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

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

doi: 10.21656/1000-0887.380151
Funds:  The National Natural Science Foundation of China(11672060)
  • Received Date: 2017-05-23
  • Rev Recd Date: 2017-11-16
  • Publish Date: 2018-01-15
  • 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.
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  • [1]
    ALLEN M J, VLAHOPOULOS N. Integration of finite element and boundary element methods for calculating the radiated sound from a randomly excited structure[J]. Computers & Structures,2000,77(2): 155-169.
    [2]
    MONTGOMERY J M. Modeling of aircraft structural-acoustic response to complex sources using coupled FEM-BEM analyses[C]//10th AIAA/CEAS Aeroacoustics Conference . Manchester, Great Britain, 2004: AIAA 2004-2822.
    [3]
    刘宝山, 赵国忠. 随机激励下结构振动声辐射的灵敏度分析和优化设计[J]. 振动工程学报, 2011,24(3): 309-314.(LIU Baoshan, ZHAO Guozhong. Sensitivity analysis and design optimization of acoustic radiation from random excited structures[J]. Journal of Vibration Engineering,2011,24(3): 309-314.(in Chinese))
    [4]
    凌芳芳. 湍流边界层脉动压力激励潜艇模型振动声辐射[D]. 硕士学位论文. 大连: 大连理工大学, 2013.(LING Fangfang. Vibration and noise of submarine model excited by TBL dynamic pressure[D]. Master Thesis. Dalian: Dalian University of Technology, 2013.(in Chinese))
    [5]
    蔡承德, 陈永琴, 张龙. 统计能量法在分析船舶结构噪声中的应用[J]. 中国造船, 1992(1): 58-70.(CAI Chengde, CHEN Yongqin, ZHANG Long. Application of statistical energy analysis to ship structure-borne noise analysis[J]. Shipbuilding of China,1992(1): 58-70.(in Chinese))
    [6]
    HAN F, BERNHARD R J, MONGEAU L G. Prediction of flow-induced structural vibration and sound radiation using energy flow analysis[J]. Journal of Sound and Vibration,1999,227(4): 685-709.
    [7]
    NEWLAND D E. An Introduction to Random Vibrations, Spectral & Wavelet Analysis [M]. New York: Longman, 2012.
    [8]
    THOMAS D R, NELSON P A. Feedback control of sound radiation from a plate excited by a turbulent boundary layer[J]. The Journal of the Acoustical Society of America,1995,98(5): 2651-2662.
    [9]
    LIU B. Noise radiation of aircraft panels subjected to boundary layer pressure fluctuations[J]. Journal of Sound and Vibration,2008,314(3/5): 693-711.
    [10]
    刘钊, 陈心昭. 求解随机振动结构声辐射的统计边界元方法[J]. 声学学报, 1997,22(6): 495-500.(LIU Zhao, CHEN Xinzhao. Statistic boundary element analysis for structural sound radiation of random vibration[J]. Acta Acustica,1997,22(6): 495-500.(in Chinese))
    [11]
    王秀峰, 陈心昭. 随机振动结构声辐射的统计边界点法分析[J]. 声学技术, 2001,20(3): 107-109, 128.(WANG Xiufeng, CHEN Xinzhao. The statistical boundary point analysis of acoustic radiation problem caused by the random vibrating body[J]. Technical Acoustics,2001,20(3): 107-109, 128.(in Chinese))
    [12]
    高煜. 基于波叠加方法的声辐射与声学灵敏度算法的若干关键问题研究[D]. 博士学位论文. 合肥: 合肥工业大学, 2009.(GAO Yu. Research on several key problems of the acoustic radiation and the acoustic sensitivity analysis based on the wave superposition approach[D]. PhD Thesis. Hefei: Hefei University of Technology, 2009.(in Chinese))
    [13]
    姚伟岸, 钟万勰. 辛弹性力学[M]. 北京: 高等教育出版社, 2002.(YAO Weian, ZHONG Wanxie.Symplectic Elasticity[M]. Beijing: Higher Education Press, 2002.(in Chinese))
    [14]
    鲍四元, 邓子辰. 哈密顿体系下矩形薄板自由振动的一般解[J]. 动力学与控制学报, 2005,3(2): 10-16.(BAO Siyuan, DENG Zichen. A general solution of free vibration for rectangular thin plates in Hamilton systems[J]. Journal of Dynamics and Control,2005,3(2): 10-16.(in Chinese))
    [15]
    钟阳, 李锐, 田斌. 矩形中厚板自由振动问题的哈密顿体系与辛几何解法[J]. 动力学与控制学报, 2009,7(4): 302-307.(ZHONG Yang, LI Rui, TIAN Bin. On Hamilton system and new symplectic approach for free vibration of moderately thick rectangular plates[J]. Journal of Dynamics and Control,2009,7(4): 302-307.(in Chinese))
    [16]
    李锐. 矩形板问题的Hamilton求解方法[D]. 博士学位论文. 大连: 大连理工大学, 2012.(LI Rui. Hamiltonian solution approach for the problems of rectangular plates[D]. PhD Thesis. Dalian: Dalian University of Technology, 2012.(in Chinese))
    [17]
    邹贵平. 反对称铺设层合板动力问题的Hamilton体系及辛几何解法[J]. 固体力学学报, 1996,17(4): 312-319.(ZOU Guiping. An exact symplectic solution for the dynamic analysis of shear deformable antisymmetric angle-ply laminated plates[J]. Acta Mechanica Solida Sinica,1996,17(4): 312-319.(in Chinese))
    [18]
    姚伟岸. 平面各向异性哈密顿体系及圣维南问题的解析解[J]. 大连理工大学学报, 1999,39(5): 612-615.(YAO Weian. Hamiltonian system for plane anisotropic elasticity and analytical solutions of Saint-Venant problem[J]. Journal of Dalian University of Technology,1999,39(5): 612-615.(in Chinese))
    [19]
    周晓楠, 姜哲, 吴苏萍. 基于时域声辐射模态的结构噪声主动控制研究[J]. 振动与冲击, 2006,25(6): 29-34.(ZHOU Xiaonan, JIANG Zhe, WU Suping. Study on active control of structural noise based on acoustic radiation modes in time domain[J]. Journal of Vibration and Shock,2006,25(6): 29-34.(in Chinese))
    [20]
    LIN Y K. Probabilistic Theory of Structural Dynamics [M]. New York: McGraw-Hill, 1967.
    [21]
    CORCOS G M. The structure of the turbulent pressure field in boundary-layer flows[J]. Journal of Fluid Mechanics,1964,18(3): 353-378.
    [22]
    BIRGERSSON F, FERGUSON N S, FINNVEDEN S. Application of the spectral finite element method to turbulent boundary layer induced vibration of plates[J]. Journal of Sound and Vibration,2003,259(4): 873-891.
    [23]
    曹志远. 板壳振动理论[M]. 北京: 中国铁道出版社, 1983.(CAO Zhiyuan. Vibration Theory of Plates and Shells [M]. Beijing: China Railway Publishing House, 1983.(in Chinese))
    [24]
    张亚辉, 马永彬. 薄板振动分析的辛空间波传播方法[J]. 振动与冲击, 2014,33(12): 1-6.(ZHANG Yahui, MA Yongbin. A wave propagation method in symplectic space for vibration analysis of thin plates[J]. Journal of Vibration and Shock,2014,33(12): 1-6.(in Chinese))
    [25]
    LIN S Y. Study on the radiation acoustic field of rectangular radiators in flexural vibration[J]. Journal of Sound and Vibration,2002,254(3): 469-479.
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