Elastoplastic Response Spectra–Based Evaluation and Analytical Design of Inerter-Incorporated Nonlinear Structures

Inerter-based dampers have been proven effective as a seismic resilience–oriented control strategy to minimize damage probabilities, the parameter design and working mechanism for which are restricted mainly to elastic structures. Dealing with the understanding and seismic design of inerter-based nonlinear structures, this study establishes elastoplastic response spectra as a rapid performance evaluation tool and formulates a corresponding design strategy supported by analytical expressions, aiming to address the high computational cost associated with existing optimization algorithm–based parameter design methods. A mechanical model of a viscous mass damper (VMD), as a representative inerter-based damper, and a prototypical bilinear structural model were developed, upon which the governing equations of VMD-incorporated nonlinear structure were established, and the structural equivalent period and damping ratio were derived based on the ductility coefficient. Following the response spectra–based performance evaluation approach, the elastoplastic response spectra were established against various structural nonlinearity parameters, site conditions, fortification intensities, and design parameters of the VMD, correspondingly yielding the elastoplastic response spectra–based design strategy and curves anchored in spectral response mitigation ratios. The effectiveness of the proposed VMD design strategy was validated using design cases and evaluated using nonlinear time history analysis. The results show that the elastoplastic response spectra are quick-to-determine performance evaluation tools for VMD-incorporated nonlinear structures, and elucidated their roles in period modulation and acceleration–displacement control. The proposed elastoplastic response spectra–based design approach and analytical formulae facilitate the theoretical relationship among structural nonlinearity, VMD parameters, and vibration mitigation targets, thereby providing a simplified seismic design approach that avoids iterative computations. Overall, the elastoplastic response spectra, design strategy, and analytical formula bridge structural nonlinearity and inerter-based control strategies, offering a scalable approach adaptable to diverse structural states.