Stochastic sensitivity of steel frames with connection dampers by modal analysis

A procedure for evaluation of dynamic response sensitivity of multistory steel frames with added visco-elastic beam to column connections by modal analysis is presented. The connection behavior is modeled by a Kelvin-Voigt element, consisting of a rotational spring and a dashpot connected in parallel. Consistent mass, stiffness and damping matrices of the multistory frame are utilized, leading to a structure modeling as a non-classically damped system. The procedure is based on the dynamic modification method, that allows to evaluate the response of non-classically damped structure by modal superposition, without transformation in the complex space. The differential equations governing the evolution of the derivatives of the responses (the so-called sensitivity equations) with respect to the stiffness and damping of the connections are derived in the modal subspace by a time domain approach. By means of an extensive employing of the Kronecker algebra the formulation is extended for evaluation of stochastic sensitivity of the dynamic response to a white noise excitation. The effectiveness of the proposed procedure in aiding the structural design is shown by evaluation of the response sensitivity of a eight-story steel frame with added visco-elastic connections. The analysis allows to evaluate the parameter ranges for which the uncertainty in their evaluation results to a small risk level, due to a small sensitivity of the response.