Review: Critical Excitation Problems for Elastic–Plastic Structures Under Simple Impulse Sequences

This review paper treats critical excitation methods and discusses the possibility of a paradigm shift in nonlinear structural dynamics for building structures with hysteresis using input model transformation without structural model transformation. Long-term key issues in the earthquake-resistant design of building structures are combats with resonance and damping. Nonlinear resonance problems are reformulated as critical excitation problems for elastic–plastic structures under a simple impulse sequence. The double impulse (DI) with two impulses of opposite directions is introduced as a simple representative model of near-fault pulse-type ground motions. The interval of such impulses is treated as a parameter to derive the critical input. Another critical excitation problem is considered for elastic–plastic building structures under the multi impulse (MI) representing long-period, long-duration ground motions. These critical excitation problems are solved by using an energy balance approach between the kinetic energy and the strain-dissipated energy. It is pointed out that this paradigm shift enables a smart capture of nonlinear resonance in structural dynamics, which has been thought to need intrinsic repetition of numerical computation. It is also found that this paradigm shift fills a gap between two historical hypotheses (constant energy criterion, constant displacement criterion) in the earthquake-resistant design of building structures.