﻿ 大型舰船总振动固有频率近似计算研究
 舰船科学技术  2016, Vol. 38 Issue (12): 39-43 PDF

Approximate calculation study on the hull vibration natural frequency of laegr ships
ZHANG Jia-dong, CHEN Zhi-jian, TANG Yu-hang
Naval University of Engineering, Department of Naval Architecture Engineering, Wuhan 430033, China
Abstract: Based on the design rule of our country ships, a virtual design method for the initial data of a precise calculation of the hull vibration natural frequency of large ships is proposed.By using the prototype of the ship, a series of virtual ships within the legth of 165 m to 200 m is designed, then, the principal dimensions and the hull equivalent beam date are calculated for the hull vibration natural frequency. these data extends the statistical smaple range, which is ued to calculate the statistical coefficient in the hull vibration natural frequency approximation formula. According to these data, the experiential formula in order to etsimate lagre ships' vibration natural frequency is proposed.
Key words: virtual ship form design     the global vibration natural frequency     experiential formula
0 引 言

1 船体固有频率数学模型及近似计算公式

 $f = {\left( {\frac{{4.730}}{{2\pi }}} \right)^2}\sqrt {\frac{{EI}}{{\rho A{l^4}}}} \text{，}$ (1)

 $\left. \begin{array}{l} \Delta = {C_1}\rho Al\\ B{H^3} = {C_2}EI\\ {L_{pp}} = l \end{array} \right\} \text{，}$ (2)

 \left. \begin{aligned} & {f_{v2}} = {C_3}\sqrt {\frac{B}{\Delta }} \sqrt {\frac{{{H^3}}}{{L_{pp}^3}}} \\ & {f_{h2}} = {C_4}\sqrt {\frac{B}{\Delta }} \sqrt {\frac{{{H^3}}}{{L_{pp}^3}}} \end{aligned} \right\} \text{，} (3)

 \left. \begin{aligned} & {f_{v2}} = 0.94 \times {10^3}\sqrt {\frac{B}{\Delta }} \sqrt {\frac{{{H^3}}}{{L_{pp}^3}}} \\ & {f_{h2}} = 1.74 \times {10^3}\sqrt {\frac{B}{\Delta }} \sqrt {\frac{{{H^3}}}{{L_{pp}^3}}} \end{aligned} \right\}{\text{，}} (4)

 \left. \begin{aligned} & {f_{v2}} = \frac{{3.45}}{{\sqrt {1.2 + \frac{{{B_w}}}{{3D}}} }} \times \sqrt {\frac{{EI_{mid}^V}}{{L_{pp}^3}}} \\ & {f_{h2}} = \frac{{2.65}}{{\sqrt {1.2 + \frac{{{B_w}}}{{3D}}} }} \times \sqrt {\frac{{EI_{mid}^H}}{{L_{pp}^3}}} \end{aligned} \right\} \text{，} (5)

 \left. \begin{aligned} & {f_{v2}} = {\rm{1}}.{\rm{03}}4 \times {10^3}\sqrt {\displaystyle\frac{B}{\Delta }} \sqrt {\frac{{{H^3}}}{{L_{pp}^3}}} \\ & {f_{h2}} = 1.{\rm{91}}4 \times {10^3}\sqrt {\displaystyle\frac{B}{\Delta }} \sqrt {\frac{{{H^3}}}{{L_{pp}^3}}} \end{aligned} \right\} \text{，} (6)

 \left. \begin{aligned} & {f_{v2}} = \displaystyle\frac{{3.{\rm{968}}}}{{\sqrt {1.2 + \frac{{{B_w}}}{{3D}}} }} \times \sqrt {\frac{{EI_{mid}^V}}{{L_{pp}^3}}} \\ & {f_{h2}} = \displaystyle\frac{{{\rm{3}}.{\rm{44}}5}}{{\sqrt {1.2 + \frac{{{D_w}}}{{3B}}} }} \times \sqrt {\frac{{EI_{mid}^H}}{{L_{pp}^3}}} \end{aligned} \right\} \text{。} (7)
2 177～200 m 舰船船体模拟设计

 \begin{aligned} {m_v}(x) = \frac{\pi }{2}{\alpha _v}{k_i}{C_v}\rho {b^2}\text{，}\\ {m_h}(x) = \frac{2}{\pi }{\alpha _h}{k_i}{C_h}\rho {d^2}\text{。} \end{aligned} (8)

 $\frac{{{N_{\rm{n}}}}}{{\sqrt {\frac{{{I_{\rm{n}}}}}{{{\Delta _{\rm{n}}}L_{\rm{n}}^3}}} }}({\text{新设计船}}){\rm{ = }}\frac{{{N_0}}}{{\sqrt {\frac{{{I_0}}}{{{\Delta _0}L_0^3}}} }}(\text{母型船}) \text{。}$ (9)

3 大型舰船船体总振动频率近似计算方法 3.1 船体梁模型仿真分析

 图 1 第 1 阶垂向总振动 Fig. 1 The hull vertical vibration

 图 2 第 2 阶水平总振动 Fig. 2 The hull horizontal vibration
3.2 经验公式估算

 图 3 各船体垂向总振动固有频率 Fig. 3 The hull vertical vibrationnatural frequency

 图 4 各船体水平向总振动固有频率 Fig. 4 The hull vertical vibration natural frequency

1）随着船长的增大，其固有频率值逐步变小；

2）按母型船设计规律设计出的 177～200 m 船长范围内大型舰船的垂直向总振动固有频率计算值，与新准则中所推荐的设计阶段固有频率经验公式的垂直向总振动计算值符合良好，相互误差在 6% 左右；而水平向总振动计算值相互误差较大，达到 18%～30%；

3）虽然实船水平向总振动固有计算值与新准则中所推荐的设计阶段固有频率经验公式中水平向总振动计算值相互误差较大，但 2 种公式的估算结果误差波动幅值仅有 $\pm 1.15\%$，这可以通过修正固有频率近似公式中水平总振动的统计系数予以完善；

3.3 公式修正

 $f_{h2}'{\rm{ = }}\eta {f_{h2}} \text{，}$ (10)

η 以本文的样本扩展数据为基础、按文献[12]的数据拟合方法而得出：

 \left\{ \begin{aligned} & {\eta _1} = 0.75\text{，}\text{方案设计阶段}\text{，}\\ & {\eta _2} = 1.2\text{，} \text{深化方案设计阶段}\text{。}\end{aligned} \right. (11)

 \left. \begin{aligned} {f_{v2}} = {\rm{1}}.{\rm{03}}4 \times {10^3}\sqrt {\frac{B}{\Delta }} \sqrt {\frac{{{H^3}}}{{L_{pp}^3}}} \\ f_{h2}' = 1.436 \times {10^3}\sqrt {\frac{B}{\Delta }} \sqrt {\frac{{{H^3}}}{{L_{pp}^3}}} \end{aligned} \right\} \text{；} (12)

 \left. \begin{aligned} & {f_{v2}} = \frac{{3.{\rm{968}}}}{{\sqrt {1.2 + \frac{{{B_w}}}{{3D}}} }} \times \sqrt {\frac{{EI_{mid}^V}}{{L_{pp}^3}}} \\ & f_{h2}' = \frac{{4.134}}{{\sqrt {1.2 + \frac{{{D_w}}}{{3B}}} }} \times \sqrt {\frac{{EI_{mid}^H}}{{L_{pp}^3}}} \end{aligned} \right\} \text{。} (13)
4 结 语

1）经验式（6）和式（7）基本符合固有频率变化规律，垂直向总振动固有频率估算值与精确方法计算结果具有较好的一致性，但水平向固有频率估算值与精确方法计算结果存在较大误差；

2）式（12）和式（13）可以提高方案设计阶段与深化方案设计阶段对舰船船体水平向总振动固有频率计算值的精度；

3）基于舰船设计规律设计出虚拟船型进行固有频率的精确计算可行，可将船长扩展到关注的任意船长范围。

 [1] 王显正, 赵德有, 孙超, 等. 船舶总振动固有频率实用算法[J]. 中国舰船研究 , 2007, 2 (1) :56–58. WANG Xian-zheng, ZHAO De-you, SUN Chao, et al. Improved algorithm for the natural frequencies of ship vibration[J]. Chinese Journal of Ship Research , 2007, 2 (1) :56–58. [2] 翁长俭, 张保玉. 船舶设计时振动的预防[J]. 武汉造船 , 1979 (1) :25–42. [3] 解放军总装备部军标出版发行部. 舰船通用规范:GJB 4000-2000[S]. 北京:总装备部军标出版发行部, 2000. [4] 陈翔, 夏利娟, 丁金鸿, 等. 散货船的总振动模态计算和动力响应预报[J]. 舰船科学技术 , 2013, 35 (3) :115–120. CHEN Xiang, XIA Li-juan, DING Jin-hong, et al. The global vibration and dynamic response evaluation of a bulk carrier[J]. Ship Science and Technology , 2013, 35 (3) :115–120. [5] 水面舰艇结构设计计算方法:GJB/Z 119-99[S]. 北京:总装部军标出版发行部, 1999. [6] 陈志坚. 舰艇振动学[M]. 北京: 国防工业出版社, 2010 : 225 -226. [7] JOHANNESSEN H, SKAAR K T. Guidelines for prevention of excessive ship vibration[J]. SNAME Transaction , 1980, 88 :319–356. [8] 唐志拔. 水面舰艇设计[M]. 北京: 国防工业出版社, 1993 : 88 -99. [9] 邵开文, 马运义. 舰船技术与设计概论[M]. 北京: 国防工业出版社, 2005 . [10] 王晓宇, 伍友军. 某型测量船的船体总振动固有频率预报方法分析[J]. 船舶 , 2008, 19 (4) :18–26. WANG Xiao-yu, WU You-jun. Prediction methods for global vibration natural frequency of a survey ship[J]. Ship & Boat , 2008, 19 (4) :18–26. [11] 郭日修, 索志强. 我国船舶振动研究的回顾与展望(下)[J]. 振动与冲击 , 1989 (2) :66–69. [12] 程正兴. 数据拟合[M]. 西安: 西安交通大学出版社, 1986 : 1 -97.