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. An explicit expression is derived on the maximum elastic–plastic response of a singledegree-of-freedom 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. Owing to the existence of only the free vibration under the double impulse, the approach of energy balance for the kinetic energy, hysteretic and strain energies, and damping energy plays a crucial role for deriving the explicit expression on a complicated damped bilinear hysteretic response. It is shown that the critical elastic–plastic deformation and the critical impulse timing, the interval of two impulses, can be derived depending on the input level. The accuracy and reliability of the proposed simplified but smart methodology are investigated through the comparison with the results by 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.