Combined dynamic response of primary and multiply connected cascated secondary subsystems

A method is proposed for the deterministic and stochastic non-stationary analysis of linear composite systems with cascaded secondary subsystems subjected to a seismic input. This method makes it possible to evaluate, by means of a unitary formulation, the deterministic and non-stationary stochastic response of both classically and non-classically damped subsystems and of secondary subsystems multiply supported on the primary one, as well as the ground. The proposed procedure is very efficient from a computational point of view, because of the Kronecker algebra systematically employed. Indeed, by using this algebra, it is possible to obtain in a very compact and elegant from the eigenproperties of the composite system as a function of the eigenproperties of the two subsystems taken separately. Moreover, it is possible to write the first order differential equations governing the evolution of the second order moments of the response and to solve them in a simple way.