Abstract
The movement of ground surface during an earthquake will not be identical even in relatively limited plane, but possible to have spatial variation. According to the reference 1), the mathematical form of the cross spectral density function between ground motions, where the statistic correlation decreases in an exponential manner as the distance increases, can be regarded as the most realistic idealization. The purpose of the paper is to investigate theoretically the stochastic response of the structure subjected to multiple excitations which have the above-mentioned characteristic. The paper mainly consists of the following contents. At first the system, where a rigid slab is supported by a lot of columns, the bottom ends of which are subjected to horizontal multiple inputs, is supposed, and then the frequency response functions of the absolute acceleration of a rigid slab and of the relative displacement of columns are mathematically derived. Next the stochastic response quantities are analytically evaluated in a frequency domain in case that ground motions are assumed to be band limited white noises with spatial variation. Finally the response values due to two different noises given concretely as the simulation of typical earthquake motions are numerically estimated as examples. In conclusion the essential point of the paper lies in the fact that the spatial variation of excitations is possible to have a great ifluence upon the response of structures.
