Surface motion of a cylindrical hill of circular—arc cross-section for incident plane SH waves

Yuan, Xiaoming; Liao, Zhenpeng

doi:10.1016/0267-7261(95)00040-2

Cited by 74 publications

(25 citation statements)

References 10 publications

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“…It is shown from Figure 6 that, as the incident frequency increases, the surface displacement amplitudes gradually become complex and the maximal surface displacement amplitudes gradually increase; the maximal surface displacement amplitudes appear at the surface of either the half-space or the hill, which is different from that for SH waves incidence at all: the maximal displacement amplitude is located at the surface of the hill for η≈1.0 (Yuan and Liao, 1996). This is Figure 5 The stress and displacement residuals at boundaries (θ β =0°, η =3.0) because of the transformation between the horizontal and vertical displacement components, which is due to the mode conversion of P waves (LIANG et al, 2005b) and SV waves.…”

Section: Numerical Results and Discussionmentioning

confidence: 94%

“…The scattering waves are discussed next. By using the technique of auxiliary functions (Yuan and Men, 1992;Yuan and Liao, 1996), the model is divided into two regions ( Figure 2): region Ω includes the hill, whose upper boundary is L and lower boundary is Γ; region D is the half-space with boundary Π and the common boundary Γ between region Ω and region D. For convenience, a very large circle is used here to imitate the surface of the half-space. It was shown that when the radius R of the large circle is large enough, the solution converges to its exact solution.…”

Section: Modelmentioning

confidence: 99%

“…Up to now, there are limited analytical solutions for hills: scattering of plane SH waves by a semi-circular hill (Yuan and Men, 1992) and a circular-arc hill (Yuan and Liao, 1996). For the case of incident plane P and SV waves, the problems are much more complicated due to the wave mode conversion; the authors recently developed an analytical solution for scattering of plane P waves by a semi-cylindrical hill (LIANG et al, 2005b).…”

Section: Introductionmentioning

confidence: 98%

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Surface motion of a semi-cylindrical hill for incident plane SV waves: Analytical solution

2006

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An analytical solution for surface motion of a semi-cylindrical hill for incident plane SV waves was derived by using the wave function expansion method and the auxiliary function technique, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and angle as well as hill width on the surface motion of the hill was discussed by numerical examples. It was shown that, a hill greatly amplifies incident plane SV waves, and the maximal amplification may reach 4 times of that for free-field response; and for incident waves of low frequency, the maximal displacement amplitudes emerge mostly at the half-space, however, for incident waves of high frequency, the maximal displacement amplitudes appear mostly at the hill.

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Section: Numerical Results and Discussionmentioning

confidence: 94%

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Surface motion of a semi-cylindrical hill for incident plane SV waves: Analytical solution

2006

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“…However surface motion of a semi-cylindrical or a shallow circular hill for incident plane SH waves were developed more recently by Yuan and Men (1992) and Yuan and Liao (1996) using auxiliary function method. Then the solutions were improved to higher incident frequency by sine and cosine series expansion technique (Lee et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Surface motion of a semi-elliptical hill for incident plane SH waves

Liang

2011

Earthq Sci

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A closed-form analytical solution of surface motion of a semi-elliptical cylindrical hill for incident plane SH waves is presented. Although some previous analytical work had already dealt with hill topography of semi-circular and shallow circular, our work aims at calculating surface motion of very prolate hill for high incident frequency, and explaining the special vibrating properties of very prolate hill. Accuracy of the solution is checked by boundary conditions, numerical results for surface motion of oblate and prolate hills are calculated, and some conclusions are obtained.

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“…Δʺ mn =0, Δʹʺ mn =0, Λʺ mn =0, Λʹʺ mn =0, and the right values of equation (46) and equation (48) are equal to zero , which lead to C n =0, D n =0. Finally, the solution simplify to the known solutions [5] as following:…”

Section: Solving Equationsmentioning

confidence: 99%

Scattering Of SH Waves By a Circular Inclusion Under a Variable Circular-Arc Hill

Gao¹,

Liu²

2017

Proceedings of the 2016 4th International Conference on Renewable Energy and Environmental Technology (ICREET 2016)

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Abstract. An inclusion under a hill would amplify the ground motion tremendously. However, Few analytic solutions achieved for this problem have limitations on a special semi-cylindrical hill or a underground cavity. Here we derive one for a new model with the wave functions expansion and auxiliary functions technique. It is reduced to solving a set of infinite linear algebraic equation using Fourier expansion for auxiliary functions based on boundary condition. The solution can be degenerated to the ones of the model ignoring the hill or the inclusion. Finally, numerical solutions are obtained by truncation of the infinite equations. The results indicate that the ground motion could be seen as the superposition of the effect of the inclusion and the hill qualitatively; and when the inclusion degenerates to a cavity, amplification frequencies on the hilly boundary can be obtained by the wave speed in half-space and the vertical distance between the flat surface and the tunnel. The influence of softness and hardness of inclusion and incident angles is also discussed here.

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Surface motion of a cylindrical hill of circular—arc cross-section for incident plane SH waves

Cited by 74 publications

References 10 publications

Surface motion of a semi-cylindrical hill for incident plane SV waves: Analytical solution

Surface motion of a semi-cylindrical hill for incident plane SV waves: Analytical solution

Surface motion of a semi-elliptical hill for incident plane SH waves

Scattering Of SH Waves By a Circular Inclusion Under a Variable Circular-Arc Hill

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