G. Muscolino, DYNAMICALLY MODIFIED LINEAR STRUCTURES - DETERMINISTIC AND STOCHASTICRESPONSE, Journal of engineering mechanics, 122(11), 1996, pp. 1044-1051
In the dynamical analysis structural modifications often appear for ma
ny reasons such as designer structural alterations, and discrepancies
between predicted and measured properties of the structures. Furthermo
re, sometimes evaluating the eigenproperties of several structural sys
tems, as non-classically damped structures or structural systems compo
sed by a primary and a light secondary substructure, requires the adop
tion of the perturbation approach by considering the real structure as
a modification of the original structure. In this paper an unconditio
nally stable step-by-step procedure able to evaluate both deterministi
c and stochastic responses of linear structural systems with dynamical
modifications is presented. The proposed procedure overcomes the nume
rical drawbacks connected with the evaluation of the complex eigenprop
erties of the modified structure. The procedure is based on evaluating
in approximate form the fundamental operator of the numerical procedu
re, either by a closed form expression or by an always convergent Tayl
or series, as a function of the transition matrix of the unmodified st
ructure.