A long-wave model for the surface elastic wave in a coated half-space

2010 ◽  
Vol 466 (2122) ◽  
pp. 3097-3116 ◽  
Author(s):  
H.-H. Dai ◽  
J. Kaplunov ◽  
D. A. Prikazchikov
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Half Space ◽  
Elliptic Equations ◽  
Ad Hoc ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Wave Model ◽  
Destructive Testing ◽  
Long Wave

The paper deals with the three-dimensional problem in linear isotropic elasticity for a coated half-space. The coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long-wave limit. An explicit model is derived for the surface wave using the perturbation technique, along with the theory of harmonic functions and Radon transform. The model consists of three-dimensional ‘quasi-static’ elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two-dimensional hyperbolic equation singularly perturbed by a pseudo-differential (or integro-differential) operator. The latter equation governs dispersive surface wave propagation, whereas the elliptic equations describe spatial decay of displacements and stresses. As an illustration, the dynamic response is calculated for impulse and moving surface loads. The explicit analytical solutions obtained for these cases may be used for the non-destructive testing of the thickness of the coating and the elastic moduli of the substrate.

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.

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.

Propagation of Rayleigh waves in an incompressible rotating orthotropic elastic solid half-space with impedance boundary conditions

2017 ◽  
Vol 26 (3-4) ◽  
pp. 73-78 ◽  
Author(s):  
Baljeet Singh ◽  
Baljinder Kaur
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Half Space ◽  
Wave Speed ◽  
Secular Equation ◽  
Tangential Displacement ◽  
Rayleigh Surface Wave ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Dimensional Wave

AbstractIn this paper, the governing equations of an incompressible rotating orthotropic elastic medium are formulated and are solved to obtain Rayleigh surface wave solutions in a particular half-space. The surface of half-space is subjected to impedance boundary conditions, in which normal and tangential stresses are proportional to frequency times normal and tangential displacement components, respectively. A secular equation for Rayleigh surface wave is obtained. With the help of MATLAB, the secular equation is solved numerically to obtain non-dimensional wave speed. The dependence of non-dimensional wave speed on non-dimensional material constant, rotation parameter and impedance parameters is shown graphically.

scholarly journals On the existence of high-frequency boundary resonances in layered elastic media

2015 ◽  
Vol 471 (2178) ◽  
pp. 20140878 ◽  
Author(s):  
K. D. Cherednichenko ◽  
S. Cooper
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
High Frequency ◽  
Three Dimensional ◽  
Homogeneous Medium ◽  
Elastic Media ◽  
Displacement Boundary ◽  
Boundary Spectrum ◽  
New Type ◽  
High Frequency Vibrations

We analyse the asymptotic behaviour of high-frequency vibrations of a three-dimensional layered elastic medium occupying the domain Ω =(− a , a ) 3 , a >0. We show that in both cases of stress-free and zero-displacement boundary conditions on the boundary of Ω a version of the boundary spectrum, introduced in Allaire and Conca (1998 J. Math. Pures. Appl. 77, 153–208. ( doi:10.1016/S0021-7824(98)80068-8 )), is non-empty and part of it is located below the Bloch spectrum. For zero-displacement boundary conditions, this yields a new type of surface wave, which is absent in the case of a homogeneous medium.

Three-Dimensional Green’s Functions in an Anisotropic Half-Space With General Boundary Conditions

2003 ◽  
Vol 70 (1) ◽  
pp. 101-110 ◽  
Author(s):  
E. Pan
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Different Boundary Conditions

This paper derives, for the first time, the complete set of three-dimensional Green’s functions (displacements, stresses, and derivatives of displacements and stresses with respect to the source point), or the generalized Mindlin solutions, in an anisotropic half-space z>0 with general boundary conditions on the flat surface z=0. Applying the Mindlin’s superposition method, the half-space Green’s function is obtained as a sum of the generalized Kelvin solution (Green’s function in an anisotropic infinite space) and a Mindlin’s complementary solution. While the generalized Kelvin solution is in an explicit form, the Mindlin’s complementary part is expressed in terms of a simple line-integral over [0,π]. By introducing a new matrix K, which is a suitable combination of the eigenmatrices A and B, Green’s functions corresponding to different boundary conditions are concisely expressed in a unified form, including the existing traction-free and rigid boundaries as special cases. The corresponding generalized Boussinesq solutions are investigated in details. In particular, it is proved that under the general boundary conditions studied in this paper, the generalized Boussinesq solution is still well-defined. A physical explanation for this solution is also offered in terms of the equivalent concept of the Green’s functions due to a point force and an infinitesimal dislocation loop. Finally, a new numerical example for the Green’s functions in an orthotropic half-space with different boundary conditions is presented to illustrate the effect of different boundary conditions, as well as material anisotropy, on the half-space Green’s functions.

Dispersion Study of Propagation of Torsional Surface Wave in a Layered Structure

2017 ◽  
Vol 33 (3) ◽  
pp. 303-315 ◽  
Author(s):  
S. Gupta ◽  
N. Bhengra
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Boundary Conditions ◽  
Half Space ◽  
Layered Structure ◽  
Transversely Isotropic ◽  
Whittaker Function ◽  
Anisotropic Layer ◽  
Surface Wave Propagation ◽  
Torsional Surface Wave

AbstractThis paper presents the feasibility of torsional surface wave propagation in an anisotropic layer sandwiched between two anisotropic inhomogeneous media. The anisotropy considered in the upper layer and the lower half-space is of transversely isotropic kind while the sandwiched anisotropic layer is a porous layer. The directional rigidities and density have been considered linearly and exponentially varying in the half-space and in the upper layer respectively, while it is taken as a variable in the sandwiched layer. The compact form of dispersion equation governing the propagation of the torsional surface wave has been derived by using the Whittaker function under appropriate boundary conditions. The dispersion of the torsional wave and the effects of inhomogeneity parameters, initial stress and poroelastic constant have been calculated numerically and demonstrated through graphs.

A Surface Wave Model for Coupling with Numerical Ocean Circulation Models

2008 ◽  
Vol 25 (10) ◽  
pp. 1785-1807 ◽  
Author(s):  
George L. Mellor ◽  
Mark A. Donelan ◽  
Lie-Yauw Oey
Keyword(s):  
Surface Wave ◽  
Shallow Water ◽  
Hurricane Katrina ◽  
Ocean Circulation ◽  
Three Dimensional ◽  
Wave Model ◽  
Third Generation ◽  
Model Calculations ◽  
Coupling Terms ◽  
Buoy Data

Abstract A surface wave model is developed with the intention of coupling it to three-dimensional ocean circulation models. The model is based on a paper by Mellor wherein depth-dependent coupling terms were derived. To be compatible with circulation models and to be numerically economical, this model is simplified compared to popular third-generation models. However, the model does support depth and current refraction, deep and shallow water, and proper coupling with depth-variable currents. The model is demonstrated for several simple scenarios culminating in comparisons of model calculations with buoy data during Hurricane Katrina and with calculations from the model Simulating Waves Nearshore (SWAN); for these calculations, coupling with the ocean was not activated.

scholarly journals Numerical Simulations Using Various Models for Tsunamis Due to a Fluid or Rigid Bodies Falling Down a Uniform Slope

2021 ◽  
Vol 16 (7) ◽  
pp. 994-1004
Author(s):  
Taro Kakinuma ◽  
Mitsuru Yanagihara ◽  
Tsunakiyo Iribe ◽  
Kuninori Nagai ◽  
Chisato Hara ◽  
...  
Keyword(s):  
Water Level ◽  
Numerical Models ◽  
Three Dimensional ◽  
Wave Model ◽  
Rigid Bodies ◽  
Type Model ◽  
Three Dimensional Model ◽  
Long Wave ◽  
Surface Displacements ◽  
Level Model

Tsunami generation due to a landslide has been simulated using various numerical models, and the resulting water surface displacements from the models, as well as the corresponding experimental data, are compared. The numerical models used in this study are a two-layer long-wave model, a two-level non-hydrostatic model, a three-dimensional model, a lattice-Boltzmann-type model, an SPH-type model, and an MPS-type model. Tsunamis generated by a fluid falling down a uniform slope are accurately reproduced by the models, especially when the wave height of the tsunami is not large. When using the two-layer long-wave model, in which the two layers of a falling fluid and seawater are assumed not to mix, the parameters including the seabed friction coefficient, adjusted in one case, are not appropriate for other mixing conditions. The two-level model with non-hydrostatic pressure exhibits wave disintegration owing to the effects of both nonlinearity and dispersion, although the second wave generated by the reflection of a wave traveling towards the shore is not simulated accurately. Tsunamis caused by a group of rigid cylinders falling down a uniform slope have also been simulated using two Lagrangian models, namely the SPH- and MPS-type models. Although the first peak at the water level is accurately reproduced by both models, the water level at the trough between the first and second crests is overestimated.

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