计及自由液面影响的水下有限深度圆柱壳自由振动分析  

Free vibration of a submerged cylindrical shell with a finite submerged depth considering the effect of free surface

作　　者：郭文杰[1,2] 李天匀[1,2,3] 朱翔[1,2] 缪宇跃[1,2] 杨国栋[1,2] 

机构地区：[1]华中科技大学船舶与海洋工程学院,武汉430074 [2]船舶与海洋水动力湖北省重点实验室,武汉430074 [3]高新船舶与深海开发装备协同创新中心,上海200240

出　　处：《振动与冲击》2017年第10期1-6,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51379083;51479079;51579109);高等学校博士学科点专项科研基金项目(20120142110051)

摘　　要：提出了一种求解有限浸没深度下圆柱壳振动特性的解析方法。采用镜像原理和Graf加法定理得到流体速度势的解析表达式,然后再结合能量泛函变分方法推导出计及自由液面影响的壳-液耦合振动方程,通过求解该方程,得到结构各阶固有频率。研究表明,相比于无限域,自由液面的存在会增大同阶次模态固有频率,而且离自由液面越近,固有频率越大,但是随着浸没深度逐渐增加,自由振动特性很快趋近于无限域。与有限元软件Nastran计算结果对比表明该方法准确、可靠、简便,且具有计算量小、易于参数优化的优点,也为近水面结构流固耦合振动特性分析提供了新的思路。An analytical method was proposed to solve the vibration characteristics of a submerged finite cylindrical shell with a finite submerged depth from the fluid free surface.Based on the image method and the Graf 's addition theorem,the analytical expression of the velocity potential of fluid was obtained.According to the energy functional variation principle,combined with the velocity potential of fluid,a fluid-structure coupling equation of the submerged finite cylindrical shell was deduced,and the natural frequencies of the shell were calculated.It is found that,with the same modal order,the natural frequency of the submerged finite cylindrical shell with the consideration of the effect of free surface is larger than that in an infinite fluid field.The natural frequency increases as the submerged depth of the finite cylindrical shell decreases.Moreover,the free vibration characteristics of the submerged finite cylindrical shell with considering the free surface tend to be the same as those without considering the free surface as the submerged depth increases.The reliability and efficiency of the present method were validated by comparing with the finite element method.The work provides more understanding on the vibration characteristics of the submerged finite cylindrical shell with finite submerged water depth.

关 键 词：自由液面 能量泛函变分 镜像原理 Graf加法定理 

分 类 号：U661.44[交通运输工程—船舶及航道工程]