Exploring the Design, Modeling, and Identification of Beneficial Nonlinear Restoring Forces: A Review

Exploring the design of beneficial nonlinear restoring force structures has become a highly popular topic due to their extensive applications in energy harvesting, actuation, energy absorption, robotics, etc. However, the current literature lacks a systematic review and classification that addresses the design, modeling, and parameter identification of nonlinear restoring forces. Thus, the present paper provides a thorough examination of the latest advancements in the design of nonlinear restoring forces, as well as modeling and parameter identification in contemporary beneficial nonlinear designs. The seven design methodologies, namely magnetic coupling, oblique spring linkages, static or dynamic preloading, metamaterials, bio-inspired, MEMS (Micro-Electromechanical Systems) manufacturing, and dry friction applied approaches, are classified. The polynomial, hysteretic, and piecewise linear models are summarized for nonlinear restoring force characterization. The system parameter identification methods covering restoring force surface, Hilbert transform, time-frequency analysis, nonlinear subspace identification, unscented Kalman filter, optimization algorithms, physics-informed neural networks, and data-driven sparse regression are reviewed. Moreover, possible enhancement strategies for nonlinear system identification of nonlinear restoring forces are presented. Finally, broader implications and future directions for the design, characterization, and identification of nonlinear restoring forces are discussed.