Experimental Assessment of Fractional Linear Models for Liquid-Based Vibration Control Devices

The accurate assessment of the dynamic performance of vibration control devices for structural vibration mitigation commonly relies on simplified models that preserve key physical features and reduce computational complexity. In this framework, equivalent linearization approaches are frequently adopted to model nonlinear damping, a phenomenon that often governs the intricate dynamic response of engineering structures. Nevertheless, most existing techniques are formulated for systems under random excitations and are not easily applicable when other types of loading are considered. In particular, under deterministic inputs, typically used in laboratory experiments, these methods often fail to yield closed-form solutions, limiting their applicability. This study introduces a novel equivalent linearization framework based on fractional calculus, capable of predicting the response of systems with weakly nonlinear damping subjected to both stochastic and deterministic excitations. The method reformulates the governing nonlinear differential equation into a fractional-order linear equation. Fractional derivatives provide an enhanced mathematical representation of frequency-dependent damping, simultaneously modifying both the resonance frequency and damping ratio. To validate the proposed approach, small-scale dynamic experiments were performed on two representative liquid-based vibration control devices. These systems exhibit nonlinear fluid–structure interactions due to wave breaking and liquid impact. Experimental results, supported by numerical analyses, demonstrate that the fractional linearization accurately reproduces the observed dynamics, confirming the effectiveness of fractional operators in modeling nonlinear damping phenomena in liquid vibration absorbers.