid and preceded by capillary ripples on a thin residual film, segregate the flow field into two regions: an inertia-dominated one in the large humps, where the local Reynolds number is up to five times larger than its mean value, and a visco-capillary region, where capillary and/or viscous forces dominate. In the inertial region, an intricate structure of different-scale vortices arises, which is more complicated than film thickness variations there suggest. Conversely, the flow in the visco-capillary region of large-$\textit {Ka} $ fluids is entirely governed by the local free-surface curvature through the action of capillary forces, which impose the pressure distribution in the liquid film. This results in flow separation zones underneath the capillary troughs and a spanwise cellular flow pattern in the region of capillary wave interference. In some cases, capillary waves bridge the large horseshoe humps in the spanwise direction, coupling the two aforementioned regions and leading the flow to oscillate between three- and two-dimensional wave patterns. This persists over long times, as we show by simulations with the low-dimensional model of Scheid et al. (J. Fluid Mech., vol. 562, 2006, pp. 183–222) after satisfactory comparison with our direct simulations at short times. The governing mechanism is connected to the bridging capillary waves, which drain liquid from the horseshoe humps, decreasing their amplitude and wave speed and causing them to retract in the streamwise direction. Overall, it is observed that spanwise flow structures (not accounted for in two-dimensional investigations) are particularly complex due to the absence of gravity in this direction.

Calculation of ground motion in a three-dimensional model of the 1966 Parkfield earthquake

1976 ◽  
Vol 66 (2) ◽  
pp. 405-423
Author(s):  
N. A. Levy ◽  
A. K. Mal
Keyword(s):  
Surface Waves ◽  
Ground Motion ◽  
Near Field ◽  
Three Dimensional ◽  
Vertical Component ◽  
Elastic Half Space ◽  
The Body ◽  
Body Waves ◽  
Three Dimensional Model ◽  
Ground Displacements

abstract Near-field ground displacements are calculated from an earthquake source in a homogeneous, elastic half-space. An analytical formulation of the problem is presented that requires no physical approximations except at the source. A model of the source is constructed by retaining the essential kinematic character of the faulting process. A computer program is developed to calculate ground motion from an assumed model of the 1966 Parkfield, California earthquake. Favorable agreement is obtained between the theoretically computed ground displacements and those derived from the recorded accelerations. The relative contributions of the body waves and surface waves to the displacement field are examined. The results indicate that a significant portion of near-field motion may consist of surface waves, especially in the vertical component of the ground motion.

scholarly journals The Hydration, Mechanical, Autogenous Shrinkage, Durability, and Sustainability Properties of Cement–Limestone–Slag Ternary Composites

2021 ◽  
Vol 13 (4) ◽  
pp. 1881
Author(s):  
Mei-Yu Xuan ◽  
Yi Han ◽  
Xiao-Yong Wang
Keyword(s):  
Compressive Strength ◽  
Electrical Resistivity ◽  
Experimental Studies ◽  
Autogenous Shrinkage ◽  
Ultrasonic Pulse Velocity ◽  
Ultrasonic Pulse ◽  
Pulse Velocity ◽  
Hydration Heat ◽  
Granulated Blast Furnace Slag ◽  
Binder Ratio

This study examines the hydration–mechanical–autogenous shrinkage–durability–sustainability properties of ternary composites with limestone filler (LF) and ground-granulated blast furnace slag (BFS). Four mixtures were prepared with a water/binder ratio of 0.3 and different replacement ratios varying from 0 to 45%. Multiple experimental studies were performed at various ages. The experimental results are summarized as follows: (1) As the replacement levels increased, compressive strength and autogenous shrinkage (AS) decreased, and this relationship was linear. (2) As the replacement levels increased, cumulative hydration heat decreased. At the age of 3 and 7 days, there was a linear relationship between compressive strength and cumulative hydration heat. (3) Out of all mixtures, the ultrasonic pulse velocity (UPV) and electrical resistivity exhibited a rapid increase in the early stages and tended to slow down in the latter stages. There was a crossover of UPV among various specimens. In the later stages, the electrical resistivity of ternary composite specimens was higher than plain specimens. (4) X-ray diffraction (XRD) results showed that LF and BFS have a synergistic effect. (5) With increasing replacement ratios, the CO2 emissions per unit strength reduced, indicating the sustainability of ternary composites.

Sign in / Sign up

Export Citation Format

Share Document