A note on surface motion of inhomogeneous alluvial valleys due to incident plane SH waves

1994 ◽  
Vol 84 (1) ◽  
pp. 192-201
Author(s):  
David L. Clements ◽  
Ashley Larsson
Keyword(s):  
Numerical Solutions ◽  
Boundary Integral Equations ◽  
Layered Material ◽  
Boundary Integral ◽  
Sh Waves ◽  
New Formalism ◽  
Surface Motion ◽  
Wave Solutions ◽  
Incident Plane ◽  
Plane Sh Waves

Abstract The scattering and diffraction of harmonic SH waves by an arbitrarily shaped inhomogeneous alluvial valley in a layered material is considered. A new formalism is used to obtain the appropriate wave solutions for inhomogeneous media, and these are employed together with the boundary integral equations to obtain numerical solutions for some important particular problems.

scholarly journals Ground motion on alluvial valleys under incident plane SH waves

1991 ◽  
Vol 33 (2) ◽  
pp. 240-253 ◽  
Author(s):  
David L. Clements ◽  
Ashley Larsson
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Ground Motion ◽  
Boundary Integral Equations ◽  
Layered Material ◽  
Boundary Integral ◽  
Alluvial Valley ◽  
Sh Waves ◽  
Incident Plane ◽  
Plane Sh Waves

AbstractThe scattering and diffraction of harmonic SH waves by an arbitrarily shaped alluvial valley in a layered material is considered. The problem is solved in terms of boundary integral equations which yield a numerical solution.

Surface motion of a semi-cylindrical alluvial valley for incident plane SH waves

1971 ◽  
Vol 61 (6) ◽  
pp. 1755-1770 ◽  
Author(s):  
M. D. Trifunac
Keyword(s):  
Incidence Angle ◽  
Alluvial Valley ◽  
Sh Waves ◽  
Surface Motion ◽  
Wave Interference ◽  
Incident Plane ◽  
Wave Propagation Problem ◽  
Wave Patterns ◽  
Closed Form Analytical Solution ◽  
Plane Sh Waves

abstract The nature of surface motion in and around a semi-cylindrical alluvial valley is investigated for the case of incident plane SH waves. The closed-form analytical solution of this two-dimensional wave-propagation problem displays complicated wave-interference phenomena characterized by nearly-standing wave patterns, rapid changes in the ground-motion amplification along the free surface of the valley, and significant dependence of motion on the incidence angle of SH waves. Although simple, this model may qualitatively explain some vibrating characteristics of long and deep alluvial valleys.

scholarly journals Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Pan Cheng ◽  
Ling Zhang
Keyword(s):  
Asymptotic Expansion ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Boundary Integral Equations ◽  
Logarithmic Singularity ◽  
Nonlinear Problems ◽  
Boundary Integral ◽  
Convergence Theory ◽  
Mechanical Quadrature ◽  
Quadrature Methods

This paper will study the high accuracy numerical solutions for elastic equations with nonlinear boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simultaneously. Mechanical quadrature methods (MQMs) are presented to solve the nonlinear equations where the accuracy of the solutions is of three orders. According to the asymptotical compact convergence theory, the errors with odd powers asymptotic expansion are obtained. Following the asymptotic expansion, the accuracy of the solutions can be improved to five orders with the Richardson extrapolation. Some results are shown regarding these approximations for problems by the numerical example.

Interaction of a shear wall with the soil for incident plane SH waves

1972 ◽  
Vol 62 (1) ◽  
pp. 63-83
Author(s):  
M. D. Trifunac
Keyword(s):  
Incidence Angle ◽  
Closed Form Solution ◽  
Shear Wall ◽  
Elastic Half Space ◽  
Form Solution ◽  
Angle Of Incidence ◽  
Sh Waves ◽  
Incident Plane ◽  
Interaction Equation ◽  
Plane Sh Waves

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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