A 2D boundary element method with material damping is developed in order to seismic investigation of constructions with different configurations. The boundary element algorithm, which utilized the time-convoluted kernels is employed in order to incorporate proportional damping. In order to investigate the seismic reaction of two dimensional double and triple semi-sine formed hills subjected to vertical P and SV waves by using a developed viscoelastic boundary element algorithm and responses are presented in the form of graphs, amplification pictures and displacement. In addition, the influences of various damping proportions on site of semi-sine hills with various shapes are analyzed. It can be concluded from the results that the crest of homogeneous adjacent hills have similar shape ratio, potential and larger maximum amplification in comparison with the crest of single hills. Although this difference is increased by increasing shape ratio, it is negligible within the proportions of study shape. In addition, multiplicity of hills increased frequency characteristic of amplification curve and the number of peaks and valleys.
Keywords: Civil engineering; Geophysics; Mechanical engineering; Structural engineering.