A New Theoretical Framework for Nonlinear Vibration-Based Condition Monitoring of Lithium-Ion Batteries

Vibration-based methods offer a promising nondestructive approach for monitoring lithium-ion battery (LIB) condition; however, most existing approaches rely primarily on linear or locally linear vibration models. This study develops a theoretical framework for characterizing the nonlinear vibration response of a cased LIB cell under impact, harmonic, and random excitations. A lumped-parameter model is formulated with a general constitutive relation incorporating nonlinear elastic and hysteretic behavior, while state of charge (SOC), state of health (SOH), and temperature are treated as quasi-static over the vibration time scale. Polynomial nonlinearities are analyzed using single-mode approximations. Quadratic and cubic stiffness terms generate distinct harmonic components and amplitude-dependent frequency shifts, while harmonic excitation can produce resonance bending and jump phenomena. Random excitation is represented by a bounded narrow-band stochastic process as a basis for analyzing stochastic amplitude and phase behavior. Hysteresis is examined using a bilinear internal-variable formulation that introduces history-dependent stiffness, amplitude-dependent effective properties, energy dissipation, and higher-harmonic components. The resulting analytical relationships provide theoretical baselines for nonlinear vibration features that may support LIB condition monitoring. Experimental identification and validation are required before these features can be associated with specific battery states or failure mechanisms.