半無限弾性体地表面点加振解の無限積分を有限積分で表す方法 : (続)内部減衰を考慮する場合

抄録

In the solution of the semi-infinite elastic medium for a point load excitation of the soil surface, an infinite integral appears. In order to evaluate the resoonse, the value of this infinite integral must be obtained. The method to transform this infinite integral to a finite integral has been already reported in the case of no internal damping of the soil. In this paper, a same kind of method is introduced to transform the infinite integral to finite integral considering internal damping of the soil. In this method, an adequate complex function corresponding to the integrand is adopted and an identical equation which involves the infinite integral is obtained based on Cauchy's theorem. Using this identical equation, the infinite integral in the original solution can be teplaced by the finite integral. This method is very useful by the following reasons. 1) If the numerical integral procedure is applied directly to the infinite integral, it is impossible to execute it to infinite range. It must be stopped at a suitable range. In this case, a cut off error is produced. But when the numerical integral procedure is applied after transforming the infinite integral to finite integral, this cut off error is not produces. 2) There is the Rayleigh oole near or on the contour of the infinite integral. Near the pole, the integrand falls into ill condition for a numerical integration and special procedure is required especially in the case of small or zero internal damping of soil. But this pole does not exist near the contour of the transformed finite integral and there is no difficulty in the numerical integral process. 3)The range of numerical integral is very short. It is only from 0 to 1.