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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

潘晨鸽 李榆银 张亚辉

潘晨鸽, 李榆银, 张亚辉. 湍流边界层作用下薄板随机振动声辐射的辛方法[J]. 应用数学和力学, 2018, 39(1): 50-63. doi: 10.21656/1000-0887.380151
引用本文: 潘晨鸽, 李榆银, 张亚辉. 湍流边界层作用下薄板随机振动声辐射的辛方法[J]. 应用数学和力学, 2018, 39(1): 50-63. doi: 10.21656/1000-0887.380151
PAN Chenge, LI Yuyin, ZHANG Yahui. Random Sound Radiation of Thin Plates Under Turbulent Boundary Layer Excitations With a Symplectic Method[J]. Applied Mathematics and Mechanics, 2018, 39(1): 50-63. doi: 10.21656/1000-0887.380151
Citation: PAN Chenge, LI Yuyin, ZHANG Yahui. Random Sound Radiation of Thin Plates Under Turbulent Boundary Layer Excitations With a Symplectic Method[J]. Applied Mathematics and Mechanics, 2018, 39(1): 50-63. 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
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

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

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

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