31 RANDOM VffiRATIONS OF STRUCTURES UNDER PROPAGATING EXCITATIONS by Zbigniew ZEMBATY Technical University of Opole, ul.Mikolajczyka 5, 45-233 Opole, POLAND l.Introduction The problem of vibrations of structures under incoherent or, in particular, propagating excitations is important for large, extended civil engineering structures like bridges, lifelines, dams, offshore structures or for aircraft structures. In seismic engineering spatial ground motion models have been studied for more than a decade but credible, stochastic characteristics are available only since SMART -1 accelerograph array is in operation at Lotung in Taiwan. Based on the spatial ground motion models the structural response can be analyzed in form of spatial response spectra [1-4] or for various specific types of structures, e.g. [5-11]. In present paper the problem is analyzed again and illustrated by an example of random vibrations of a bridge structure under kinematic wave excitations. 2.Equations of motion and mean square response Consider equation of motion of discrete systems under kinematic excitations: (1) where [M], [C], [K] are mass, damping and stiffness matrices, vector {q'} = {q;, q', ... , q'}T represents total displacements (fixed reference) and symbol T stands for 2 n transposition. These n degrees of freedom can be divided onto n. structural degrees and ng degrees associated with ground motion (n =n. +ng). Then eq .1 takes form + {tt} + {tt} ( 2 ) R. Rackwitz et al. (eds.), Reliability and Optimization of Structural Systems © Springer Science+Business Media Dordrecht 1995