A perturbation approach for the response of dynamically modified structural systems

The problem of the structural analysis under changes of dynamical parameters is of particular interest. This is due to the fact that often the real structures are different from the predicted ones. In this paper, an unconditionally stable step-by-step procedure, able to evaluate the deterministic response of linear structures with modifications, is presented. The proposed procedure requires the evaluation of the transition matrix, which is the fundamental operator of the step-by-step solution, by means of a perturbation approach. This technique overcomes the difficulties connected with the evaluation of the eigenproperties of the modified structures usually required to obtain the transition matrix. Furthermore, it is successfully applicable, even in the presence of large structural modifications. An application to a simple case shows the advantages of the method proposed herein.