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.

Simultaneous Optimization of Elastic-Plastic Building Structures and Viscous Dampers Under Critical Double Impulse

“…where V is the velocity amplitude, δ(t) is the Dirac delta function and t 0 is the time interval of two impulses. Some investigations using the double impulse have been made for single-degree-offreedom (SDOF) models (Kojima and Takewaki, 2015;Akehashi et al, 2018a,b), investigations on MDOF models are extremely limited (Saotome et al, 2018;Shiomi et al, 2018;Takewaki, 2019, 2020). This may result from the fact that the simple energy balance law for the simple evaluation of the maximum response cannot be expected in MDOF models because of the phase lag.…”

Optimal Viscous Damper Placement for Elastic-Plastic MDOF Structures Under Critical Double Impulse

“…Figure 1A shows the acceleration, velocity and displacement of the double impulse together with those of the corresponding one-cycle sine wave of acceleration. While several investigations using the double impulse have been made for single-degree-of-freedom (SDOF) models Takewaki, 2015, 2016;Kojima et al, 2017;Akehashi et al, 2018a,b), researches on MDOF models are few (Taniguchi et al, 2016; Saotome et al, 2018;Shiomi et al, 2018). This is due to the fact that the simple energy balance law for the simple derivation of the maximum response is difficult to apply for MDOF models because of the phase lag.…”

Pseudo‐multi impulse for simulating critical response of elastic–plastic high‐rise buildings under long‐duration, long‐period ground motion

“…[21] The critical responses under MI have been investigated for elastic-plastic MDOF models so far. [22,23] However, the use of MI may lead to the overestimation of the acceleration responses under the corresponding multi-cycle sine wave (MSW) as a representative of long-duration ground motions due to its impulsive nature. Since an impulse input equally and simultaneously excites all the eigenmode responses, floor accelerations are apt to become excessive.…”