Critical Response of Single-Degree-of-Freedom System with Bilinear Hysteresis and Viscous Damping under Triple Impulse

Kotaro Kojima ^1* Izuru Takewaki ²

• ¹ Kyoto Institute of Technology, Kyoto, Japan
• ² Kyoto Arts and Crafts University, Kyoto, Japan

A triple impulse is used as a mathematical model of forward-directivity inputs, which are faultnormal components of near-fault earthquake ground motions. In this paper, two types of the triple impulse input are employed. One is the triple impulse with the same time interval. The critical triple impulse of this sequence is defined as the triple impulse with the critical time intervals maximizing the displacement response, and the critical time intervals are necessary to be captured by changing the time intervals. The other is the triple impulse whose second and third impulses act at zero restoring force points. The elastic-plastic responses of single-degree-of-freedom (SDOF) systems with bilinear hysteresis and viscous damping under the two types of triple impulse are obtained by time-history response analysis and compared. Furthermore, approximate expressions are derived for the responses of the damped bilinear hysteretic SDOF system under the triple impulse (the latter one stated above) whose impulses act at the zero-restoring force timing. In the response derivation, a quadratic function approximation of the damping force-displacement relation and an energy balance approach are employed. The validity of the triple impulse as the model of the forward-directivity input and the accuracy of approximate expressions to the triple impulse (the latter one stated above) are checked by comparing them with responses under the equivalent three wavelets of sinusoidal waves and the Ricker wavelet.