Isospectral Stiffness Matrix Identification for the Equivalent Frame Modeling of Buildings

Seismic assessment and structural monitoring of monumental buildings are challenging tasks that often require simplified schemes to reduce the complexity of computational models. In earthquake engineering, a common modeling approach for masonry buildings is the Equivalent Frame Model (EFM). This technique discretizes masonry walls as an assembly of beam-column elements, where the nonlinear response is localized. Compared to more refined Finite Element Models (FEM), this strategy drastically reduces the computational burden of linear and nonlinear simulations. Moreover, it can also be effective in supporting Structural Health Monitoring applications, even if it entails a certain degree of approximation in reproducing the actual dynamic behavior of the structure. The work investigates one of the intrinsic assumptions of the EF approach, lumping the wall masses at the floor level, a strategy that can have significant implications for the predicted modal parameters – especially for monumental palaces with thick walls, large inter-story heights, or an irregular layout of the openings. This, in turn, can influence the accuracy of digital twinning procedures, which typically involve tuning the model’s mechanical parameters to match the experimental natural frequencies. The article leverages an inverse methodology recently proposed by the authors to analytically identify the stiffness matrix of a lumped-parameter EFM that is isospectral (i.e. has the same subset of natural frequencies) to a reference distributed-parameter FEM.