周期加强薄板声辐射数值方法研究
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摘要
加筋板壳结构在船舶、机械工程和航空航天等领域有着广泛的应用。它具有刚度大重量轻、力学性能良好等特点。加筋薄板结构在流体中受到外部激励作用产生的振动声辐射,成为水下噪声的来源之一,所以目前对水下结构振动声辐射的研究越来越受到人们的重视。常见的加筋板壳结构有单周期加强筋和双周期加强筋。加筋可以增强薄板的稳定性,同时在一定频域内能够降低结构的声辐射。在目前结构声辐射的计算方法中,统计能量方法和动态刚度阵法用来计算中高频段的结构声辐射,而对于低频段的计算,近年来主要采用有限元法、边界元法和耦合有限元/边界元方法。
本文运用耦合有限元/边界元方法研究分析了三种周期加强薄板的声学性质。首先介绍了声压、质点振速和声强等基本声学量的概念,对声压级、声振速级和声强级做了简要阐述。然后建立了三种耦合结构的有限元模型,分别为薄板与梁耦合结构、薄板与方形块状实体耦合结构和薄板与回字形实体耦合结构。这三种加强结构在薄板上均为双周期分布,其中薄板与梁耦合结构即为常见的双周期加筋薄板。通过有限元分析软件ANSYS对三种结构进行单元属性配置及网格划分。接着对边界元方法在结构声学中的计算做了详细的介绍。重点推导了基于表面Rayleigh积分方程,并对其进行离散化,得出辐射声压的求解表达式。针对边界积分方程离散后出现的奇异积分性,采用退化单元来消除,对于非唯一性问题和多频计算问题的解决采用SECHIEF方法。在分析边界元方法与有限元方法的耦合理论基础上,对结构一声场的耦合方程进行了推导,给出了流体中结构振动辐射声压级、声振速级和声强级的求解表达式。最后将ANSYS软件中划分好的三种周期加强薄板结构导入到专门从事振动—噪声分析方面的CAE软件SYSNOISE中,计算不同边界条件、流体域以及不同角度外部平面声源载荷激励对三种周期结构振动辐射声压级、声振速级和声强级的影响,并对结果进行了分析。
The structure of stiffened plate and shell has a wide application in the fields of ship, mechanical engineering, aerospace and so on, with the features of big stiffness, light weight, good mechanical performances. The vibration and acoustic radiation becomes one of the main sources of noise pollution that generated by stiffened-plate structure forced by outside excitement in the fluid. Therefore, the research on the underwater structure's vibration and acoustic radiation gets more and more people's emphasis presently. The common forms of stiffened-plate structure are stiffened periodically in one dimension or two dimensions. Stiffening can improve plate's stability, also reduce structure's acoustic radiation in some particular frequency areas. Statistical energy method and dynamic stiffness method are used to calculate structure's acoustic radiation in the high frequency area. And for the low frequency area, people mainly use FEM, BEM and coupled FEM/BEM.
In this paper, coupled FEM/BEM is used to research and analyze the acoustic natures of three kinds of periodically stiffened plate. At first, it introduces the concepts of acoustic pressure, particle's vibrating velocity, acoustic intense, etc. Then the finite element models of three kinds of coupled structures are established: coupled structure of plate and stiffeners, coupled structure of plate and quadrate entity, coupled structure of plate and circle entity. Those three kinds of stiffened structures are distributed in two dimensions on plate, and the coupled structure of plate and stiffeners is the common two-dimensional periodically stiffened plate. The element's natures are prescribed and the grids are divided for the three different models by using the ANSYS software. After that, it gives specific introduce to calculation of the BEM in structure acoustics. It mainly derive Rayleigh integral equation based on surface, and discretize it. For the singular integral nature appearing after discretizing the BEM integral equation, degenerating element is used to eliminate it. And the SECHIEF method is applied to solve the non-sole problem and multiple-frequency calculation problems. On the basis of analyzing deeply the couples theory of BEM and FEM, it derive specifically the coupled equation of structure and acoustic field, gives the expression of SPL, SVL and SIL for the structure's acoustic radiation in the fluid. At last, it imports the three kinds of periodically stiffened plate divided in the ANSYS software into SYSNOISE software, which is used specially in the analysis of vibration and noise, to calculate the influence of different boundary conditions, different fluid fields and different incidence angles for the outside excitement on the SPL, SVL and SIL for the structure's acoustic radiation, the results are also analyzed.
本文运用耦合有限元/边界元方法研究分析了三种周期加强薄板的声学性质。首先介绍了声压、质点振速和声强等基本声学量的概念,对声压级、声振速级和声强级做了简要阐述。然后建立了三种耦合结构的有限元模型,分别为薄板与梁耦合结构、薄板与方形块状实体耦合结构和薄板与回字形实体耦合结构。这三种加强结构在薄板上均为双周期分布,其中薄板与梁耦合结构即为常见的双周期加筋薄板。通过有限元分析软件ANSYS对三种结构进行单元属性配置及网格划分。接着对边界元方法在结构声学中的计算做了详细的介绍。重点推导了基于表面Rayleigh积分方程,并对其进行离散化,得出辐射声压的求解表达式。针对边界积分方程离散后出现的奇异积分性,采用退化单元来消除,对于非唯一性问题和多频计算问题的解决采用SECHIEF方法。在分析边界元方法与有限元方法的耦合理论基础上,对结构一声场的耦合方程进行了推导,给出了流体中结构振动辐射声压级、声振速级和声强级的求解表达式。最后将ANSYS软件中划分好的三种周期加强薄板结构导入到专门从事振动—噪声分析方面的CAE软件SYSNOISE中,计算不同边界条件、流体域以及不同角度外部平面声源载荷激励对三种周期结构振动辐射声压级、声振速级和声强级的影响,并对结果进行了分析。
The structure of stiffened plate and shell has a wide application in the fields of ship, mechanical engineering, aerospace and so on, with the features of big stiffness, light weight, good mechanical performances. The vibration and acoustic radiation becomes one of the main sources of noise pollution that generated by stiffened-plate structure forced by outside excitement in the fluid. Therefore, the research on the underwater structure's vibration and acoustic radiation gets more and more people's emphasis presently. The common forms of stiffened-plate structure are stiffened periodically in one dimension or two dimensions. Stiffening can improve plate's stability, also reduce structure's acoustic radiation in some particular frequency areas. Statistical energy method and dynamic stiffness method are used to calculate structure's acoustic radiation in the high frequency area. And for the low frequency area, people mainly use FEM, BEM and coupled FEM/BEM.
In this paper, coupled FEM/BEM is used to research and analyze the acoustic natures of three kinds of periodically stiffened plate. At first, it introduces the concepts of acoustic pressure, particle's vibrating velocity, acoustic intense, etc. Then the finite element models of three kinds of coupled structures are established: coupled structure of plate and stiffeners, coupled structure of plate and quadrate entity, coupled structure of plate and circle entity. Those three kinds of stiffened structures are distributed in two dimensions on plate, and the coupled structure of plate and stiffeners is the common two-dimensional periodically stiffened plate. The element's natures are prescribed and the grids are divided for the three different models by using the ANSYS software. After that, it gives specific introduce to calculation of the BEM in structure acoustics. It mainly derive Rayleigh integral equation based on surface, and discretize it. For the singular integral nature appearing after discretizing the BEM integral equation, degenerating element is used to eliminate it. And the SECHIEF method is applied to solve the non-sole problem and multiple-frequency calculation problems. On the basis of analyzing deeply the couples theory of BEM and FEM, it derive specifically the coupled equation of structure and acoustic field, gives the expression of SPL, SVL and SIL for the structure's acoustic radiation in the fluid. At last, it imports the three kinds of periodically stiffened plate divided in the ANSYS software into SYSNOISE software, which is used specially in the analysis of vibration and noise, to calculate the influence of different boundary conditions, different fluid fields and different incidence angles for the outside excitement on the SPL, SVL and SIL for the structure's acoustic radiation, the results are also analyzed.
引文
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[2]张升明,潘旭初.板架结构的振动噪声研究[J].噪声与振动控制,1995,(5):9-13.
[3]Berry A,Locqueteau C.Vibration and sound radiation of fluid-loaded stiffened plates with consideration of in-plane deformation[J].Acoustic Society Of America,1996,100(1):312-319.
[4]Nelisse H,Beslin O,Nicolas J.A generalized approach for the acoustic radiation from a baffled or unbaffled plate with arbitrary boundary conditions immersed in a light or heavy fluid[J].Journal of Sound and Vibration,1998,211(2):207-225.
[5]Moyne S L,Tebec J L,Kraemer J C.Source effect of ribs in sound radiation of stiffened plates:experimental and calculation investigation[J].Acoustic,2000,(86)457-464.
[6]Laulagnet B,Guyader J L.Sound radiation from a finite cylindrical shell partially covered with longitudinal strips of compliant layer[J].Journal of Sound and Vibration,1995,186(5):723-742.
[7]陈炜,骆东平,张书吉,等.敷设阻尼材料的环肋柱壳声辐射性能分析[J].声学学报,2000,25(1):27-32.
[8]汤渭霖,范军.水中弹性球壳的共振卢辐射理论[J].声学学报,2000,25(4):308-312.
[9]闫再友,严明.无界流场中弹性壳体声散射和声辐射综述[J].振动与冲击,1998,17(4):30-34.
[10]Mukherjee A,Mukhopadhyay M.Review of dynamic behavior of stiffened plates[J].Shock and Vibration Digest,1986,18(6):3-8.
[11]Mead D J,Yaman Y.The harmonic response of rectangular sandwich plates with multiple stiffened:A flexural wave analysis[J].Journal of Sound and Vibration,1991,145(3):409-428.
[12]Ohtomi K.Free vibration of rectangular plates stiffened with viscoelastic beam [J].Journal of Applied Mechanics,1985,52(2):397-401.
[13]Gupta B V R,Ganesan N,Narayanan S.Finite element free vibration analysis of damped stiffened panels[J].Computers & Structures,1986,24:485-489.
[14]桂洪斌,赵德有,金咸定.用粘弹性梁控制加筋板稳态简谐响应的研究[J].船舶力学,2003,7(3):76-85.
[15]孙社营.阻尼压筋板的动态力学性能研究[J].噪声与振动控制,2000,2:19-23.
[16]胡选利,戴宗妙.阻尼夹层筋板结构有限元动力分析[J].应用力学学报,1998,15(1):10-15.
[17]姚德源,王其政.统计能量分析及其应用[M].北京:北京理工大学,1995.
[18]周平,赵德有.动态刚度阵法的研究概况[J].振动与冲击,2006,25(4):104-108.
[19]Photiadis D M.The relationships of singular value decomposition to wave-vector by three-dimensional structures[J].Acoustic Society of America,1990,88(4):1152-1159.
[20]Borgiotti G V.The power radiated by a vibrating body in an acoustic fluid and its determination from boundary measurements[J].Acoustic Society of America,1990,88(4):1884-1893.
[21]Ellitto S J.Radiation modes and the active control of sound power[J].Acoustic Society of America,1993,94(4):2194-2204.
[22]Cunfare K A.On the exterior acoustic radiation modes of structure[J].Acoustic Society of America,1994,96(4):2302-2312.
[23]何祚镛.结构振动与声辐射[M].哈尔滨:哈尔滨工程大学出版社,2001.
[24]Kenneth A,Cunefare,Gary H K.A boundary element approach to optimization of active noise control sources on three-dimensional structures[J].Journal of Vibration and Acoustics,1991,113(3):387-394.
[25]Currey M N,Nenneth A.The radiation modes of baffled finite plates[J].Acoustic Society of America,1995,98(3):2570-2580.
[26]Zienkiewicz O C,Nelly D W,Betess P.The coupling of the finite element method and boundary solution procedures[J].International Journal of Numerical Methods in Engineering,1977,(11):355-375.
[27]Smith R R,Hunt J T,Barach D.Finite element analysis of acoustically structures with application to sonar transducers[J].Acoustic Society of America,1973,54(3):1277-1288.
[28]Wilton D T.Acoustic radiation and scattering from elastic structures[J].International Journal of Numerical Methods in Engineering,1978,13(2):123-138.
[29]Mathews I C.Numerical techniques for three-dimensional steady-state fluid-structure interaction[J].Acoustic Society of America,1986,79(5):1317-1325.
[30]崔宏武,赵德有,罗志雍,等.结构振动的水准声辐射计算[J].中国造船,1990,31(4):49-54.
[31]Everstine G C,Henderson F M.Coupled finite element/boundary element approach for fluid-structure interaction[J].Acoustic Society of America,1990.87(5):1938-1947.
[32]张敬东,何祚镛.有限元+边界元—修正的模态分解法预报水下旋转薄壳的振动和声辐射[J].声学学报,1990,15(1):12-19.
[33]Chen P T,John S H,Cha K C.A symmetric formulation of coupled BEM/FEM in solving responses of submerged elastic structures for large degrees of freedom[J].Journal of Sound and Vibration,2000,233(3):407-422.
[34]Chen P T,Ginsberg J H.Complex power reciprocity and radiation modes for submerged bodies[J].Acoustic Society of America,1995,98(6):3343-3351.
[35]Ciskowski R D,Brebbia C A.Boundary Element Methods in Acoustic[M].Southampton:Computational Mechanics Publications,1991.
[36]何祚镛,赵玉芳.声学理论基础[M].北京:国防工业出版社,1981.
[37]何祚镛.声学基础讲义[M].哈尔滨:船舶工程学院出版社,1976.
[38]曾攀.有限元分析及应用[M].北京:清华大学出版社,2004.
[39]徐芝纶.弹性力学[M].北京:人民教育出版社,1980.
[40]杨德全,赵忠生.边界元理论及应用[M].北京:北京理工大学出版社,2006.
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