The Interaction Of Isosceles Triangular And Semi-circular Hill By Incident SH-wave

In earthquake engineering, one of the main concerns is to study the effects of surface topography on ground motions. This work is based on 'conjunction' in complex plane, to study the interaction of an isosceles triangle and a semi-circular hill under incident SH-wave.Firstly, the model can be divided into three domains, where domain I involves an isosceles triangular hill and a semi-circular bottom, domain II is a half space with two nearby semi-circular canyons, domain III is an elastic cylindrical object including the semi-circular hill and the semi-circular canyon. A standing wave function which is a fractional-order Bessel's function is constructed in domain I, which satisfies the condition of traction free at the triangular edges. In domain II, two scattering wave functions generated by the nearby two semicircular canyons which satisfy the condition of traction free at the horizontal surface are constructed. In domain III another standing wave function can be constructed with the condition of traction free at upside but random at the bottom. After all, this problem can be reduced another one, which satisfies the condition of displacement and stress continuity at the interfaces between the two boundaries. Furthermore based on the method of transformed coordinate in complex plane and Fourier expansion technique are employed to obtain a series of infinite linear algebraic equations. Finally, numerical examples are presented to show influences of wave number and angle of the incident waves on ground motion.