Seismic Behavior of a Secondary System on a Yielding Torsionally Coupled Primary System

Dynamic analysis of a secondary system mounted on a torsionally coupled non-linear primary system is presented for bi-directional random earthquake excitation, which is idealized as a broad band stationary random process. The hysteretic force deformation behavior of the non-linear primary system is modelled by a set of coupled non-linear differential equations. The responses are obtained by the linearized frequency domain spectral analysis and are compared with those obtained by the time domain simulation procedure. The response quantities of interest are the relative displacement between the primary and the secondary structural systems and the absolute acceleration of the secondary system itself. The response behavior of the secondary system is examined under a set of parametric variations. These parameters include the uncoupled lateral frequencies of the primary and the secondary structural systems; the ratio of the uncoupled lateral to rotational frequencies of the primary system; the hysteretic parameters of the primary system; eccentricity ratios of the primary and the secondary structural systems in x and y directions; damping ratios of the primary and the secondary structural systems; and the mass ratio of the two sub-systems. Some of the results of the study show that the responses of the secondary system increase with the increase in normalized eccentricities of the primary system under the tuned condition. However, an opposite trend is observed under the untuned condition. Responses of the secondary system is found to be more if the interaction between the primary and the secondary structural systems is considered. Further, responses of the secondary system decrease with the increase in the mass ratio between the secondary and the primary systems.