Fractional Calculus Application in Modelling Non-Linear Sloshing

Many models exist to describe the nature of sloshing, an intricate phenomena, including the linear mechanical model and the Duffing oscillator. This paper attempts to provide an alternative model that describes the maximum slosh wave height (MSWH) of different sloshing liquids, to more accurately predict the nuanced phenomena as well as to better understand the inherent nature of sloshing. We explore three different models, the classical linear mechanical model, the non-linear Duffing model and finally the novel fractional visco-elastic model. The latter illustrates promising results after being validated via experimentation. The paper leads to the conclusion that sloshing of liquids, particularly low-viscosity fluids, is better described to have a spectrum of fractional-order visco-elastic forces at near and post resonant excitation frequencies rather than independent viscous and elastic forces as assumed by the linear and non-linear mechanical models.