Critical earthquake response of a SDOF elastic‐perfectly plastic model with viscous damping under double impulse as a substitute for near‐fault ground motion.

The double-impulse input is introduced as a substitute for the fling-step near-fault ground motion, and a closed-form solution for the approximate elastic-plastic response of a structure with viscous damping under the “critical double impulse” is derived. Since only the free vibration appears under such a double impulse, the energy approach plays an important role in the derivation of the closed-form solution for a complicated elastic-plastic response with viscous damping. The quadratic function approximation for the damping force-deformation relationship is introduced. The validity and accuracy of the proposed theory are investigated through comparison of the results of the response analysis to the corresponding one-cycle sinusoidal input and actual recorded ground motions.