TRANSMISSION AND REFLECTION OF RAYLEIGH WAVES BY WEDGES

Geophysics ◽  
1960 ◽  
Vol 25 (6) ◽  
pp. 1203-1214 ◽  
Author(s):  
L. Knopoff ◽  
A. F. Gangi
Keyword(s):  
Incident Wave ◽  
Line Source ◽  
Rayleigh Waves ◽  
Wave Form ◽  
Reflected Waves ◽  
Wave Shapes ◽  
Transmission And Reflection

Experimental observations have been made of the transmission and reflection of Rayleigh waves by wedges. Results are reported for Rayleigh waves in aluminum wedges. It is observed that the wave shapes of the transmitted and reflected waves differ from that of the incident wave and depend on the angle of the wedge. The change of shape is attributed to an interference between part of the incident wave‐form and the radiation from a line source placed at the vertex. A procedure is given for the calculation of the partition between the two terms.

Transmission of Rayleigh waves at a corner

1966 ◽  
Vol 56 (2) ◽  
pp. 455-466 ◽  
Author(s):  
A. K. Mal ◽  
L. Knopoff
Keyword(s):  
Integral Equations ◽  
Rayleigh Waves ◽  
Wedge Angle ◽  
Body Waves ◽  
Algebraic Equations ◽  
Reflected Waves ◽  
Transmission And Reflection Coefficients ◽  
Transmitted Waves ◽  
New Feature ◽  
Transmission And Reflection

abstract Using a Green's function method of approximation, transmission and reflection coefficients are computed for the problem of Rayleigh waves normally incident upon the corner of a homogeneous elastic wedge formed by two stress-free planes. The Rayleigh waves are incident from infinity and travel along one surface of the wedge. The transmitted waves on the second surface and the reflected waves on the first surface are calculated by the application of Huygens' principle. A pair of coupled integral equations for the displacements are obtained by means of a representation theorem. Neglecting the diffracted body waves near the corner, the coupled integral equations are reduced to a pair of algebraic equations. A new feature of the calculation involves consideration of diffracted surface waves travelling toward the vertex. Numberical values of the phase shifts and attenuation factors in the transmitted and reflected waves are computed as functions of the wedge angle. Comparison with experimental results show considerably better agreement than has been obtained previously.

scholarly journals A Broadband Ultrathin Nonlinear Switching Metamaterial

2017 ◽  
Vol 6 (2) ◽  
pp. 64
Author(s):  
E. Zarnousheh Farahani ◽  
S. Jarchi ◽  
A. Keshtkar
Keyword(s):  
Incident Wave ◽  
Optimization Method ◽  
Resonant Mode ◽  
Unit Cell ◽  
Incident Power ◽  
Full Wave ◽  
Effective Impedance ◽  
Nonlinear Simulations ◽  
Switching Property ◽  
Transmission And Reflection

In this paper, an ultrathin planar nonlinear metamaterial slab is designed and simulated. Nonlinearity is provided through placing diodes in each metamaterial unit cell. The diodes are auto-biased and activated by an incident wave. The proposed structure represents a broadband switching property between two transmission and reflection states depending on the intensity of the incident wave. High permittivity values are presented creating a near zero effective impedance at low power states, around the second resonant mode of the structure unit cell; as the result, the incident wave is reflected. Increasing the incident power to the level which can activate the loaded diodes in the structure results in elimination of the resonance and consequently a drop in the permittivity values near the permeability one as well as a switch to the transmission state. A full wave as well as a nonlinear simulations are performed. An optimization method based on weed colonization is applied to the unit cell of the metamaterial slab to achieve the maximum switching bandwidth. The structure represents a 24% switching bandwidth of a 10 dB reduction in the reflection coefficient.

Scattering of plane elastic waves at rough surfaces. II

1963 ◽  
Vol 59 (1) ◽  
pp. 231-248 ◽  
Author(s):  
Iya Abubakar
Keyword(s):  
Incident Wave ◽  
Elastic Waves ◽  
Rayleigh Waves ◽  
Irregular Surfaces ◽  
Elliptic Orbits ◽  
Incident Plane ◽  
Diffraction Of Elastic Waves ◽  
Axis Of Symmetry ◽  
Point Of Intersection ◽  
Second Wave

AbstractThis is a continuation of (1) on the two-dimensional problem of the diffraction of elastic waves by irregular surfaces. The effect of an irregular surface with an isolated irregularity like a trough or ditch on incident plane harmonic P- and SV-waves is discussed. The maximum depth of the ditch is assumed small compared to the wavelength of the incident wave.It is found that, when either a P- or an SV-wave is incident on such a boundary, besides the specularly reflected P- and SV-waves whose amplitudes are independent of the curvature of the surface there exist scattered waves travelling in various directions. In particular the diffracted zone contains the following second wave-types whose amplitudes are proportional to the depth of the ditch: (i) direct reflected P- and SV-waves, which at large distances appear to diverge from the point of intersection of the axis of symmetry of the ditch and the horizontal plane asymptotic to the boundary if the ratio of the wavelength of the incident wave to the half-width of the ditch is large. If the ratio is small these waves are reflected in the specular directions, (ii) A ‘secondary S-wave’ which finishes as P having travelled most of the way as an SV-wave. Its energy is confined to the neighbourhood of the free surface, (iii) A secondary P-wave which travels along the surface and finally emerges into the medium as an SV-wave at the critical angle for the medium, (iv) Rayleigh waves whose particle motion is in elliptic orbits.

scholarly journals EXTENSION OF THE PUFEM TO ELASTIC WAVE PROPAGATION IN LAYERED MEDIA

2012 ◽  
Vol 20 (02) ◽  
pp. 1240006 ◽  
Author(s):  
O. LAGHROUCHE ◽  
A. EL-KACIMI ◽  
J. TREVELYAN
Keyword(s):  
Finite Element Method ◽  
Elastic Wave ◽  
Rayleigh Waves ◽  
Partition Of Unity ◽  
Elastic Media ◽  
Elastic Wave Equation ◽  
Wave Problems ◽  
Numer Math ◽  
Basis Decomposition ◽  
Transmission And Reflection

This work deals with the extension of the partition of unity finite element method (PUFEM) "(Comput. Meth. Appl. Mech. Eng.139 (1996) pp. 289–314; Int. J. Numer. Math. Eng.40 (1997) 727–758)" to solve wave problems involving propagation, transmission and reflection in layered elastic media. The proposed method consists of applying the plane wave basis decomposition to the elastic wave equation in each layer of the elastic medium and then enforce necessary continuity conditions at the interfaces through the use of Lagrange multipliers. The accuracy and effectiveness of the proposed technique is determined by comparing results for selected problems with known analytical solutions. Complementary results dealing with the modeling of pure Rayleigh waves are also presented where the PUFEM model incorporates information about the pressure and shear waves rather than the Rayleigh wave itself.

Kelvin wave attenuation along nearly straight boundaries

1972 ◽  
Vol 53 (2) ◽  
pp. 273-286 ◽  
Author(s):  
H. G. Pinsent
Keyword(s):  
Incident Wave ◽  
Wave Attenuation ◽  
Plane Waves ◽  
Kelvin Waves ◽  
Kelvin Wave ◽  
Incident Wavelength ◽  
Reflected Waves ◽  
Linearized Theory ◽  
Coastal Boundary ◽  
Wave Problems

Two related wave problems are considered for a rotating sea of nearly uniform depth bounded by a coastline which is nearly straight. The depth changes are assumed to be independent of the distance from the coastline. The first problem, which is concerned with the origin of Kelvin waves in a coastal wave record, deals with a system of plane waves incident on the coastline and giving rise, in addition to reflected waves, to a Kelvin wave moving along the coast. Linearized theory is used to obtain details of the Kelvin wave for arbitrary perturbations in coastline and depth. Results suggest that the depth changes have their greatest effect in producing Kelvin waves if the incident wave crests are nearly parallel, but not exactly so, to the line of the depth changes. On the other hand when the wave crests are parallel to the coast, Kelvin waves are produced only by changes in the coastal boundary. In the second problem a Kelvin waye is assumed to be the incident wave. To find the energy propagated away from the coastline it is necessary to extend the theory to second order in the perturbations. It is shown that for a fixed wave period less than a pendulum day this energy has a maximum for a perturbation whose length is of comparable magnitude to the incident wavelength. Finally, the theory is applied to Kelvin waves propagating along the Californian coastline. Results obtained tend to confirm the suspicion that coastal irregularities are responsible for certain anomalies detected in tidal wave constituents by Munk, Snodgrass & Wimbush (1970).

scholarly journals Reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids

2021 ◽  
Author(s):  
Pham Chi Vinh ◽  
Do Xuan Tung ◽  
Nguyen Thi Kieu
Keyword(s):  
Incident Wave ◽  
Elastic Layer ◽  
Incident Angle ◽  
P Wave ◽  
Rough Interface ◽  
Elastic Solids ◽  
P Waves ◽  
Reflection And Transmission ◽  
Reflected Waves ◽  
Transmission Coefficients

This paper deals with the reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids. The interface is assumed to oscillate between two straight lines. By mean of homogenization, this problem is reduced to the reflection and transmission of P-waves through an inhomogeneous orthotropic elastic layer. It is shown that a P incident wave always creates two reflected waves (one P wave and one SV wave), however, there may exist two, one or no transmitted waves. Expressions in closed-form of the reflection and transmission coefficient have been derived using the transfer matrix of an orthotropic elastic layer. Some numerical examples are carried out to examine the reflection and transmission of P-waves at a very rough interface of tooth-comb type, tooth-saw type and sin type. It is found numerically that the reflection and transmission coefficients depend strongly on the incident angle, the incident wave frequency, the roughness and the type of interfaces.

scholarly journals MEASUREMENT OF INCIDENT WAVE HEIGHT IN COMPOSITE WAVE TRAINS

1974 ◽  
Vol 1 (14) ◽  
pp. 21
Author(s):  
Ake Sandstrom
Keyword(s):  
Wave Height ◽  
Incident Wave ◽  
Wave Train ◽  
Wave Length ◽  
Wave Theory ◽  
Arithmetic Mean ◽  
Reflected Waves ◽  
Wave Heights ◽  
Wave Trains ◽  
Composite Wave

A method is proposed for measurement of the incident wave height in a composite wave train. The composite wave train is assumed to consist of a superposition of regular incident and reflected waves with the same wave period. An approximate value of the incident wave height is obtained as the arithmetic mean of the wave heights measured "by two gauges separated a quarter of a wave length. The accuracy of the method in relation to the location of the gauges and the wave parameters is investigated using linear and second order wave theory. Results of the calculations are presented in diagrams.

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