Scattering of SH waves by a non-symmetrical V-shaped canyon with a shallow cavity in half-space

Both surface motion and hole stress concentration have always been concerned in engineering design. In this paper, a theoretical approach is used to study the scattering problem of circular cavities under a non-symmetrical V-shaped canyon. The wave displacement function is obtained by solving the He...

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Bibliographic Details
Published in:Waves in random and complex media 2024-03, Vol.34 (2), p.823-844
Main Authors: Yang, Zailin, Sun, Yingchao, Wang, Guangyi, Song, Yunqiu, Yang, Yong
Format: Article
Language:English
Subjects:
Algebra
Boundary conditions
Canyons
Design engineering
Displacement
earthquake dynamics
Earthquake ground motions
Finite element method
Free boundaries
Free surfaces
Half spaces
Helmholtz equations
Holes
Incident waves
least square method
Polar coordinates
Scattering
SH waves
Shape
Stress concentration
Surface motion
theoretical seismology
transient deformation
wave propagation
wave scattering and diffraction
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Summary:Both surface motion and hole stress concentration have always been concerned in engineering design. In this paper, a theoretical approach is used to study the scattering problem of circular cavities under a non-symmetrical V-shaped canyon. The wave displacement function is obtained by solving the Helmholtz equation that meets the zero-stress boundary conditions by adopting the method of separation of variables and the symmetric method. Based on the complex function method, multi-polar coordinate method and region-matching technique, algebraic equations are established at relevant conditions, which include auxiliary and free boundary conditions. Then, according to sample statistics, a least-square method is used instead of the Fourier expansion method to solve the undetermined coefficients of the algebraic equations by discrete boundary. Numerical results show that the theoretical method is verified valid by the finite element method and the reduced model, and the displacement of the free surface and the stress of the circular cavity are related to the shape of the canyon, the position of the circular cavity, the direction of the incident wave and the frequency content of the excitation.
ISSN:1745-5030
1745-5049
DOI:10.1080/17455030.2021.1918799