湍流边界层作用下薄板随机振动声辐射的辛方法

潘晨鸽; 李榆银; 张亚辉

doi:10.21656/1000-0887.380151

湍流边界层作用下薄板随机振动声辐射的辛方法

doi: 10.21656/1000-0887.380151

工业装备结构分析国家重点实验室(大连理工大学), 辽宁大连 116024

基金项目: 国家自然科学基金（11672060）

详细信息

作者简介:
潘晨鸽（1990—），女，博士生（E-mail: panchenge152@163.com）；李榆银（1989—），男，博士生（E-mail: liyuyin@mail.dlut.edu.cn）；张亚辉（1972—），男，教授，博士生导师（通讯作者. E-mail: zhangyh@dlut.edu.cn）.

中图分类号: O324
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- 被引次数: 0
出版历程
- 收稿日期: 2017-05-23
- 修回日期: 2017-11-16
- 刊出日期: 2018-01-15

Random Sound Radiation of Thin Plates Under Turbulent Boundary Layer Excitations With a Symplectic Method

State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology), Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China（11672060）

摘要

摘要: 基于辛对偶体系，研究了湍流边界层作用下薄板随机振动的声辐射问题.首先对湍流边界层的互功率谱密度函数进行Fourier级数展开，从而可将随机场激励下结构随机声辐射问题转化为在空间和时间简谐压力作用下结构确定性响应的求解；然后将薄板的运动方程导入辛对偶体系，并采用分离变量法得到辛本征问题；最后采用辛本征向量对待求的响应向量和作用力向量进行展开，即可得到解耦后的方程，由此降低了方程的求解难度，并可得到问题的辛解析解.由于该文方法在辛对偶体系下进行求解，相比模态叠加法，避免了模态截断问题，在精度上具有较大优势.算例部分首先考虑空间和时间简谐压力作用的情况，通过与模态叠加法结果的对比，验证了该文方法的有效性.随后采用该文方法求解了湍流边界层作用下随机声场的声压功率谱密度函数的声压级，讨论了因Fourier级数截断而产生的收敛性问题，并研究了薄板随机振动辐射声场的指向性.
- 辛对偶体系 /
- 湍流边界层 /
- 随机振动 /
- 随机声辐射
Abstract: The random sound radiation of thin plates subjected to turbulent boundary layer (TBL) excitations was studied in the symplectic duality system. Firstly, the cross power spectral density of the TBL was represented by a Fourier series, and the problem of the random sound radiation of structures excited by a random field was reduced to solve the deterministic response function, i.e. the structural response to a spatial and temporal harmonic pressure of unit magnitude. Secondly, the free vibration analysis of thin plates was introduced to the symplectic duality system, then a symplectic eigenproblem was formed with the method of separation of variables. Finally, the decoupled governing equations were derived through expansion of the response and excitation vectors in the symplectic space, to reduce the difficulty of solving the equations, and the symplectic analytical solution was obtained. In contrast to the modal decomposition method (MDM), the presented method is formulated in the symplectic duality system and does not need modal truncation, hence the computations are of high precision. In the numerical examples, the harmonic response functions for the thin plate were studied, and a comparison was made with the MDM to verify the effectiveness of the presented method. Thereafter, the sound pressure levels (SPL) of the power spectral density of the sound pressure response to the TBL were obtained, the convergence induced by the Fourier series expansions was examined, and the directivity functions of the radiation sound field were extensively investigated.
- symplectic duality system /
- turbulent boundary layer /
- random vibration /
- random sound radiation

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参考文献(25)

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湍流边界层作用下薄板随机振动声辐射的辛方法

doi: 10.21656/1000-0887.380151

作者简介:
潘晨鸽（1990—），女，博士生（E-mail: panchenge152@163.com）；李榆银（1989—），男，博士生（E-mail: liyuyin@mail.dlut.edu.cn）；张亚辉（1972—），男，教授，博士生导师（通讯作者. E-mail: zhangyh@dlut.edu.cn）.

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Random Sound Radiation of Thin Plates Under Turbulent Boundary Layer Excitations With a Symplectic Method

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留言板

湍流边界层作用下薄板随机振动声辐射的辛方法

doi: 10.21656/1000-0887.380151

作者简介: 潘晨鸽（1990—），女，博士生（E-mail: panchenge152@163.com）；李榆银（1989—），男，博士生（E-mail: liyuyin@mail.dlut.edu.cn）；张亚辉（1972—），男，教授，博士生导师（通讯作者. E-mail: zhangyh@dlut.edu.cn）.

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出版历程

Random Sound Radiation of Thin Plates Under Turbulent Boundary Layer Excitations With a Symplectic Method

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出版历程

目录

作者简介:
潘晨鸽（1990—），女，博士生（E-mail: panchenge152@163.com）；李榆银（1989—），男，博士生（E-mail: liyuyin@mail.dlut.edu.cn）；张亚辉（1972—），男，教授，博士生导师（通讯作者. E-mail: zhangyh@dlut.edu.cn）.