Ghost hammering in a randomly excited nonlinear dynamical system

Random phenomena are widespread across disciplines such as Engineering, Physics, Geophysics, and Medicine, often arising from the inherent variability of natural systems. In Structural Mechanics, sources of randomness include environmental forces like wind, seismic activity, and manufacturing tolerances, which can induce vibrations with unpredictable features. While linear methods have traditionally been used to analyse such vibrations, they often fail to capture the complex behaviour that emerges in nonlinear systems. This study investigates the dynamic response of a circular cylindrical shell subjected to high-energy, narrowband random seismic excitation. Experimental observations revealed the occurrence of irregular, high-amplitude spikes in the system's response, events unpredictable and incomprehensible by using linear models. These phenomena bear a strong resemblance to Extreme Events (EE), Stochastic Resonance (SR), Bursting Behaviour (BB), and Spiking Oscillations (SO) observed in fields like Neuroscience, Optics, and Electronics, but rarely documented in Solid Mechanics. The observed spikes, termed “Ghost Hammering (GH),” appear as transient oscillations at the system's natural frequencies, resembling sudden impacts despite the absence of external impulses. Their behaviour suggests strong nonlinear interactions triggered by random excitation. Models used in neuroscience and nonlinear physics, such as van der Pol, FitzHugh–Nagumo, and Langevin systems, offer promising frameworks for interpreting these phenomena. The paper details the experimental setup and standard modal analysis of the shell, followed by a focused discussion of the extreme events observed. These findings highlight the need to expand the application of stochastic nonlinear models to structural systems, offering new perspectives on how randomness can drive unexpected behaviours in mechanical structures.