Diffraction of Plane SH Waves by a Cylindrical Cavity in an Infinite Wedge

Abstract The closed-form solution of the dynamic interaction of a shear wall and the isotropic homogeneous and elastic half-space, previously studied only for vertically-incident SH waves, is generalized to any angle of incidence. It is shown that the interaction equation is independent of the incidence angle, while the surface-ground displacements heavily depend on it. For the two-dimensional model studied, it is demonstrated that disturbances generated by waves scattering and diffracting around the rigid foundation mass are not a local phenomenon but extend to large distances relative to the characteristic foundation length.

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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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Torsional response of structures for SH waves: The case of hemispherical foundations

Bulletin of the Seismological Society of America ◽

10.1785/bssa0660010109 ◽

1976 ◽

Vol 66 (1) ◽

pp. 109-123

Author(s):

J. E. Luco

Keyword(s):

Closed Form Solution ◽

Form Solution ◽

Basic Step ◽

Sh Waves ◽

Torsional Response ◽

Obliquely Incident ◽

Incident Plane ◽

Interaction Problem ◽

Plane Sh Wave ◽

Plane Sh Waves

abstract A study is made of the harmonic torsional response of an elastic structure placed on a rigid hemispherical foundation which is supported on an elastic medium and is subjected to the action of obliquely incident plane SH waves. As a basic step in the solution of the torsion interaction problem, a closed-form solution is obtained for the torsional response of a rigid hemispherical foundation excited externally by a harmonic torque and through the soil by an obliquely incident plane SH wave. Comparisons between the results for a hemispherical foundation with those for a circular plate allow the estimation of the effects that the embedment of the foundation has on the torsional response of the superstructure.

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Scattering of Plane SH Waves Induced by a Semicylindrical Canyon with a Subsurface Circular Lined Tunnel

International Journal of Geomechanics ◽

10.1061/(asce)gm.1943-5622.0001137 ◽

2018 ◽

Vol 18 (6) ◽

pp. 06018012 ◽

Cited By ~ 11

Author(s):

Yufeng Gao ◽

Xin Chen ◽

Ning Zhang ◽

Denghui Dai ◽

Xin Yu

Keyword(s):

Sh Waves ◽

Plane Sh Waves

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Effects of Surface Energy on Scattering of SH Waves by an Elastic Half-Plane with a Semi-Cylindrical Cavity

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.627.698 ◽

2012 ◽

Vol 627 ◽

pp. 698-704

Author(s):

Zhi Ying Ou ◽

Xiao Wei Liu ◽

Qiong Deng

Keyword(s):

Surface Energy ◽

Cylindrical Cavity ◽

Dynamic Stress ◽

Shear Waves ◽

Surface Elasticity ◽

Expansion Method ◽

Stress Fields ◽

Sh Waves ◽

Wave Function Expansion Method ◽

Incident Waves

When the radius of materials and structral devices reduces to nanometers, the inﬂuence of surface energy becomes prominent in its mechanical behavior. In the frame of surface elasticity, the scattering of anti-plan shear waves by an elastic half-plan with a semi-cylindrical cavity considered the surface energy are investigated in this paper. When the boundary condition at the straight edge of the half-plan is traction free, the analytical solutions of stress fields of the half plan with semi-culindrical cavity are expressed by employing a wave function expansion method. The results show that surface energy has a signiﬁcant effect on the scattering of anti-plan shear waves as the radius of the semi-cylindrical cavity shrinks to nanoscale. The effects of incident waves with different frequencies and incident angel, radius of semi-cylindrical cavity and surface energy on the dynamic stress concentration around the semi-cylindrical cavity are discussed in detail.

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