液舱三维晃荡运动二阶共振理论解及特性分析  

Theoretical solution and analysis of second-order sloshing resonance in a 3D tank

作　　者：杨小岩[1] 张洪生[1] 吴鹏飞[1,2] 

机构地区：[1]上海海事大学海洋科学与工程学院,上海201306 [2]上海交通大学海科集团有限公司,上海200231

出　　处：《海洋工程》2015年第3期71-79,119,共10页The Ocean Engineering

基　　金：国家自然科学基金资助项目(51079082);上海市自然科学基金项目(14ZR1419600);上海市教委一流学科建设项目;2013年上海市研究生教育创新计划实施项目(第二批)

摘　　要：从无旋运动的理论出发,并利用微扰法,推导了液舱三维晃荡运动二阶共振问题的理论解。考虑纵荡和横荡运动情况,对液舱三维晃荡二阶共振问题进行了分析。当两个晃荡方向的和频(即其外部激发频率的和)或差频(即其外部激发频率的差值)等于液舱固有频率时,二阶共振发生;当某一晃荡方向(横荡或纵荡)外部激发频率与另一晃荡方向(纵荡或横荡方向)液舱某一固有频率的和或差值等于液舱另一固有频率时,二阶共振也会发生。进一步研究了各个二阶共振激发频率下水深变化对晃荡振幅的影响。结果表明,对于两个晃荡方向外部激发频率的和频和单一晃荡方向(纵荡或横荡)某一个激发频率与另一晃荡方向(横荡或纵荡)某一个属于奇模的固有频率的和频所引发的共振情况,水深变化对共振振幅大小的影响比较大;而对于相应差频所引发的共振情况,水深变化对共振振幅大小的影响比较小。Based on the velocity potential and perturbation theory, the problem of second-order sloshing in a three dimensional tank in combination with surge and sway motions is analyzed. When excitation is applied in both horizontal directions, the second-order resonance can occur when the sum frequency or the difference frequency of any two excitation components is equal to one of the natural frequencies. The resonance can also occur when the sum or difference frequency of one of the excitation frequencies and one of the natural frequencies is equal to another natural frequency. Furthermore, the effects of different water depths on the amplitudes of the second-order resonance are investigated. The analysis shows that the influence of water depth on the amplitudes of the second-order resonance which is caused by the sum frequency is more than that on the amplitudes of the second-order resonance which is caused by the difference frequency.

关 键 词：晃荡运动 二阶共振 液舱晃荡 激发振幅 黏性 船舶 

分 类 号：U663.85[交通运输工程—船舶及航道工程]