Analytical and numerical techniques in frequency domain response computation

In this paper the analytical formulation of frequency domain analysis is reviewed, under a unifying approach, for deterministic and random dynamic loading. In the random case both stationary and nonstationary excitations are considered. It is shown how, in all cases, a complex linear system must be solved at each frequency step; if the solutions are carried on independently, the solution cost grows almost linearly with the number of steps. Aiming at a computationally more efficient approach, iterative procedures are here proposed and developed, allowing for the simultaneous solution for a large number of frequencies. Some of the prolems arising in applications involving " large " systems are then discussed and solved. Examples are given with particular reference to 3D soil-structure finite-element models.