Scattering of Anti-plane (SH) Waves by a Hill with Complex Slopes

ABSTRACT

This paper presents an analytical solution to the ground motion of an isosceles hill with slope change under incident SH waves. A new partitioning method, multi-region-matching technique (MRMT), is proposed in this paper to establish an accurate analytical solution model. Based on the complex function method and multipolar coordinate transformation, the infinite algebraic equations are established according to the continuity conditions at the two auxiliary boundaries. Fourier series expansion method in complex-domain is adopted to solve the unknown coefficients in wave field expressions. Numerical results demonstrate the slope of the hill is an important parameter affecting the anti-plane response.

KEYWORDS:

• Complex Topography
• Multi-Region-Matching Technique (MRMT)
• Complex Function Method
• Multipolar Coordinates
• SH Waves

Additional information

Funding

This work is supported by the National Key R&D Program of China [grant number 2019YFC1509301]; the National Natural Science Foundation of China [grant number 11872156]; the Fundamental Research Funds for the Central Universities [grant number 3072020CFT0202]; the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures; and the program for Innovative Research Team in China Earthquake Administration.