Future directions


In this book, an innovative approach was introduced in nonlinear structural dynamics and earthquake-resistant design based on the smart use of impulse and energy balance law. The approach can overcome the long-time difficulty (many repetitions and large computational load) encountered first around 1960 in the field of nonlinear structural dynamics. The critical excitation problems as a worst input for elastic-plastic structures are tackled in a more direct way than the previous methods (Takewaki 2007) using the equivalent linearization methods (Caughey 1960a, b) and the mathematical programming including laborious nonlinear time-history analysis (Moustafa et al. 2010). The approach does not need any time-history response analysis which is believed to be inevitable in nonlinear structural dynamics. The approximate transformation of ground motions into impulses and the smart use of the energy balance approach enabled such dramatic progress. It may be said that the approach opened the door for an innovative field of nonlinear structural dynamics.

In this chapter, some future directions for further development of the approach explained in this book are presented.

Treatment of noncritical case

In this book, only the critical case (resonant case) was treated. The critical case was characterized by the input timing of the second impulse in the double impulse corresponding to the zero restoring force in SDOF models and the zero restoring force in the first story of the MDOF models. If the energy balance approach is applicable to noncritical cases, it is useful from the viewpoint of avoiding laborious nonlinear time-history response analysis.

In the previous researches, some presentations of such cases were made. Kojima and Takewaki (2015) showed briefly, in their appendix, the expression for noncritical case for demonstrating the criticality of input timing of the second impulse in the double impulse. Kojima and Takewaki (2016a) presented compactly, in their appendix, the expression for noncritical case.

Taniguchi et al. (2017) derived an expression in the nonresonant case for rocking vibration of a rigid block. Homma et al. (2020) investigated the general dynamic collapse criterion for elastic-plastic structures under the double impulse including noncritical case and clarified that the resonant case is not necessarily the critical case giving the lowest limit level of the input velocity.

More advanced developments are desired from the viewpoint of efficient evaluation of the resonance of nonlinear hysteretic vibrating system.

Extension to nonlinear viscous damper and hysteretic damper

It is well known that passive dampers, whether viscous or hysteretic, exhibit nonlinear behaviors in the large amplitude range (Soong and Dargush 1997, Hanson and Soong 2001, Lagaros et al. 2013, De Domenico et al. 2019). Tamura et al. (2019) presented the closed-form critical response of elastic- perfectly plastic SDOF systems with nonlinear viscous damping under the multi-impulse as a representative of long-duration ground motions. They used an approximation in the modeling of the damping force of oil dampers in the nonlinear range by extending the method explained in Chapter 5. Shiomi et al. (2016, 2018) demonstrated that the energy balance approach can be applied to the elastic-perfectly plastic SDOF models with single hysteretic and dual hysteretic dampers. The dual hysteretic damper system includes the hysteretic damper for small-amplitude vibration suppression and the hysteretic damper with a gap mechanism for large-amplitude vibration mitigation in parallel. Shiomi et al. (2016, 2018) showed that the present approach can be applied to nonlinear systems with general restoring-force characteristics.

Treatment of uncertain fault-rupture model and uncertain deep ground property

The uncertainties in the modeling of earthquake ground motions are critical for the reliable analysis of seismic safety of structures and infrastructures. In previous studies, many attempts to include various kinds of uncertain parameters have been conducted. However, the viewpoint from the critical response of structures for uncertain parameters in the fault-rupture model and the deep ground model seems missing. To overcome such drawbacks, Makita et al. (2018a, b, 2019) and Kondo and Takewaki (2019) presented some methods for including the uncertainties in the modeling of fault-rupture and deep ground. Application to a broader class of practical structures is desired.

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