Boundary element method in nonlinear sloshing analysis for shells of revolution under longitudinal excitations

Abstract

Processes of liquid sloshing in rigid shells of revolution filled with an ideal incompressible liquid are studied. The shells are subjected to longitudinal excitations. The liquid motion in these containers is supposed to be irrotational. The problems of liquid sloshing are considered in weakly nonlinear formulations when the free surface elevation is small compared with the shell radius. The spectral boundary problem on natural sloshing modes and frequencies is solved using the in-house computational tool based on boundary element methods. The linear and constant interpolations of unknown functions inside boundary elements are involved. The modes obtained are considered as basic functions for analysis of forced liquid vibrations. The numerical procedure based on boundary element method and the multimodal approach is developed for numerical analysis of nonlinear sloshing effects in rigid shells of revolution under longitudinal excitations. The free-surface elevation and velocity potential are expanded into infinite series with obtained basic functions and unknown time-dependent coefficients. The problems of liquid vibrations are reduced to solving nonlinear systems of second order ordinary differential equations about these coefficients that in linear formulation turns to the system of uncoupled Mathieu equations. The parametric oscillations are considered both in linear and nonlinear statements.