Dynamic response of the long channel resting on the soil and Excited by SH waves

The purpose of this paper is to discuss the response of the channel having semi-circular crosssection and the constant thickness in the case of SH waves. The dynamic interaction of soil and the channel that takes place during the passage of seismic waves through the soil has been of much interest to engineers. It has a bearing on the stresses in the channel and the changes in the time history of incident ground motion. It is assume that the channel is flexible, stiff and rigid, and soil is only elastic. The results are calculated from flexible case to stiff one for comparison. They are also determined for rigid case. If the channel is stiff enough, it might be assumed as rigid. An analytical solution is derived using wave-expansion method in polar coordinates for elastic channel. For the solutions of rigid channel, the equation of motion(Newton Second Law) is derived. This solution method takes into account dynamic interactions between soil and the structure. The results are derived depending on the incident wave angles and dimensionless wave numbers. Absolute responses of the channel are illustrated with respect to dimensionlessfrequencies and compared.