Critical Response of Single-Degree-of-Freedom Damped Bilinear Hysteretic System under Double Impulse As Substitute for Near-Fault Ground Motion

A double impulse input is used as a substitute for near-fault earthquake ground motions. A closed-form expression is derived in the maximum elastic-plastic response of a single-degree-of-freedom (SDOF) damped structure with bilinear hysteresis under the ‘critical double impulse input’ which causes the maximum response for variable impulse interval with the input level kept constant. Since only the free-vibration exists under the double impulse, the energy balance approach for the kinetic energy, hysteretic and strain energies, and damping energy plays a key role in the derivation of the closed-form expression of a complicated damped bilinear hysteretic response. It is shown that the critical elastic-plastic deformation and the corresponding critical impulse timing can be derived depending on the input level. The accuracy of the proposed simplified but smart methodology is confirmed through the comparison with the response analysis to the critical double impulse and the corresponding one-cycle sine wave as a representative for the near-fault earthquake ground motion.