双层周期加筋板声学特性数值方法研究
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摘要
板壳以及由其组成的复杂结构是工程领域中的常见结构形式,它具有刚度大、重量轻、力学性能好等优点,在船舶、建筑、机械工程和航空航天等领域有着广泛的应用。在各类加筋结构中,周期加筋板是最常用的结构之一。在过去几十年里,周期加筋板的振动声辐射与声传输又是该领域研究的热点。由于周期加筋板经常受到空气或流体等外部激励影响,因此,需要有效的分析方法来研究该结构在这些条件下的动态特性。到目前为止,对周期加筋板研究的方法已经很多,如Rayleigh-Ritz能量法、有限元法、传递矩阵法、模态叠加法、空间谐波法等。
本文采用有限元和边界元相结合的数值方法主要分析了三种双层和单层双周期加筋板结构的声学特性。首先深入研究了相关有限元理论和边界元理论,并简单介绍了有限元分析商业软件ANSYS和声学边界元商业软件SYSNOISE主要功能和分析步骤；然后详细讨论了适用于薄板的弯曲板单元、适用于厚板的Mindlin板单元、适用于非细长梁的Timoshenko梁单元及ANSYS软件中部分单元的属性,如梁单元、板壳单元和流体单元,并在ANSYS软件中建立了由板与梁组合成的双周期加筋板有限元模型；接着,介绍了ANSYS与SYSNOISE进行数据交换时所存在的问题及结构声场分析流程,为了克服所存在的问题,利用APDL语言编写了ANSYS与SYSNOISE进行所需数据交换的程序。
最后,推导出了周期加筋板结构的振动声辐射和声传输的数值计算模型,结合ANSYS和SYSNOISE两款商业软件仿真分析了双层周期加筋板结构的振动声辐射和声传输等声学特性,得到了周期加筋板的振动图、声压图和声传输损失曲线,并分析了部分结构参数对周期加筋板声学特性的影响。通过仿真分析发现,对双层周期加筋板的板间距、板厚、筋间距、筋横截面积等主要结构参数做适当地调节,可以在特定频率范围内,较好地改善加筋板结构的振动声辐射和声传输性能,并且双周期筋不同的布置方式对周期加筋板振动声辐射也有较大的影响。
Structures consist of stiffened plates and shells often find wide application in bridge engineering, aircraft and ship industries owing to their high strength and stiffness, light-weight and low-cost properties. Among various kinds of stiffened structures, periodic stiffened plate is one of the most common used constructions. For the past decades, the study of vibration responses, acoustic radiations and sound transmission from periodic stiffened plates has always been one of the research topics in these fields. Stiffened plates are often subjected to dynamic forces such as air blast loadings or fluid pressures, for which effective analysis method is required to study their dynamic performances under these conditions. So far, many approaches have been proposed such as Rayleigh-Ritz energy method, finite element method, transfer matrix method, modal decomposition method and space harmonic method, etc.
In this thesis, both single and double panels stiffened by periodic structures in two directions are investigated employing the finite element method and boundary element method, and acoustic characteristics of three kinds of double dual-dimensional stiffened panels are especially analyzed. The analysis process in this paper includes the following steps: (a) theories of relevant FEM and BEM are researched and major functions and analysis steps of business software ANSYS about FEM and SYSNOISE software about acoustic BEM are simply introduced. (b) Several finite elements such as bending plate element, Mindlin plate element and Timoshenko beam element, which are mainly used to analyze thin plate, thick plate and non-slender beam respectively, are introduced. And some important elements of ANSYS software such as beam elements, shell elements and fluid elements are moderately discussed and introduced. Subsequently, the FEM modes of dual-dimensional stiffened panels consisted of plates and stiffeners are established in ANSYS software. (c) The main acoustic analysis processes and some existing problems are stated, when using ANSYS software combined with SYSNOISE software. To solve these problems and exchange required data between two software, APDL language programs are designed.
At last, sound radiation and transmission models of periodic stiffened panels are derived and established, and the acoustic characteristics of the periodic structure are simulated by ANSYS and SYSNOISE software. A number of vibration diagrams, sound pressure and transmission curves are given in this thesis, and the effects of structural parameters on acoustic characters of the periodic stiffened panels are analyzed. Through numerical results, it can be found that if structural parameters are properly adjusted, such as plate's thickness and mass density, stiffener's spacing and cross section, the distance between two panels, the acoustic properties can be improved in specific frequency ranges. It can also be noted that different periodic geometrical structures have significant effects on the vibration response and acoustic radiation on the panels.
本文采用有限元和边界元相结合的数值方法主要分析了三种双层和单层双周期加筋板结构的声学特性。首先深入研究了相关有限元理论和边界元理论,并简单介绍了有限元分析商业软件ANSYS和声学边界元商业软件SYSNOISE主要功能和分析步骤；然后详细讨论了适用于薄板的弯曲板单元、适用于厚板的Mindlin板单元、适用于非细长梁的Timoshenko梁单元及ANSYS软件中部分单元的属性,如梁单元、板壳单元和流体单元,并在ANSYS软件中建立了由板与梁组合成的双周期加筋板有限元模型；接着,介绍了ANSYS与SYSNOISE进行数据交换时所存在的问题及结构声场分析流程,为了克服所存在的问题,利用APDL语言编写了ANSYS与SYSNOISE进行所需数据交换的程序。
最后,推导出了周期加筋板结构的振动声辐射和声传输的数值计算模型,结合ANSYS和SYSNOISE两款商业软件仿真分析了双层周期加筋板结构的振动声辐射和声传输等声学特性,得到了周期加筋板的振动图、声压图和声传输损失曲线,并分析了部分结构参数对周期加筋板声学特性的影响。通过仿真分析发现,对双层周期加筋板的板间距、板厚、筋间距、筋横截面积等主要结构参数做适当地调节,可以在特定频率范围内,较好地改善加筋板结构的振动声辐射和声传输性能,并且双周期筋不同的布置方式对周期加筋板振动声辐射也有较大的影响。
Structures consist of stiffened plates and shells often find wide application in bridge engineering, aircraft and ship industries owing to their high strength and stiffness, light-weight and low-cost properties. Among various kinds of stiffened structures, periodic stiffened plate is one of the most common used constructions. For the past decades, the study of vibration responses, acoustic radiations and sound transmission from periodic stiffened plates has always been one of the research topics in these fields. Stiffened plates are often subjected to dynamic forces such as air blast loadings or fluid pressures, for which effective analysis method is required to study their dynamic performances under these conditions. So far, many approaches have been proposed such as Rayleigh-Ritz energy method, finite element method, transfer matrix method, modal decomposition method and space harmonic method, etc.
In this thesis, both single and double panels stiffened by periodic structures in two directions are investigated employing the finite element method and boundary element method, and acoustic characteristics of three kinds of double dual-dimensional stiffened panels are especially analyzed. The analysis process in this paper includes the following steps: (a) theories of relevant FEM and BEM are researched and major functions and analysis steps of business software ANSYS about FEM and SYSNOISE software about acoustic BEM are simply introduced. (b) Several finite elements such as bending plate element, Mindlin plate element and Timoshenko beam element, which are mainly used to analyze thin plate, thick plate and non-slender beam respectively, are introduced. And some important elements of ANSYS software such as beam elements, shell elements and fluid elements are moderately discussed and introduced. Subsequently, the FEM modes of dual-dimensional stiffened panels consisted of plates and stiffeners are established in ANSYS software. (c) The main acoustic analysis processes and some existing problems are stated, when using ANSYS software combined with SYSNOISE software. To solve these problems and exchange required data between two software, APDL language programs are designed.
At last, sound radiation and transmission models of periodic stiffened panels are derived and established, and the acoustic characteristics of the periodic structure are simulated by ANSYS and SYSNOISE software. A number of vibration diagrams, sound pressure and transmission curves are given in this thesis, and the effects of structural parameters on acoustic characters of the periodic stiffened panels are analyzed. Through numerical results, it can be found that if structural parameters are properly adjusted, such as plate's thickness and mass density, stiffener's spacing and cross section, the distance between two panels, the acoustic properties can be improved in specific frequency ranges. It can also be noted that different periodic geometrical structures have significant effects on the vibration response and acoustic radiation on the panels.
引文
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[12]London A. Transmission of reverberant sound through double walls[J]. Acoust. Soc. Am.,1950,22,270-279.
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[18]Takahashi D. Sound radiation from periodically connected double-plate structures [J]. Journal of Sound and Vibration,1983,90:541-557.
[19]Yairi M, Sakagami K, Sakagami E, et al. Sound radiation from a double-leaf elastic plate with a point force excitation:Effect of an interior panel on the structure-borne sound radiation[J]. Appl. Acoust.,2002,63:737-757.
[20]Kropp W, Rebillard E. On the air-borne sound insulation of double wall constructions[J] Acust. Acta Acust.,1999,85:707-720.
[21]Pellicier A, Trompette N. A review of analytical methods, based on the wave approach, to compute partitions transmission loss[J]. Appl. Acoust.,2007,68:1192-1212.
[22]Berry A, Guyader J L, Nicolas J, A general formulation for the sound radiation from rectangular, baffled plates with arbitrary boundary conditions[J]. Acoust. Soc. Am.,1990,88:2792-2802.
[23]Takahashi D. Effects of panel boundedness on sound transmission problems[J]. Acoust. Soc. Am.,1995,98:2598-2606.
[24]Kim B K, Kang H J, Kim J S, et al. Tunneling effect in sound transmission loss determination:Theoretical approach[J]. Acoust. Soc. Am.,2004,115:2100-2109.
[25]Sgard F C, Atalla N, Nicolas J. A numerical model for the low frequency diffuse field sound transmission loss of double-wall sound barriers with elastic porous linings[J]. Acoust. Soc. Am.,2000,108:2865-2872.
[26]Panneton R, Atalla N. Numerical prediction of sound transmission through finite multilayer systems with poroelastic materials[J]. Acoust. Soc. Am.,1996,100:346-354.
[27]Villot M, Guigou C, Gagliardin L. Predicting the acoustical radiation of finite size multi-layered structures by applying spatial windowing on infinite structures[J]. Journal of Sound and Vibration,2001,245:433-455.
[28]Cheng L, Li Y Y, Gao J X. Energy transmission in a mechanically-linked double-wall structure coupled to an acoustic enclosure[J]. Acoust. Soc. Am.,2005,117:2742-2751.
[29]Leppington F G, Broadbent E G, Butler G F. Transmission of sound through a pair of rectangular elastic plates[J]. IMA J. Appl. Math.,2006,71:940-955.
[30]Chazot J D, Guyader J L. Prediction of transmission loss of double panels with a patch-mobility method[J]. Acoust. Soc. Am.2007,121:267-278.
[31]Carneal J P, Fuller C R. An analytical and experimental investigation of active structural acoustic control of noise transmission through double panel systems[J]. Journal of Sound and Vibration,2004,272:749-771.
[32]李德花,陆秋海.实验模态分析及其应用[M].北京：科学出版社,2001.
[33]Ellitto S J. Radiation modes and the active control of sound power[J]. Acoustic Society of America,1993,94(4):2194-2204.
[34]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.
[35]Currey M N, Kenneth A. The radiation modes of baffled finite plates[J].Acoustic Society of America,1995,98(3):2570-2580.
[36]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
[37]Williams W H, Wittrick F W. Buckling and Vibration of Anisotropic or Isotropic Plate Assemblies under Combined Loadings[J]. International Journal of Mechanical Sciences,1974,16(4):209-239
[38]Langley R S, Application of the Dynamic Stiffness Method to the Free and Forced Vibration of Aircraft Panels[J]. Journal of Sound and Vibration,1989,135:319-331.
[39]Bercin A N, Langley R S. Application of the Dynamic Stiffness Technique to the In-plane Vibration of Plate structures[J].Computers and Structures,1996,59(5):869-875.
[40]Bercin A N. Analysis of Energy Flow in Thick Plate Structure[J]. Computers and Stmctures,1997,62(4):747-756.
[41]周平,赵德有.基于动态刚度阵法的加筋板间能量流研究[J].大连理工大学学,2008,48(1)：98-104
[42]周平,赵德有.带有加强筋的Mindlin板动态刚度阵法[J].振动与冲击,2007,26(6)：139-145
[43]姚德源,王其政.统计能量分析原理及其应用[M].北京：北京理工大学,1995.
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