scholarly journals An explicit relation for the apparent phase velocity of Rayleigh waves in a vertically heterogeneous elastic half-space

2014 ◽  
Vol 199 (2) ◽  
pp. 673-687 ◽  
Author(s):  
Carlo G. Lai ◽  
Maria-Daphne Mangriotis ◽  
Glenn J. Rix
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Explicit Relation

scholarly journals Surface waves in multilayered elastic media I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space

1964 ◽  
Vol 54 (2) ◽  
pp. 627-679
Author(s):  
David G. Harkrider
Keyword(s):  
Surface Waves ◽  
Frequency Domain ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Love Waves ◽  
Displacement Fields ◽  
Matrix Formulation ◽  
Total Displacement ◽  
Rayleigh And Love Waves

ABSTRACT A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at any depth in a multilayered elastic isotropic solid half-space. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The solutions are then generalized to include the effect of a surface liquid layer. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point force, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. From these results we are able to show certain reciprocity relations for surface waves which had been previously proved for the total displacement field. The theory presented here lays the ground work for later papers in which theoretical seismograms are compared with observations in both the time and frequency domain.

scholarly journals The Complex Rayleigh Waves in a Functionally Graded Piezoelectric Half-Space: An Improvement of the Laguerre Polynomial Approach

Materials ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2320 ◽  
Author(s):  
Ke Li ◽  
Shuangxi Jing ◽  
Jiangong Yu ◽  
Xiaoming Zhang ◽  
Bo Zhang
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Wave Mode ◽  
Functionally Graded ◽  
Function Technique ◽  
Complex Wave ◽  
Acoustic Wave Devices ◽  
Functionally Graded Piezoelectric

The research on the propagation of surface waves has received considerable attention in order to improve the efficiency and natural life of the surface acoustic wave devices, but the investigation on complex Rayleigh waves in functionally graded piezoelectric material (FGPM) is quite limited. In this paper, an improved Laguerre orthogonal function technique is presented to solve the problem of the complex Rayleigh waves in an FGPM half-space, which can obtain not only the solution of purely real values but also that of purely imaginary and complex values. The three-dimensional dispersion curves are generated in complex space to explore the influence of the gradient coefficients. The displacement amplitude distributions are plotted to investigate the conversion process from complex wave mode to propagating wave mode. Finally, the curves of phase velocity to the ratio of wave loss decrements are illustrated, which offers extra convenience for finding the high phase velocity points where the complex wave loss is near zero.

Dynamic response of an elastic half-space to time-dependent surface tractions over an embedded spherical cavity. III (With comments on a paper by R. D. Gregory)

1969 ◽  
Vol 309 (1498) ◽  
pp. 313-329 ◽  
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Rayleigh Waves ◽  
Spherical Cavity ◽  
Elastic Half Space ◽  
Time Dependent ◽  
Plane Boundary ◽  
Surface Motion ◽  
Harmonic Solution ◽  
Time Harmonic

Discussion of the problem of an elastic half-space with spherical cavity is continued in respect of Rayleigh waves on the plane boundary. Displacements in the initial and first group of higher order Rayleigh waves are derived by using the time-harmonic solution developed in part I of this series with attention confined to the case of time-harmonic normal stress at the cavity. These are employed to find also the response to an exponential shock at the cavity and graphs are presented showing the surface motion due to the initial Rayleigh waves. Finally, in an appendix to the paper, some comments are given on a recent paper by R. D. Gregory on the problem of the half-space with cavity.

Analysis of gravity and non-homogeneity on Rayleigh wave in anisotropic elastic-viscoelastic half space of higher order

2015 ◽  
Vol 11 (1) ◽  
pp. 120-130 ◽  
Author(s):  
Rajneesh Kakar
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Mass Density ◽  
Wave Number ◽  
Inhomogeneous Layer ◽  
Third Order ◽  
Content Type ◽  
Anisotropic Elastic ◽  
Mathematical Techniques

Purpose – The purpose of this paper is to illustrate the propagation of Rayleigh waves in an anisotropic inhomogeneous layer placed over an isotropic gravitational viscoelastic half space of third order. Design/methodology/approach – It is considered that the mass density and the elastic coefficients of the layer are space dependent. Dispersion properties of waves are derived with the simple mathematical techniques. Graphs are plotted between phase velocity ‘k’ and wave number ‘c’ for different values of inhomogeneity parameters for a particular model and the effects of inhomogeneity and gravity are studied. Findings – The wave analysis indicates that the phase velocity of Rayleigh waves is affected quite remarkably by the presence of inhomogeneity, gravity and strain rates of strain parameters in the half space. The effects of inhomogeneity and depth on the phase velocity are also shown in corresponding figures. Originality/value – The results presented in this study may be attractive and useful for mathematicians, seismologists and geologists.

Propagation of Cylindrical Rayleigh Waves in a Transversly Isotropic Thermoelastic Diffusive Solid Half-Space

2013 ◽  
Vol 43 (3) ◽  
pp. 3-20 ◽  
Author(s):  
Rajneesh Kumar ◽  
Tarun Kansal
Keyword(s):  
Phase Velocity ◽  
Boundary Conditions ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Attenuation Coefficients ◽  
Special Cases ◽  
Phase Velocity And Attenuation

Abstract The propagation of cylindrical Rayleigh waves in a trans- versely isotropic thermoelastic diffusive solid half-space subjected to stress free, isothermal/insulated and impermeable or isoconcentrated boundary conditions is investigated in the framework of different theories of ther- moelastic diffusion. The dispersion equation of cylindrical Rayleigh waves has been derived. The phase velocity and attenuation coefficients have been computed from the dispersion equation by using Muller’s method. Some special cases of dispersion equation are also deduced

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.

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