计及自由液面影响的水下有限深度圆柱壳自由振动分析

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

振动与冲击 ›› 2017, Vol. 36 ›› Issue (10) : 1-6.

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (10) : 1-6.
论文

计及自由液面影响的水下有限深度圆柱壳自由振动分析

  • 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
作者信息 +

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

  •   GUO Wenjie1,2 LI Tianyun1,2,3 ZHU Xiang1,2 MIAO Yuyue1,2 YANG Guodong1,2
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摘要

本文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计算结果对比表明本文方法准确、可靠,且具有方法简便、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。

Abstract

An analytical method is proposed to solve the vibration characteristics of a submerged finite cylindrical shell at finite depth from the free surface. Based on the image method and the Graf’s addition theorem, the analytical expression of the velocity potential of fluid is obtained. By combining the velocity potential of fluid and the energy functional variation principle, the fluid-structure coupling equation of the submerged finite cylindrical shell are deduced, then the natural frequencies of the submerged finite cylindrical shell can be calculated. It is found that, with the same modal order, the natural frequency of the submerged finite cylindrical shell with the free surface is larger than that without the free surface. The natural frequency increases as the finite cylindrical shell approaches the free surface. Moreover, the free vibration characteristics of the submerged finite cylindrical shell with the free surface tend to be the same as those without the free surface as the increase of the submerged depth. The reliability and efficiency of the present method are validated by comparison with the finite element method. The work provides more understanding on the vibration characteristics of a submerged finite cylindrical shell in finite water depths.

关键词

自由液面 / 能量泛函变分 / 镜像原理 / Graf加法定理

Key words

free surface / energy functional variation / image method / Graf’s addition theorem

引用本文

导出引用
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. 计及自由液面影响的水下有限深度圆柱壳自由振动分析[J]. 振动与冲击, 2017, 36(10): 1-6
GUO Wenjie1,2 LI Tianyun1,2,3 ZHU Xiang1,2 MIAO Yuyue1,2 YANG Guodong1,2. Free vibration of a submerged cylindrical shell considering the effect of free surface in finite depth[J]. Journal of Vibration and Shock, 2017, 36(10): 1-6

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