Global Maximum Response of Linear Systems with Uncertain Damping to Irregular Excitation

In the evaluation of the global maximum response of a structure subjected to its design load, damping effects must be included; however, the structure damping is often uncertain. This study develops an efficient method to compute the probability density function (PDF) of the global maximum dynamic response for multi-degree-of-freedom (MDOF) linear systems with uncertain damping when the external excitation is highly irregular. Operated in the complex plane, the proposed method is a pole-residue method that formulates a closed-form solution for the uncertain response at any instant time in terms of the poles and residues of the excitations and those of the system. While the poles and residues of an irregular excitation are deterministic quantities, those of the system are treated as random variables. In the numerical studies, a 100-story shear building subjected to a realistic ground motion is demonstrated, and the correctness of the proposed method is verified by Monte Carlo simulations.