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.

In-plane Auto-Parametric Vibration of Inclined Cables under Random Transverse Excitation

In-plane auto-parametric stochastic vibration of inclined cables subjected to Gaussian white noise in transverse bridge orientation is investigated. Based on Newton＇s laws of motion and Galerkin＇s modal truncation principle, the influences of geometry nonlinearity induced by sag and large displacement of cables and the initial equilibrium state are taken into account. Meanwhile, the three-dimensional non-linear differential equations of inclined cables for coupling vibration are deduced, equivalent stochastic linearization method is applied to derive the 14-dimensional first-order nonlinear differential equations of state vectors, and the Runge-Kutta integration method is utilized to obtain the root mean square （RMS） response. Results show that when the transverse random excitation imposed on the stayed cable exceeds a critical value, the in-plane transverse vibration of the cable are excited due to tim auto-parametric nonlinear coupling, and the critical value of random excitation increases with the damping ratio. In this motion, the cable response possesses non-stationary characteristics, even though the loading keeps stationary.