Scattering of SH waves by an isosceles flat-topped hill with multistage slopes

This paper presents a flexible mechanical model, which can be used to study the dynamic response of irregular surfaces with complex shapes under the action of seismic waves. Take flat-topped hill as an example, an isosceles model with complex boundaries is established, and an appropriate multi-region-matching technique (MRMT) is proposed to simplify the complex boundary value problem and solve it analytically. Based on the wave function expansion method and the complex function method, the wave field expressions of each subregion, including the singular shape subregion, are constructed. By introducing multipolar coordinate transformation and combining the continuous conditions at three auxiliary boundaries, the infinite algebraic equations are established. To solve the unknown coefficients in the wave field expressions, the Fourier series expansion method in the complex domain is adopted. Finally, some typical numerical examples are calculated to analyze the influence of the shape parameters of the flat-topped hill, the incident angle and the wave number of seismic waves on surface displacement amplitudes.