Sub-critical excitations of SDOF elasto-plastic systems

The critical excitation of a dynamical system is defined as the excitation that drives the system from one state to another with minimum energy. It plays an important role in both deterministic and stochastic problems of vibrations. For linear-elastic systems it can be directly obtained by calculus of variation, but the approach is not applicable to general non-linear-hysteretic systems. For single-degree-of-freedom (SDOF) elasto-plastic systems, the critical excitation has been found recently using a time-domain parameterization scheme, which also suggested the existence of ‘sub-critical excitations’ stemming from the local optima of the associated optimization problem. This paper presents a study of the sub-critical excitations based on the theoretical background laid out in the previous work. The sub-critical excitations are investigated in terms of their time-domain characteristics, energy, abundance and distribution. It is found that sub-critical excitations exist in abundance and their number grows in a combinatorial manner with the target duration. When mapped on a polar plot relative to the critical excitation, their distribution exhibits structures of progressively fine scale as the target duration increases.