56 相異した地動が作用する相異した単振子の複素化応答の間における時間軸にそった相乗累積値の直接評価式

概要

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A strict formulation is provided to evaluate the cross-product integral along total time axis for the complex-valued drift response of different simple oscillators subjected to different earthquake motions. Without resorting to any use of time-history response, the integral is straightforwardly related to discrete data of earthquake motions under their segmentally linear interpolation. Its evaluation reduces to determination of a certain complex-valued combination factor specified by an apparently somewhat involved definite integral. The latter is advantageously resolved into a finite difference expression of order four, where deliberate operation of improper integrals becomes essential. Together with the elementary exponential and circular functions, the imaginary part is featured by participation of the exponential integral function (or the auxiliary functions associated with the sine and cosine integrals) of a complex variable. The non-elementary term is then shown to be turned into evaluation of the auxiliary functions for a positive real variable by means of a power-series expansion with respect to damping factor.
一般社団法人日本建築学会の論文
1997-03-20