An efficient complex modal decomposition method for inelastic stochastic design spectrum-based analysis

An efficient stochastic modal decomposition method for random vibration analysis of non-classically damped nonlinear multi-degree-of-freedom (MDOF) systems is proposed in accordance with contemporary aseismic code provisions (e.g., EC8). Specifically, relying on statistical linearization and state-variable formulation, the complex eigenvalue problem considering inelastic MDOF structural systems subject to stochastic seismic processes is formulated and solved. To this aim, equivalent linear modal properties (EMPs), i.e., natural frequencies and damping ratios, are appropriately defined and evaluated based on an iterative scheme involving the determination of the system response covariance matrix as well. Note that the stochastic excitations are characterized by power spectra compatible in a stochastic sense with a given elastic response uniform hazard spectrum (UHS) of specified modal damping ratio. Next, the system EMPs are utilized in conjunction with the response elastic UHS for determining peak nonlinear responses in modal coordinates. Further, modal participation factors are evaluated for the complex-valued mode shapes and the generalized complete-quadratic-combination (CQC) is employed as the modal combination rule for determining the peak total responses. The reliability of the proposed framework is assessed by considering a 3-storey nonlinear frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear response time-history analysis (RHA) involving a large ensemble of Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed approach.