Critical response of elastic-plastic SDOF systems with nonlinear viscous damping under simulated earthquake ground motions

Abstract

Multi impulse with constant time interval is used as a representative of a long-duration earthquake ground motion. An analytical expression is derived for the elastic-plastic response of a single-degree-of-freedom (SDOF) model with nonlinear viscous damping subjected to the “critical multi impulse” which maximizes the response. The fact that only free vibration appears under such multi impulse enables the smart application of an energy approach in deriving the analytical expression for a complicated elastic-plastic response with nonlinear viscous damping. The nonlinear viscous damping characteristic for deformation is approximated in terms of a quadratic or elliptical function. The critical timing of the impulses is found to correspond to the zero restoring-force timing or the maximum velocity timing depending on the input level. It is shown that the nonlinearity in viscous damping causes a remarkable influence on the earthquake response in some cases. The reliability and accuracy of the proposed theory are investigated through the comparison with the results by the time-history response analysis to the tuned sine wave as a representative of the long-duration earthquake ground motion.

Robust Optimal Damper Placement of Nonlinear Oil Dampers With Uncertainty Using Critical Double Impulse

“…The critical double impulse consisting of two inversely-directed impulses with the same velocity amplitude has been proposed by Kojima and Takewaki (2015) for the evaluation of the upper bound of elastic-plastic building responses under pulse-type ground motions. This can be easily used as the input excitation to MDOF building models in the time-history response analysis, since it is also easy to find the critical impulse timing (Akehashi and Takewaki, 2019;Tamura et al, 2019;Akehashi and Takewaki, 2020). Compared with conventional design earthquake ground motions such as actually recorded earthquake ground motions and artificial seismic waves, the input critical to building structures is used in this critical double impulse.…”

Critical Response of Multi-Story Damped Bilinear Hysteretic Shear Building Under Multi Impulse as Representative of Long-Period, Long-Duration Earthquake Ground Motions

“…In a similar way, a long-period and long-duration ground motion can be treated appropriately by introducing the multi impulse (Kojima and Takewaki, 2015b;Akehashi et al, 2018a;Hayashi et al, 2018;Tamura et al, 2019). When using the multi impulse, the free vibration analysis can be conducted without specification of input frequency before the second impulse is applied.…”

“…In this paper, the critical response is investigated for a multistory damped bilinear hysteretic shear building model under a multi impulse as a representative of long-period, long-duration earthquake ground motions. The critical response of an elasticplastic SDOF model under a multi impulse was derived in the previous papers (Kojima and Takewaki, 2015b;Akehashi et al, 2018a;Hayashi et al, 2018;Tamura et al, 2019). However, it is difficult to derive an explicit critical response for a MDOF model under a multi impulse because the phase lag among masses induces a complicated situation.…”