On the nonlinear energy interactions in harmonically excited cantilever in the presence of friction

The influence of nonlinearities in mechanical oscillators is a crucial factor which affects their dynamic behavior and often leads to energy interactions and intricate responses. Among these nonlinearities, friction, particularly on the excitation side, can play a significant role by introducing complex energy interactions even in systems that would otherwise exhibit linear behavior. Understanding the effects of excitation-side friction is vital, as it can lead to challenges in control, unexpected energy transfer, and even structural failure if not adequately understood and addressed. Despite its importance, the effects of excitation-side friction on the dynamics of both linear and nonlinear oscillators remain seldom explored. This study aims to investigate the effects of excitation-side friction on a harmonically base-excited cantilever through a theoretical framework. A mathematical model is developed to analyze the system’s response. The investigation reveals nonlinear phenomena such as Localized Energy Transfer, Symmetric Mean-Switching Modulation, and Energy Dispersion. Localized Energy Transfer unveils how friction-driven energy interactions amplify energy at specific harmonics, which can be leveraged in vibration-based energy harvesting and damping applications. Symmetric Mean-Switching Modulation demonstrates a unique oscillatory behavior that resembles bistable systems. It offers insights into friction-driven modulation mechanisms relevant to precision control and sensing technologies. Energy Dispersion highlights the transition to wide band low energy vibratory responses possessing chaotic characteristics, which has implications for structural health monitoring of the engineering systems. Various plots from the theoretical analysis are utilized to examine these effects comprehensively. The findings provide new insights into friction-induced nonlinear energy interactions under harmonic excitation and enhance understanding of oscillator dynamics, offering valuable contributions to theoretical research and practical applications.