Propagation of SH waves in a visco-elastic layer overlying an inhomogeneous isotropic half-space

The problem of the elastic SH-wave diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The solution is obtained by the Wiener- Hopf method. The dependences of the scattered field on the structure parameters are presented in analytical form. Verifica¬tion of the obtained solution is presented.

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Creeping effect across a buried, inclined, finite strike-slip fault in an elastic-layer overlying an elastic half-space

GEM - International Journal on Geomathematics ◽

10.1007/s13137-020-00170-y ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Piu Kundu ◽

Seema Sarkar (Mondal) ◽

Debabrata Mondal

Keyword(s):

Half Space ◽

Elastic Layer ◽

Elastic Half Space ◽

Strike Slip ◽

Strike Slip Fault

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Bounds on the Maximum Contact Stress of an Indented Elastic Layer

Journal of Applied Mechanics ◽

10.1115/1.3408862 ◽

1971 ◽

Vol 38 (3) ◽

pp. 608-614 ◽

Cited By ~ 35

Author(s):

Y. C. Pao ◽

Ting-Shu Wu ◽

Y. P. Chiu

Keyword(s):

Half Space ◽

Contact Stress ◽

Elastic Layer ◽

Theory Of Elasticity ◽

Contact Conditions ◽

Practical Applications ◽

Method Of Solution ◽

Elastic Layers ◽

Maximum Contact ◽

Contact Stress Distribution

This paper is concerned with the plane-strain problem of an elastic layer supported on a half-space foundation and indented by a cylinder. A study is presented of the effect of the contact condition at the layer-foundation interface on the contact stresses of the indented layer. For the general problem of elastic indenter or elastic foundation, the integral equations governing the contact stress distribution of the indented layer derived on the basis of two-dimensional theory of elasticity are given and a numerical method of solution is formulated. The limiting contact conditions at the layer-foundation interface are then investigated by considering two extreme cases, one with the indented layer in frictionless contact with the half space and the other with the indented layer rigidly adhered to the half space. Graphs of the bounds on the maximum normal stress occurring in indented elastic layers for the cases of rigid cylindrical indenter and rigid half-space foundation are obtained for possible practical applications. Some results of the elastic indenter problem are also presented and discussed.

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Rotation and Magnetic Field Effect on Surface Waves Propagation in an Elastic Layer Lying over a Generalized Thermoelastic Diffusive Half-Space with Imperfect Boundary

Mathematical Problems in Engineering ◽

10.1155/2015/671783 ◽

2015 ◽

Vol 2015 ◽

pp. 1-15 ◽

Cited By ~ 16

Author(s):

S. M. Abo-Dahab ◽

Kh. Lotfy ◽

A. Gohaly

Keyword(s):

Magnetic Field ◽

Surface Waves ◽

Half Space ◽

Attenuation Coefficient ◽

Elastic Layer ◽

Finite Thickness ◽

Relaxation Times ◽

Magnetic Field Effect ◽

Plane Boundary ◽

Special Cases

The aim of the present investigation is to study the effects of magnetic field, relaxation times, and rotation on the propagation of surface waves with imperfect boundary. The propagation between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half-space with rotation in the context of Green-Lindsay (GL) model is studied. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness, and then deduced for normal stiffness, tangential stiffness and welded contact. The amplitudes of displacements, temperature, and concentration are computed analytically at the free plane boundary. Some special cases are illustrated and compared with previous results obtained by other authors. The effects of rotation, magnetic field, and relaxation times on the speed, attenuation coefficient, and the amplitudes of displacements, temperature, and concentration are displayed graphically.

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Dynamic Interaction of Two Independent SDOF Oscillators Supported by a Flexible Foundation Embedded in a Half-Space: Closed-Form Analytical Solution for Incident Plane SH-Waves

Journal of Earthquake and Tsunami ◽

10.1142/s1793431121500263 ◽

2021 ◽

pp. 1-24

Author(s):

Liguo Jin ◽

Liting Du ◽

Haiyan Wang

Keyword(s):

Analytical Solution ◽

Closed Form ◽

Half Space ◽

Strong Interaction ◽

Rigid Foundation ◽

Structural Stiffness ◽

Sh Waves ◽

Closed Form Analytical Solution ◽

Flexible Foundation ◽

Plane Sh Waves

This paper presents a closed-form analytical solution for the dynamic response of two independent SDOF oscillators standing on one flexible foundation embedded in an elastic half-space and excited by plane SH waves. The solution is obtained by the wave function expansion method and is verified by comparison with the results of the special cases of a rigid foundation and the published research result of a flexible foundation. The model is utilized to investigate how the foundation stiffness influences the system response. The results show that there will be a significant interaction between the two independent structures on one flexible foundation and the intensity of the interaction is mainly dependent on foundation stiffness and structural stiffness. For a system with more flexible foundation, strong interaction will exist between the two structures; larger structural stiffness will also lead to a strong interaction between the two structures. When the structural mass and the structural stiffness are all larger, the flexible foundation cannot be treated as a rigid foundation even if the foundation stiffness is many times larger than that of soil. This model may be useful to get insight into the effects of foundation flexibility on the interaction of two independent structures standing on one flexible foundation.

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Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6431 ◽

2020 ◽

Vol 43 (11) ◽

pp. 6888-6902

Author(s):

Guanxixi Jiang ◽

Zailin Yang ◽

Cheng Sun ◽

Baitao Sun ◽

Yong Yang

Keyword(s):

Dynamic Analysis ◽

Half Space ◽

Sh Waves ◽

Elliptical Inclusion

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Elastic Layer Pressed Against a Half Space

Journal of Applied Mechanics ◽

10.1115/1.3423375 ◽

1974 ◽

Vol 41 (3) ◽

pp. 703-707 ◽

Cited By ~ 16

Author(s):

K. C. Tsai ◽

J. Dundurs ◽

L. M. Keer

Keyword(s):

Eigenvalue Problem ◽

Integral Equations ◽

Half Space ◽

Elastic Layer ◽

Numerical Results ◽

Fredholm Integral Equations ◽

Auxiliary Functions ◽

Receding Contact ◽

Two Bodies

The paper considers the elastic layer which is pressed against a half space by loads that are not necessarily symmetric about the center of the loaded region. It is shown that the receding contact between the two bodies can be treated by means of superposition, leading to two homogeneous Fredholm integral equations for auxiliary functions that are directly related to the contact tractions. The determination of the extent of contact and the shift between the load and contact intervals can be viewed as an eigenvalue problem of the homogeneous integral equations. Specific numerical results are given for two types of triangular loads, and a comparison is made with certain symmetric loads.

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