Multimodal method for linear liquid sloshing in a rigid tapered conical tank

Abstract

PurposeThe purpose of this paper is to derive linear modal equations describing the forced liquid sloshing in a rigid truncated (tapered) conical tank, as well as to show how to couple these modal equations with “global” dynamic equations of a complex mechanical system carrying this tank.Design/methodology/approachDerivation of the modal equations can be based on the Trefftz variational method developed by the authors in a previous paper. Describing the coupled dynamics utilizes Lukovsky' formulas for the resulting hydrodynamic force and moment due to liquid sloshing.FindingsThe so‐called Stokes‐Joukowski potentials can be found by using the Trefftz method from the authors' previous paper with the same polynomial‐type functional basis. Coupling the modal equations with the global dynamic equations becomes a relatively simple task facilitated by Lukovsky's formulas. Using the linear multimodal method can be an efficient alternative to traditional numerical and analytical tools employed for studying the coupled vibrations of a tower with a conical rigid tank on the tower top.Practical implicationsThe derived modal equations are equipped by tables with the computed non‐dimensional hydrodynamic coefficients. Interested readers (engineers) can incorporate the modal equations into the global dynamic equations of a whole mechanical system without new computations of these coefficients.Originality/valueThe multimodal method can be an alternative to traditional numerical tools. Using the derived modal equations simplifies analytical studies and provides efficient calculations of the coupled dynamics of a mechanical system carrying a rigid tapered conical tank with a liquid.