Hysteresis Model for Nonlinear Dissipation Systems Based on Multistable Structures with Nonlinear Stiffness Elements

This paper presents a simplified dynamic model for capturing the hysteresis behavior of multistable energy dissipation systems. Such systems exhibit complex piecewise nonlinearities and history-dependent responses in their hysteresis loops, primarily driven by snap-through events. Despite their significant potential for shock absorption and vibration control, existing modeling methods often prove computationally inefficient for dynamic analysis. To address this, the paper proposes a simplified hysteresis model formulated as a first-order nonlinear differential equation with an additional degree of freedom. The model explicitly characterizes snap-through events and the associated discontinuities in force–displacement responses. Unlike traditional approaches, this model avoids the inefficiencies associated with dividing the program into multiple discontinuous branches and eliminates the need for implicit determination of snap-through events. The paper provides a detailed theoretical analysis and model validation, demonstrating that the proposed model can effectively capture the response of multistable energy dissipation systems under various working conditions. The model improves computational efficiency while maintaining high accuracy in predicting key response characteristics, making it a powerful tool for engineering applications of multistable energy dissipation systems.