An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations. The concentrated plastic hinges, described by the Bouc-Wen model, are assumed to occur at the two ends of a linear-elastic beam element. The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations. Then, the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems. To solve the equation of motion for equivalent linear systems, the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency. Finally, the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology, which provides a new way of obtaining the equivalent linear systems at different time instants. Based on the explicit time-domain method, the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency. Numerical examples indicate that the proposed approach has high computational efficiency, and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.