Energy-based dual-phased dynamics identification for forced nonlinear vibrations

System identification is critical to many engineering applications, especially in vibrating structures. The recently introduced Energy-based Dual-phase Dynamics Identification (EDDI) method is a data-driven technique to discover equations of motion using measured responses in compliance with physical balance laws. This work expands the original EDDI method for system identification for nonlinear single-degree-of-freedom (SDOF) oscillators under the influence of external forcing. The major innovation presented in this work is the reformulation of EDDI to incorporate external forces into the identification process. The method is deployed in two phases to systematically extract mathematical models for the damping and stiffness of the structure. At its core, EDDI leverages conservation of energy and Newton’s second law to express the measured data into a form that allows identification of the underlying dynamics. Phase I estimates the energy dissipated by the damping in the system using conservation of energy, then uses that to identify a mathematical model for the damping. Phase II applies Newton’s second law to isolate the conservative force directly, which is then used to identify a mathematical model for the stiffness of the structure. EDDI requires only the measured response, the external force, and the mass of the oscillator for the identification with no prior information of system dynamics necessary. The method is first demonstrated using a numerically simulated Duffing oscillator with negative linear stiffness, positive nonlinear stiffness, and sinusoidal forcing. The method is then applied to experimentally measured responses of a Duffing oscillator with unknown stiffness and damping excited by a nonlinear external force through a magnetic stinger and a modal shaker.