On the 3D Rayleigh wave field on an elastic half-space subject to tangential surface loads

2015 ◽  
Vol 95 (12) ◽  
pp. 1558-1565 ◽  
Author(s):  
Nihal Ege ◽  
Barış Erbaş ◽  
Danila A. Prikazchikov
Keyword(s):  
Rayleigh Wave ◽  
Wave Field ◽  
Half Space ◽  
Elastic Half Space ◽  
Tangential Surface ◽  
Surface Loads

Response of an Elastic Half Space to Expanding Surface Loads

1971 ◽  
Vol 38 (1) ◽  
pp. 99-110 ◽  
Author(s):  
D. C. Gakenheimer
Keyword(s):  
Rayleigh Wave ◽  
Exact Solutions ◽  
Half Space ◽  
Poisson’S Ratio ◽  
Elastic Half Space ◽  
Poisson's Ratio ◽  
Constant Rate ◽  
Different Depths ◽  
Surface Loads

A class of elastic half-space problems involving axisymmetric, normally applied, surface loads is investigated. Each load is assumed to suddenly emanate from a point on the surface and expand radially at a constant rate. The cases of loads shaped like a ring and a disk are considered in detail. Exact solutions are derived for the displacements at every point in the half space in terms of single integrals. Each integral is identified as a specific wave. The integrals are evaluated analytically and numerically for different depths in the half space, for loads expanding at superseismic, transeismic, and subseismic rates, and for different values of Poisson’s ratio. Moreover, the interaction of the loads and the Rayleigh wave is described. Then solutions are obtained for loads of other shapes by convoluting the ring and disk load solutions.

Rayleigh-type surface wave on a rotating orthotropic elastic half-space with impedance boundary conditions

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1980-1987
Author(s):  
Baljeet Singh ◽  
Baljinder Kaur
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Rayleigh Wave ◽  
Surface Waves ◽  
Half Space ◽  
Rotation Rate ◽  
Secular Equation ◽  
Elastic Half Space ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The propagation of Rayleigh type surface waves in a rotating elastic half-space of orthotropic type is studied under impedance boundary conditions. The secular equation is obtained explicitly using traditional methodology. A program in MATLAB software is developed to obtain the numerical values of the nondimensional speed of Rayleigh wave. The speed of Rayleigh wave is illustrated graphically against rotation rate, nondimensional material constants, and impedance boundary parameters.

Impedance of Strip-Traveling Waves on an Elastic Half Space: Asymptotic Solution

1974 ◽  
Vol 41 (2) ◽  
pp. 412-416
Author(s):  
S. H. Crandall ◽  
A. K. Nigam
Keyword(s):  
Asymptotic Solution ◽  
Rayleigh Wave ◽  
Half Space ◽  
Traveling Wave ◽  
Load Distribution ◽  
Wave Speed ◽  
Elastic Half Space ◽  
Surface Load ◽  
Shear Wave Speed ◽  
Rayleigh Wave Speed

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

scholarly journals Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

2017 ◽  
Vol 39 (4) ◽  
pp. 365-374
Author(s):  
Pham Chi Vinh ◽  
Tran Thanh Tuan ◽  
Le Thi Hue
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Layer ◽  
Approximate Formula ◽  
Elastic Half Space ◽  
Displacement Amplitude ◽  
Vertical Displacements ◽  
Thin Elastic Layer

This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the  Rayleigh wave H/V ratio.

A New Formula for the Rayleigh Wave Velocity

2012 ◽  
Vol 452-453 ◽  
pp. 233-237
Author(s):  
Xue Feng Liu ◽  
You Hua Fan
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Wave Velocity ◽  
Complex Number ◽  
Computer Time ◽  
Elastic Half Space ◽  
S Wave ◽  
Rayleigh Wave Velocity ◽  
New Formula

The formula for the Rayleigh wave velocity in isotropic elastic half-space is studied by many researchers. In their deductions, Cardan’s formula of cubic equations is often used. Based on another formula instead of Cardan’s formula, a new formula for the Rayleigh wave velocity that does not contain complex number is presented here. Our new formula is more reasonable as both the parameters and Rayleigh wave velocity are real. And the computer time can be reduced since there is no complex computation. With this new formula, the variation of Rayleigh wave velocity with the parameters is computed. It shows that Rayleigh wave velocity decreases with the increase of Poission’s ratio when S-wave velocity is fixed.

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