Nonlinear Sloshing of Liquid in a Rigid Cylindrical Container with a Rigid Annular Baffle under Lateral Excitation

Jiadong Wang,Sai Huen Lo,Ding Zhou,Yun Dong

doi:10.1155/2019/5398038

Abstract

Nonlinear response of liquid partially filled in a rigid cylindrical container with a rigid annular baffle subjected to lateral excitation is studied. A semianalytical approach is presented to determine the natural frequencies and modes of the liquid sloshing. Introducing the generalized time-dependent coordinates, the surface wave height and the velocity potential are expressed in terms of the natural modes of liquid sloshing. Based on the Bateman–Luke variational principle, the infinite-dimensional modal system is given by the variational procedure. The infinite-dimensional modal system is reduced by using the Moiseev asymptotic relations. The resultant hydrodynamic force and moment of the liquid pressure acting on the container mainly depend on the position vector of the mass center of the liquid. Expanding the integral about the weighted position coordinates into the Taylor series about the surface wave height at the unperturbed free surface gives the formula of the position vector of the mass center, which depends only on the generalized time-dependent coordinates. Excellent agreements have been achieved by comparing the present results with those obtained from Gavrilyuk’s solution and SPH solution. Finally, the surface wave height, resultant hydrodynamic force, and hydrodynamic moment for a container subjected to harmonic lateral excitation are discussed in detail.

Highlights

Liquid sloshing can cause a serious problem in liquid containers subjected to lateral excitation
Based on the velocity potential formulation and linearization theory, Goudarzi et al [7] developed an analytical model to estimate the dynamic damping ratio of liquid sloshing due to baffles in a liquid-filled rectangular container subjected to lateral excitation
A rigid cylindrical container with a thin rigid annular baffle, which is partially filled with inviscid, incompressible, and irrotational liquid, is depicted in Figure 1, where Ox′y′z′ is the absolute coordinate system and Orθz is the relative cylindrical coordinate system fixed at the container. e origin of Orθz is located at the center of the bottom of the container, and the z-axis is orthogonal to the bottom of the container

Summary

Introduction

Liquid sloshing can cause a serious problem in liquid containers subjected to lateral excitation. The linear dynamic response of liquid in a container equipped with baffles was investigated. Based on the velocity potential formulation and linearization theory, Goudarzi et al [7] developed an analytical model to estimate the dynamic damping ratio of liquid sloshing due to baffles in a liquid-filled rectangular container subjected to lateral excitation. Based on the natural frequencies and modes obtained, the linear dynamic response of the liquid in a baffled container subjected to lateral excitation was analyzed [10, 11]. Us, the proposed study focuses on the nonlinear response of the forced sloshing of the liquid in a baffled container subjected to lateral harmonic or seismic excitation. We conduct steady-state analysis in the frequency domain

Multimodal Method

Comparison Study

Findings

Conclusions