Response regimes in equivalent mechanical model of moderately nonlinear liquid sloshing

Abstract

The paper considers non-stationary responses in reduced-order model (ROM) of partially liquid-filled tank under external forcing. The model involves one common degree of freedom for the tank and the non-sloshing portion of the liquid, and the other onefor the sloshing portion of the liquid. The coupling between these degrees of freedom is nonlinear, with the lowest-order potential dictated by symmetry considerations. Since the mass of the sloshing liquid in realistic conditions does not exceed 10% of the total mass of the system, the reduced-order model turns to be formally equivalent to well-studied oscillatory systems with nonlinear energy sinks (NES). Exploiting this analogy, and applying the methodology known from the studies of the systems with NES, we predict a multitude of possible nonstationary responses in the considered ROM. These responses conform, at least on the qualitative level, to the responses observed in experimental sloshing settings, multi-modal theoretical models and full-scale numeric simulations.

A Simple Model-Based Method for Sloshing Estimation in Liquid Transfer in Automatic Machines

“…• the liquid must exert the same wrenches on the container wall. We can identify three different dynamic regimes for the motion of the liquid free surface, with each one of them corresponding to a different model [13], [16], [17]:…”

“…In ( 8), we only need to replace x G with r G and x n with r n , thus obtaining: r G m f = n r n m n . Equation ( 9) is also applicable in the radial dimension to find r G by substituting x with r. Finally, considering that r 2 n = x 2 n + y 2 n , we obtain: 17)…”

“…An important aspect to consider, in order to design the correct trajectory for a given container filled with a liquid, is the evaluation of the maximum sloshing height, namely the highest point reached by the liquid free surface during motion. As a matter of fact, the classical models known in the literature to study the liquid behavior (mass-spring-damper and pendulum models [13]- [17]) do not provide responses with a clear practical meaning: they are built with dummy masses whose displacements can be calculated, but these are not immediately related to the actual sloshing height. A simple model-based computational instrument able to analyt-ically estimate the response of the system in terms of sloshing height for an arbitrary container trajectory would be very useful, since it would allow the motion designer to reasonably assess whether the liquid is likely to spill out or surpass a given limit, without experimental testing or computationallydemanding fluidodynamical (CFD) simulations.…”

Dynamics of a hybrid vibro‐impact nonlinear energy sink

“…One can see in (), that represents the minimum amplitude of the PS possible for existence of 1:1 resonance. This expression introduces the slow invariant manifold (SIM)4,24–26 of the system. The SIM consists of two branches, stable and unstable, corresponding to the positive and negatives signs in Equation (), respectively.…”

Robust Tracking Control for Slosh-Container System Against Viscous Friction Uncertainty

“…In the previous literature review, the first step for the researchers is to develop the dynamic mathematical model of the slosh-container system. This model usually is very complex and nonlinear, as it can be represented as two degrees of the freedom pendulum system, [5,6]. Then they design their proposed controller techniques.…”