Sensitivity of seismically excited structural systems by modal analysis

A procedure for evaluation of the sensitivity of the deterministic and stochastic response of nonclassically damped discrete structural systems under seismic actions is presented. It is based on a suitable modal expansion of the response that allows, even for large MDOF systems, the derivation in analytical form of the equations governing the evolution of the derivatives of the responses (the so-called sensitivity equations) with respect to the parameters that define the structural model, and the formulation of a procedure for their numerical solution. By means of an extensive employing of the Kronecker algebra the formulation is extended for evaluation of sensitivity of the stochastic response to seismic input modeled as random processes. Numerical applications illustrate the effectiveness of the proposed procedure.