CLOSED-FORM SOLUTIONS FOR THE RESPONSE OF LINEAR-SYSTEMS TO FULLY NONSTATIONARY EARTHQUAKE EXCITATION

New explicit closed-form solutions are derived for the evolutionary co rrelation and power spectral-density (PSD) matrices characterizing the nonstationary response of linear elastic, both classically and noncla ssically damped, multi-degree-of-freedom (MDOF) systems subjected to a fully nonstationary earthquake ground motion process. The newly devel oped earthquake ground motion model considered represents the temporal variation of both the amplitude and the frequency content typical of real earthquake ground motions. To illustrate the analytical results o btained, a three-dimensional unsymmetrical building equipped with visc ous bracings is considered with a single-component ground motion actin g obliquely with respect to the building principal directions. These n ew analytical solutions for structural response statistics are very us eful in gaining more physical insight into the nonstationary response behavior of linear dynamic systems subjected to realistic stochastic e arthquake ground motion models. Furthermore, the evolution in time of the cross-modal correlation coefficients is examined and compared with the classical stationary solution for white-noise ground motion excit ation. The effects of cross-modal correlations on various mean-square response quantities also are investigated using the analytical solutio ns obtained.