Dinamically modified linear structures: deterministic and stochastic response

In the dynamical analysis structural modifications often appear for many reasons such as designer structural alterations, and discrepancies between predicted and measured properties of the structures. Furthermore, sometimes evaluating the eigenproperties of several structural systems, as non-classically damped structures or structural systems composed by a primary and a light secondary substructure, requires the adoption of the perturbation approach by considering the real structure as a modification of the original structure. In this paper an unconditionally stable step-by-step procedure able to evaluate both deterministic and stochastic responses of linear structural systems with dynamical modifications is presented. The proposed procedure overcomes the numerical drawbacks connected with the evaluation of the complex eigenproperties of the modified structure. The procedure is based on evaluating in approximate form the fundamental operator of the numerical procedure, either by a closed form expression or by an always convergent Taylor series, as a function of the transition matrix of the unmodified structure.