﻿ 流场中变截面加筋柱壳结构声振特性分析
 舰船科学技术  2016, Vol. 38 Issue (8): 29-33 PDF

1. 渤海船舶职业学院, 辽宁 葫芦岛 125015 ;
2. 哈尔滨工程大学, 黑龙江 哈尔滨 150001

Analysis on vibration and acoustic radiation of variable cross-section stiffened cylindrical shell in water
WANG Hong1, LIU Xian-He1, XU Wei2
1. Bohai Shipbuilding Vocational College, Huludao 125015, China ;
2. Harbin Engineering University, Harbin 150001, China
Abstract: Base on transfer matrix method, a solution of vibration and acoustic radiation of variable cross-section stiffened cylindrical shell in water under concentrated force and sound pressure was given. After availability of module truncation algorithm was confirmed, the research on vibration and acoustic radiation of the structure was carried out. The influence on vibration and acoustic radiation of the ring plate-cylindrical shell stiffened cylindrical shell structure was analyzed when the dissipation factor, fluid medium, shell thickness and number of ring stiffeners of the structure were changed. The results shown that the structural vibration was reduced and acoustic radiation pressure was increased when the fluid medium was existed; the vibration and acoustic radiation pressure were reduced at medium-high frequencies when the dissipation factor was increased; the vibration response of the shell was reduced with the thickness increased, and acoustic radiation pressure was reduced at the low frequencies, acoustic radiation pressure was cross fluctuations at high frequencies; the structure vibration was reduced with the ring stiffener number increased and the acoustic radiation pressure was reduced at high frequencies.
Key words: variable cross-section stiffened cylindrical shell     transfer matrix     vibration     acoustic radiation
0 前言

1 外界激励作用下的振动响应的求解

1）将结构沿着母线方向分成N个分段。

2）对N个分段分别进行分析，若第j个分段之中没有环肋或截面突变，则满足：

 $\left\{ \begin{array}{l} {T_{j + 1}} = \exp \left[ {\int_{{\xi _i}}^{{\xi _{j + 1}}} {U\left( \tau \right){\rm{d}}\tau } } \right],\\ {P_{j + 1}} = \int_{{\xi _j}}^{{\xi _{j + 1}}} {\exp \left[ {\int_\tau ^{{\xi _{j + 1}}} {U\left( s \right)ds} } \right]f\left( \tau \right){\rm{d}}\tau ,} \\ j = 1, \cdots ,n - 1. \end{array} \right.$ (1)

 $\left\{ \begin{array}{l} {T_{j + 1}} = - \exp \left[ {\int_{{\xi _i}}^{{\xi _{j + 1}}} {\rm{U}}\left( \tau \right){\rm{d}}\tau } \right]T{r_i}\exp {\left[ {\int_{{\xi _j}}^{{\xi _i}} U\left( \tau \right){\rm{d}}\tau } \right]_i},\\ {P_{j + 1}} = \exp \left[ {\int_{{\xi _i}}^{{\xi _{j + 1}}} U\left( \tau \right)d\tau } \right]T{r_i}\exp \left[ {\int_\tau ^{{\xi _i}} U\left( s \right){\rm{d}}s} \right]f\left( \tau \right){\rm{d}}\tau + \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \int_{{\xi _i}}^{{\xi _{j + 1}}} {\exp \left[ {\int_\tau ^{{\xi _{j + 1}}} {U\left( s \right){\rm{d}}s} } \right]f\left( \tau \right){\rm{d}}\tau .} \end{array} \right.$ (2)

3）计算Tj + 1Pj + 1，构造第j分段的传递关系：

 $Z\left( {{\xi }_{j+1}} \right)={{T}_{j+1}}Z\left( {{\xi }_{j}} \right)+{{P}_{j+1}}$
 $j=1,\cdots ,n$

 \begin{aligned} \int_{{\xi _j}}^{{\xi _{j + 1}}} & {\exp \left[{\int_\tau ^{{\xi _{j + 1}}} {U\left( s \right){\rm d}s} } \right]} f\left( \tau \right){\rm d}\tau = \\ & \frac{{\Delta \xi }}{2}\sum\limits_{k = 1}^n {{A_k}\exp \left[{U\left( {\bar \xi } \right)\frac{{\Delta \xi }}{2}\left( {1-{x_k}} \right)} \right]}\times \\ & f\left( {{\xi _j} + \frac{{\Delta \xi }}{2}\left( {1 + {x_k}} \right)} \right) + o\left( {\Delta {\xi ^{2n}}} \right)\text{。} \end{aligned} (3)

 \begin{aligned} Z\left( {{\xi }_{j+1}} \right)\!=\! & {{T}_{j+1}}Z\left( {{\xi }_{j}} \right)\!+\!\!\sum\limits_{k=1}^{n}{{{A}_{k}}\exp \left[U\left( {\bar{\xi }} \right)\frac{\Delta \xi }{2}\left( 1\!-\!{{x}_{k}} \right) \right]} \times\\ & f\left( {{\xi }_{j}}+\frac{\Delta \xi }{2}\left( 1+{{x}_{k}} \right) \right)+o\left( \Delta {{\xi }^{2n}} \right) \text{。}\\ \end{aligned} (4)

4）借助于有限元封装刚度阵、质量阵的思想，将N段整合成总的方程组：

 ${{\left[\begin{matrix} -{{T}_{2}} & \! \! \! \! \! \! \! I & {} & {} & {} & {} \\ {} & \! \! \! \! \! \! -{{T}_{3}} \! \! \! \! \! \! \! & I & {} & {} & {} \\ {} & {} & \! \! \! \! \! \! -{{T}_{4}} & \! \! \! \! \! \! I & {} & {} \\ {} & {} & {} & \! \! \! \! \! \! \cdots & \! \! \! \! \! \! I & {} \\ {} & {} & {} & {} & \! \! \! \! \! \! -{{T}_{n}} & \! \! \! \! \! \! I \\ \end{matrix} \right]}_{\left( 8n-8,8n \right)}}{{\left[\begin{matrix} Z\left( {{\xi }_{1}} \right) \\ Z\left( {{\xi }_{2}} \right) \\ Z\left( {{\xi }_{3}} \right) \\ \vdots \\ Z\left( {{\xi }_{n}} \right) \\ \end{matrix} \right]}_{\left( 8n,1 \right)}} \!\!\! = \! {{\left[\begin{matrix} {{P}_{2}} \\ {{P}_{3}} \\ {{P}_{4}} \\ \vdots \\ {{P}_{n}} \\ \end{matrix} \right]}_{\left( 8n-8,1 \right)}}$ (5)

2 流场辐射声压的求解

 ${{w}_{n}}\left( P \right)=w_{n}^{f}\left( P \right)+\sum\limits_{m=-\infty }^{+\infty }{{{c}_{mn}}w_{mn}^{p}\left( P \right)},P\in {{S}_{2}}\text{。}$ (6)

 ${{w}_{n}}\left( P \right)=0,P\in {{S}_{2}}\cup {{S}_{3}}\text{。}$ (7)

S2区域，以几何突变结构为例，存在关系：

 $\begin{array}{*{20}{l}} {\sum\limits_{m = - \infty }^{ + \infty } {{c_{mn}}{{K'}_{mn}}\left( P \right)} = }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \left\{ {\begin{array}{*{20}{c}} {0,P \in {S_1} \cup {S_3}}\\ {{\rho _0}{\omega ^2}\left( {w_n^f\left( P \right) + \sum\limits_{m = - \infty }^{ + \infty } {{c_{mm}}w_{mn}^p\left( P \right)} } \right),} \end{array}} \right.{\mkern 1mu} {\mkern 1mu} }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} P \in S_2^{,n \in \left( { - \infty , + \infty } \right)}} \end{array}$ (8)

 ${{\left[U \right]}_{n}}{{\left\{ c \right\}}_{n}}={{\left\{ Q \right\}}_{n}},n\in \left( -\infty ,+\infty \right)$ (9)

 {{\left[U \right]}_{q\times 2m+1}}\!\!=\!\!\left\{ \begin{aligned} & \left[{{{{K}'}}_{mn}}\left( {{P}_{sj}} \right) \right],P\!\in\! {{S}_{1}}\!\cup \!{{S}_{3}}\text{，} \\ & \left[{{{{K}'}}_{mn}}\left( {{P}_{sj}} \right)\!-\!{{\rho }_{0}}{{\omega }^{2}}w_{mn}^{p}\left( {{P}_{sj}} \right) \right],P\!\in \!{{S}_{2}} \text{。} \\ \end{aligned} \right. (10)
 {{\left[Q \right]}_{q\times 1}}=\left\{ \begin{aligned} & 0,P\in {{S}_{1}}\cup {{S}_{3}} \text{，} \\ & {{\rho }_{0}}{{\omega }^{2}}w_{m}^{f}\left( {{P}_{sj}} \right),P\in {{S}_{2}}\text{。} \\ \end{aligned} \right. (11)

3 模态的截断及算法有效性

4 变截面加筋柱壳结构声振特性分析

1）损耗因子对振动和声辐射的影响

 图 1 环板-圆柱壳加筋柱壳结构以及考核点 Fig. 1 The ring plate-cylindrical shell stiffened cylindrical shell structure and check point

 图 2 不同损耗因子下结构的振动与声辐射响应曲线 Fig. 2 The curve of structure vibration and acoustic radiation under the different dissipation factor

2）流体介质对振动和声辐射的影响

 图 3 不同流体介质下结构的振动与声辐射响应曲线 Fig. 3 The curve of structure vibration and acoustic radiation under the different fluid medium

3）壳体厚度对振动和声辐射的影响

 图 4 不同壳体厚度下结构的振动与声辐射响应曲线 Fig. 4 The curve of structure vibration and acoustic radiation under the different shell thickness

4）环肋数目对振动和声辐射的影响

 图 5 不同壳体厚度下结构的振动与声辐射响应曲线 Fig. 5 The curve of structure vibration and acoustic radiation under the different ring stiffeners number
5 结语

1）损耗因子在低频段对结构的声振响应影响较小，而在中高频段，振动响应和辐射声压均随损耗因子增加整体降低，尤其是在振动响应的峰值点则下降更显著；

2）流体介质对结构的声振特性影响较大，就振动特性而言，在频段内水中的振动小于空气中的振动，且振动峰值点被压平，曲线变平缓，对于结构声辐射，在空气中的辐射声压级明显小于水中声压，且在空气中曲线波动减少，波幅变大。

3）壳体厚度增大能够减小壳体的振动响应，降低低频段结构的声辐射，同时使中高频段的声辐射曲线出现交叉波动的复杂特征。

4）环肋数目增加后，结构振动减小，而结构辐射声压在低频段无明显变化，但在中高频段，随着环肋数目的增加，辐射声压级也有显著降低。

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