Critical earthquake response of 2dof elastic-perfectly plastic model under multiple impulse as substitute for long-duration earthquake ground motions

Abstract

An equi-spaced consecutive impulse input is treated as a simplified representative for a long-duration earthquake ground motion. The key property of such input can be captured approximately by using harmonic waves. An approximate closed-form solution is derived for the elastic-plastic response of a two-degree-of-freedom (2DOF) system under the “critical multiple impulse input” based on some assumptions. The 2DOF system is assumed to consist of an elastic-perfectly plastic restoring-force characteristic in the first story and a linear elastic restoring-force characteristic in the second story. The fact that only the free vibration emerges under such multiple impulse input enables the utilization of the energy approach in the derivation of the explicit expression for a complicated elastic-plastic response. The critical timing of the impulses is found to correspond to the zero restoring-force timing in the first story. The validation and accuracy check of the proposed theory are conducted by implementing the response analysis to the corresponding sinusoidal input as a representative of the long-duration earthquake ground motion. It is also demonstrated that the proposed theory can be applied to a base-isolated building with hysteretic property in the base-isolation story regardless of the number of stories of superstructures.