Second-order Krylov subspaces for model order reduction of buildings subjected to seismic excitation

Determining the dynamic response to earthquakes is critical for designing building structures in seismic zones. Nevertheless, a massive computational burden is usually demanded when large-scale mechanical models are required or in applications of design optimization and uncertainty quantification. Therefore, a growing interest in non-modal Model Order Reduction (MOR) strategies, initially developed in control engineering, has been observed in earthquake engineering in the last few years. In addition to avoiding the previous solution of the eigenvalue problem, they are straightforward to non-classically damped systems, a key feature for externally controlled structures. Hence, this paper presents an original non-modal MOR framework for controlled and uncontrolled buildings subjected to seismic excitations. The main aim is to combine second-order Krylov subspaces to perform the FE system projection with the Adaptative Windowing Algorithm (AWA) for an automatic definition of expansion points and subspace order, which ensures significant reductions in computational burden. The application cases, with distinct controlled and uncontrolled buildings, show that the proposed scheme can accelerate the computational time in all assessed scenarios, reaching a speed-up factor (SUF) more than 50.