ACCURACY OF THE TIME HISTORY ANALYSIS OF 2DOF SUBJECTED TO BASE EXCITATIONS BASED ON THE SUPERPOSITION OF THE ELASTO-PLASTIC RESPONSE OF EACH MODE

This paper develops the time history analysis of the elasto-plastic response of the 2DOF, consisting of two masses and springs that exhibit bilinear hysteresis, being subjected to a base excitation, based on superposition of the time history of elasto-plastic response of each mode. The essence of the proposed analysis is that the response of the 2DOF during the yielding of any springs consists of the mode frequencies, shapes and dampings that are readily specified by the eigenvalue problem employing the mass and the secondary stiffness of the spring yielded. First, the equations governing the response of each mode according to the state of spring and all quantities needed for them are described in detail. Next, a displacement time history of each mode is numerically and simultaneously analyzed, because the response of each mode is superposed at every time step to verify the elastic limit or turn-around points of each spring that are only verifiable in the global coordinates system. Once the response exceeds the elastic limit of each spring or the turn-around points, the equations of motion of each mode are switched to those of the next state of spring. Finally, the accuracy of the proposed method is thoroughly discussed. Moreover, the force-displacement diagram of each mode is presented. The applicability of the SRSS method is also examined.