Nonuniform response spectrum incorporating real mode decomposition for seismic response analysis of boundary-SSI systems featuring dual nonclassical damping

Abstract

This paper aims to develop a nonuniform seismic response spectrum to enhance both the accuracy and efficiency of seismic analysis of viscoelastic boundary-soil-structure systems with dual nonclassical damping (VBSS-DNCD). Dual nonclassical damping consists of structural nonclassical damping (induced by structural dampers) and boundary nonclassical damping (induced by artificial boundaries). Compared with systems with only boundary nonclassical damping, the presence of structural nonclassical damping complicates the implementation of real mode decomposition. Consequently, deriving the corresponding real multipoint response spectrum (RMSRS) becomes substantially more complex. First, leveraging the inherent characteristics of both boundary and structural nonclassical damping, a theoretical framework and implementation strategy for orthogonalizing dual nonclassical damping is introduced. Subsequently, using our proposed orthogonally transformed real mode decomposition, the dynamic equations for the VBSS-DNCD system in the absolute coordinate system are decoupled, overcoming the limitations associated with complex mode decomposition. Additionally, an RMSRS based on real mode decomposition (RMSRS-DNCD) for the VBSS-DNCD system under nonuniform excitations is developed. The innovation lies in orthogonalizing dual nonclassical damping and deriving the response spectrum through real mode decomposition. Finally, to validate the accuracy and efficiency of the proposed method, a boundary-soil-bridge system with dual nonclassical damping under nonuniform seismic excitations is investigated using various methods. The results indicate that the proposed method exhibits a straightforward derivation process, adequate precision and computational efficiency. Compared with the conventional complex multipoint response spectrum (CMSRS) method, the RMSRS-DNCD method reduces the modal participation and cross-correlation coefficients by 3 and 12 terms, respectively.