Deterministic Excitation Forces for Simulation and Identification of Nonlinear Hysteretic SDOF Systems

Abstract

This paper investigates how to design deterministic excitation forces in studying nonlinear single-degree-of-freedom systems, especially those with rate and path dependency and strength and stiffness degradation. One frequency-modulated periodic excitation and its amplitude-modulated counterpart are proposed as a solution, and a series of numerical exercises are carried out to show that these forces can be designed for sufficient forcing functions to study the complex nonlinear hysteresis. To rapidly reveal the underlying characteristics of the system and also to further lead to an effective system identification, four evaluation tools are proposed to be utilized together with the proposed excitation forces. These tools include the response curves, force-state map, intercycle drift, and intercycle pattern change, based on which some distinctive “patterns” are obtained to reveal the existence of nonlinearities, types of nonlinearities, existence of memory, and degradation. By using both Bouc-Wen and Bouc-Wen-Baber-Noori models for the system in all the simulations, the writers compare the commonly used forces with the proposed excitation forces to further demonstrate the advantages of the proposed excitation forces and evaluation tools. The writers also explore challenges in terms of implementing the proposed excitation forces. The results of this study are expected to benefit both physical testing and numerical simulation of complex nonlinear hysteretic systems in a time- and cost-effective manner, as well as leading to efficient schemes for system identification.