This paper investigates the coupled motion between the dynamics of $N$ vessels coupled together in a one-dimensional array by springs and the motion of the inviscid fluid sloshing within each vessel. We develop a fully nonlinear model for the system relative to a moving frame such that the fluid in each vessel is governed by the Euler equations and the motion of each vessel is modeled by a forced spring equation. By considering a linearization of the model, the characteristic equation for the natural frequencies of the system is derived and analyzed for a variety of nondimensional parameter regimes. It is found that the problem can exhibit a variety of resonance situations from the $1\text{:}1$ resonance to $(N+1)$-fold $1\text{:}\cdots \text{:}1$ resonance, as well as more general $r\text{:}s\text{:}\cdots \text{:}t$ resonances for natural numbers $r,s,t$. This paper focuses in particular on determining the existence of regions of parameter space where the $(N+1)$-fold $1\text{:}\cdots \text{:}1$ resonance can be found.

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• Interfacial flows