Liquid Cargo for Vibration Absorber Applications by Double Pendulum Modeling

Abstract

The double pendulum is a famous classical system represented as two coupled, nonlinear second order differential equations, and it is one that has been found to be particularly useful in simulating the motion of liquid cargo suspended from a floating crane in offshore contexts. The purpose of this study was to develop a practical vibration suppressor for offshore crane operations. By encouraging the sloshing of liquid cargo, it reduces the oscillation of the lifting object suspended from a crane installed on a floating offshore platform subjected to various excitation forces. Derivations are based in fundamental physics and mathematics. A parametric study is carried out to understand the sensitivity of the response to the design characteristics. Also included is discussion of the implications for use as a vibration absorber in the frequency domain. The double pendulum model is further validated by an in-house Numerical Sloshing Tank (NST) model. This is a well-tested model that calculates sloshing dynamics from nonlinear free surface boundary conditions. Subsequently, the pendulum model is simulated in the time domain with nominal prototype dimensions. The findings of this research agree well with previous studies, which included experimental validation from liquid cargo suspended below an oscillating cart. The findings are significant as they suggest a computationally cheaper alternative to CFD with which to estimate fluid behavior in this specific context. The double pendulum model can be easily extended and adjusted to minimize container motion for respective peak excitation frequencies.