加筋板拓扑结构与声辐射特性研究
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摘要
薄板作为一种常用的结构件在军民领域中发挥了很大的作用,然而薄板有其自身的不足。薄板通过加厚或其上加筋可以改善力学和声学性能,但是薄板增厚会使其自重增大,且没有充分利用材料;而对薄板加筋在一定条件可使薄板自重不增加且又能改善其性能,因而加筋成为改善薄板性能的最佳选择之一。加筋板结构比较容易通过调节板上加强筋的尺寸和间距等来满足工程设计中的强度、刚度、稳定性和声学特性等多方面的要求,所以比薄板更广泛地使用在军民用领域中。加筋板的振动与声辐射问题很早就受到了人们的高度关注。国内外学者对加筋板的承载性、极限强度、稳定性和声辐射进行了大量的研究。本文从加筋板的拓扑形状着手,具体研究了加筋板的拓扑变化和其边界条件的变动对加筋板的刚性及声辐射性能的影响。
本文以常见的“井”字型加筋板结构为研究对象,基于Mindlin板理论和空间梁元理论,根据加筋板物理模型计算简化方法,建立了以四节点壳单元和二节点偏心梁单元组合的加筋板模型并对该模型进行了验算,为后面加筋板拓扑结构与声辐射特性研究提供准确的有限元分析模型。同时基于结构声辐射机理和薄板结构振动声辐射理论,本文设计了空气介质中结构振动声辐射的分析流程。
为了研究加筋板的拓扑形状变化在不同边界条件下对其刚性的影响,本文运用有限元方法,以加筋板的第一阶固有频率为参考目标,具体分析了加强筋的结构参数、分布和类型及板的结构参数在不同边界约束条件下对加筋板一阶固有频率的影响。本文根据其一阶固有频率值的大小来评价加筋板的刚性特性,并从中得出了一些有用的结论,为后面的加筋板结构声辐射特性分析提供一定理论依据。同时本文以板、加强筋结构参数为设计变量,分析了加筋板的特征值灵敏度和振动响应灵敏度,为加筋板的结构优化指导了方向。
基于弹性结构振动方程和辐射声场的边界元理论,本文设计了空气中无限大刚性障板内加筋板结构声辐射的计算模型。结合有限元和边界元方法,根据第3章的结构声辐射分析流程,详细研究了加强筋的结构参数和分布、激励力作用位置、板长宽比、板厚与结构阻尼等对加筋板的辐射效率、辐射声功率及声辐射指向性的影响,并从中得到了一些有用的结论,为加筋板的声振优化研究提供一定的指导作用。
Thin plate is a commonly used structural part and play an important role in military and civil fields, but characteristics of the thin plate is not good enough. Adding thickness or applying stiffener may improve mechanical and acoustic performance of the thin plate. However,the thin plate increases selfweight by adding its thickness and has not high utilization of materials. So adding stiffener on the thin plate is a optimum method because of not increasing its weight. The stiffened plate structure can meet the requirements of structural strength,structural stiffness,structural stability and acoustic characteristics by adjusting size and distance of stiffener in engineering design, so it is widely used in military and civil fields. Mechanical performances and acoustic radiation problems of the stiffened plate caused researchers great interest early. Many scholars reseached its bearing capacity, maximum intensity, stability and acoustic radiation performances at home and abroad. Based on topology and shape of stiffener plate, a specific study on stiffness and acoustic radiation of the stiffened plate which may alter as the topology/shape and boundary conditions changed was completed in this paper.
This paper took commonly used stiffened plate as the research object. Based on Mindlin plate theory, spatial beam theory and methods of physical model simplify, a accurate finite element model of the stiffened plate was set up by four nodes shell element and two nodes beam element. Then the model was checked calculation for back-analysis of topology/shape and acoustic radiation of structure. In the end,a analysis process about sound radiation of vibrating structure was designed according to mechanism of sound radiation and theory of acoustic radiation from the thin plate in this paper.
By taking first-order natural frequency of the stiffened plate as target, a specific discussion was finished by changing structure parameter,types or distribution of stiffeners and boundary conditions for effects of first-order natural frequency of the stiffened plate. Then according to natural frequency value evaluated the stiffness characteristics of the stiffend plate. This discussion drawed useful conclusions and provided theoretical basis for back-analysis of acoustic radiation of the vibrating stiffened plate. This paper also designed a example of structural sensitivity analysis. By taking structure parameters of the plate and the beam as design variables, the paper studied the eigenvalue sensitivity and displacement sensitivity of the stiffened plate. This pointed out the direction for structural topology optimization of the stiffened plate.
This paper designed a calculation model about acoustic radiation of vibrating structure in infinite baffle on the basis of the flexible structure vibration equation and boundary element coupling calculation equation. Then combination of finite and boundry element methods, it discussed structure parameters of plate and stiffener, types or distribution of the stiffener, location of the force incentive, length to wide ratio and structure damping and so on for influence of sound radiation efficiency, acoustic power and radiation directivity. This discussion drawed some useful conclusions and provided theoretical basis for structural-acoustic optimization of the stiffened plate.
本文以常见的“井”字型加筋板结构为研究对象,基于Mindlin板理论和空间梁元理论,根据加筋板物理模型计算简化方法,建立了以四节点壳单元和二节点偏心梁单元组合的加筋板模型并对该模型进行了验算,为后面加筋板拓扑结构与声辐射特性研究提供准确的有限元分析模型。同时基于结构声辐射机理和薄板结构振动声辐射理论,本文设计了空气介质中结构振动声辐射的分析流程。
为了研究加筋板的拓扑形状变化在不同边界条件下对其刚性的影响,本文运用有限元方法,以加筋板的第一阶固有频率为参考目标,具体分析了加强筋的结构参数、分布和类型及板的结构参数在不同边界约束条件下对加筋板一阶固有频率的影响。本文根据其一阶固有频率值的大小来评价加筋板的刚性特性,并从中得出了一些有用的结论,为后面的加筋板结构声辐射特性分析提供一定理论依据。同时本文以板、加强筋结构参数为设计变量,分析了加筋板的特征值灵敏度和振动响应灵敏度,为加筋板的结构优化指导了方向。
基于弹性结构振动方程和辐射声场的边界元理论,本文设计了空气中无限大刚性障板内加筋板结构声辐射的计算模型。结合有限元和边界元方法,根据第3章的结构声辐射分析流程,详细研究了加强筋的结构参数和分布、激励力作用位置、板长宽比、板厚与结构阻尼等对加筋板的辐射效率、辐射声功率及声辐射指向性的影响,并从中得到了一些有用的结论,为加筋板的声振优化研究提供一定的指导作用。
Thin plate is a commonly used structural part and play an important role in military and civil fields, but characteristics of the thin plate is not good enough. Adding thickness or applying stiffener may improve mechanical and acoustic performance of the thin plate. However,the thin plate increases selfweight by adding its thickness and has not high utilization of materials. So adding stiffener on the thin plate is a optimum method because of not increasing its weight. The stiffened plate structure can meet the requirements of structural strength,structural stiffness,structural stability and acoustic characteristics by adjusting size and distance of stiffener in engineering design, so it is widely used in military and civil fields. Mechanical performances and acoustic radiation problems of the stiffened plate caused researchers great interest early. Many scholars reseached its bearing capacity, maximum intensity, stability and acoustic radiation performances at home and abroad. Based on topology and shape of stiffener plate, a specific study on stiffness and acoustic radiation of the stiffened plate which may alter as the topology/shape and boundary conditions changed was completed in this paper.
This paper took commonly used stiffened plate as the research object. Based on Mindlin plate theory, spatial beam theory and methods of physical model simplify, a accurate finite element model of the stiffened plate was set up by four nodes shell element and two nodes beam element. Then the model was checked calculation for back-analysis of topology/shape and acoustic radiation of structure. In the end,a analysis process about sound radiation of vibrating structure was designed according to mechanism of sound radiation and theory of acoustic radiation from the thin plate in this paper.
By taking first-order natural frequency of the stiffened plate as target, a specific discussion was finished by changing structure parameter,types or distribution of stiffeners and boundary conditions for effects of first-order natural frequency of the stiffened plate. Then according to natural frequency value evaluated the stiffness characteristics of the stiffend plate. This discussion drawed useful conclusions and provided theoretical basis for back-analysis of acoustic radiation of the vibrating stiffened plate. This paper also designed a example of structural sensitivity analysis. By taking structure parameters of the plate and the beam as design variables, the paper studied the eigenvalue sensitivity and displacement sensitivity of the stiffened plate. This pointed out the direction for structural topology optimization of the stiffened plate.
This paper designed a calculation model about acoustic radiation of vibrating structure in infinite baffle on the basis of the flexible structure vibration equation and boundary element coupling calculation equation. Then combination of finite and boundry element methods, it discussed structure parameters of plate and stiffener, types or distribution of the stiffener, location of the force incentive, length to wide ratio and structure damping and so on for influence of sound radiation efficiency, acoustic power and radiation directivity. This discussion drawed some useful conclusions and provided theoretical basis for structural-acoustic optimization of the stiffened plate.
引文
[1]张常伟.加筋板稳定性承载能力的研究:[上海海事大学硕士学位论文].上海:上海海事大学,2006,1-5
[2]胡家雄,伏同先.21世纪常规潜艇隐身技术发展动态.舰船科学技术, 2001,215-218
[3]吴成军,黄协清,陈花玲.复合圆柱形薄壳在重质流体中声辐射的建模与理论预估.西安交通大学学报,1998,32(9):321-326
[4]韩洪伟.加筋薄壁结构振动声辐射特性理论及应用研究:[西北工业大学硕士学位论文].西安:西北工业大学,2006,1-10
[5] Fabyy F.Sound and structural vibration.Cambridge:Academic Press,1985,112-121
[6]方同,薛璞.振动理论及应用.西安:西北工业大学出板社,1998,113-126
[7] G.Maidanik.Response of ribbed panels to Reverberant Acoustic Fields. Journal of the Acoustical Society of America,1962,(34):809-835
[8] C.E.Wallace.radiation resistance of rectangular panel. Journal of the Acoustical Society of America,1972,(53):946-952
[9] G.Maidanik.Vibrational and radiative classifications of modes of a baffled finite panel.Journal of Sound and Vibration,1974,(34):447-455
[10] H.G.Davies.Acoustic radiation from fluid loaded rectangular plates.MIT Report.1976,(76):52-56
[11] H.G.Davies.Sound from turbulent boundary layer excited panels. Journal of the Acoustical Society of America,1971,(49):878-889
[12] Takaaki.Evaluation of Acoustic Radiation Efficieney for Hull Plate Using the Reciprocity Method.JSME,1994,(3):114-120
[13] K.Renji,P.S.Nair,S.Narayanan.On Acoustic radiation of plates.Journal of Sound and Vibration,1998,212(4):583-598
[14]姜哲,郭骤.由试验模态分析确定振动物体的辐射效率.振动与冲击,1992, 44(4):45-49
[15]尹岗,陈花玲,陈天宁.薄板低频声辐射效率的研究.西安交通大学学报, 1999,(33):108-110
[16]吴文伟,冷文浩,沈顺根.具有等间距加筋板的声辐射.中国造船,1999, (146):72-81
[17]姚本炎,黄其柏.加筋薄板结构振动与声辐射特性研究.华中科技大学学报,2001,29(2):90-92
[18]黎胜,赵德有.结构声辐射的振动模态分析和声辐射模态分析研究.声学学报,2004,29(3):200-208.
[19]郭新毅,洪明.含损伤加筋板结构声辐射阻尼变异研究.船舶力学,2007,11(4):628-636
[20] J.A.Deruntz,T.L.Geerse.Added mass computation by the boundary integral method.IJNLM,1978,(12):531-550
[21] P.Orsero,J.L.Armand.A numerical determine:itian of the entrained in ship Vibration.IJNPM,1978,(13):358-361
[22] Melvyn,S.Marcus.A Finite Element Method Applied to the Vibration of Submerged Plates.Journal of Ship Research,1978,22(2):94-99
[23] G .P.Eatwell.The Response of a Fluid-loaded Beam-Stiffened Plate.Journal of Sound and Vibration,1982,84(3):450-456
[24]韩继文,汪摩宝,陆鑫森.Green函数法计算船底板振动的附连水质量.中国造船,1985,(3):42-46
[25]崔宏武,赵德有,罗志雍等.结构振动的水中声辐射计算.中国造船,1990,31(4):49-54
[26]郭兆璞,陈浩然,项晨.空间复合材料加筋板流固耦合振动分析.中国造船,1994,(3):50-59
[27]赵键.薄板和不可压流体藕合振动的边界元法研究.中山大学学报(自然科学版),1996,35(1):32-36
[28]刘连海.含损伤加筋板结构水中振动特性及声辐射研究:[大连理工大学硕士学位论文].大连:大连理工大学,2006,8-16
[29] Smith R R,Hunt J T,Barach D. Finite element analysis of acoustically radiating structures with application to sonar transducers. Journal of the Acoustical Societ -y of America,1974,(55):1277-1288
[30] Lamancusa J S.Acoustic finite element modeling using commercial structural analysis programs. Noise Control Engineering Journal,1988,30(2):65-71
[31] A stleyR J .Wave envelopand infinite elements cheme for acoustical radiation. International journal for numerical methods in engineering,1983,(3):507-526
[32] Astley R J, Eversman W.Finite element for mulation for acoustical radiation.Journal of Sound and Vibration,1983,(88):47-64
[33] Astley R J, Macaulay G J, Coyette J P. Mapped wave envelop elements for acoustic radiation and scattering.Journal of Sound and Vibration,1994, (170):97-118-envelope elements of variable order for acoustic radiation and scattering.Part1. Formulation in the frequency domain. Journal of the Acoustical Society of America,1998,103(1):49-63
[35] Zienkiewicz O C, Bando K, Bettess Petc.Mapped infinite element for exterior wave problems. International journal for numerical methods in engineering, 1985,(21):1229-1252
[36] Gorranson J P E, Davidsson C F.Three dimensional infinite element for wave propogation.Journal of Sound and Vibration,1987,(115):556-559
[37] Raveevdra S T. An efficient indirect boundary element technique for multi– Frequency acoustic analysis. International journal for numerical methods in engineering,1999,(44):59-76
[38]姚振汉,杜庆华.边界元法应用的若干近期研究及国际新进展.清华大学学报(自然科学版),2001,41(5):89-93
[39] Wang Y C, Liu Z, Wu Y. All particular solutions method in boundary element techniques. Proceedings of the 6th China-Japan symposium on BEM,Intern -ational Academic Publishers,1994,458-463
[40]王有成,刘钊,吴约.边界元结束中的全特解场方法.第四届全国工程中的边界元方法学术会议论文集,南京:河海大学出版社,1994,301-321
[41]王有成.边界元技术新探一边界点方法力学与实践,力学与实践,1997,19(4):12-16
[42]张胜勇,陈心昭.应用二次B样条函数插值的边界元法计算结构振动声辐射问题.声学技术,1998,17(1):20-23
[43]姚德源,王其政.统计能量分析原理及应用.北京:北京理工大学出版社,1995,1-6
[44] Price A J, Crocker M J. Sound transmission through double analysis. Journal of the Acoustical Society of America, 1970,47(3):688-693
[45]王兆骞.平均流流速对板振动声辐射特性影响的数值计算研究:[大连理工大学硕士学位论文].大连:大连理工大学,2006,6-9
[46]赵其昌,陈晓勇.薄板的弯曲振动.电声技术,2001,(11):23-27
[47]洪明.分层损伤复合材料层合板振动与声特性研究:[大连理工大学博士学位论文].大连:大连理工大学,2003,25-35
[48]艮田.损伤对板架结构动力特性影响:[大连理工大学硕士学位论文].大连:大连理工大学,2004.14-20
[49]付喜华.舰船加筋结构声辐射阻尼研究:[大连理工大学硕士学位论文].大连:大连理工大学,2007,10-20
[50]吴芳.板和加筋板附水质量算法研究:[大连理工大学硕士学位论文].大连:大连理工大学,2006,11-16
[51]邱菊,孙秦.基于MSC.Nastran优化梁元偏置的分析.飞机设计,2008,28(3):20-21
[52]胡海昌.多自由度结构固有振动理论.北京:科学出版社,1987,60-87
[53]何祚镛.结构振动与声辐射.哈尔滨:哈尔滨工程大学出版社,2001,80-86
[54]何琳,朱海潮,邱小军.声学理论与工程应用.北京:科学出版社,2006,213-226
[55]赵志高.结构声辐射的机理与数值方法研究:[华中科技大学博士学位论文].武汉:华中科技大学,2005,28-35
[56]潘仲麟,翟国庆.噪声控制技术.北京:化学工业出版社,2006,8-10
[57] Koorosh, Naglishinrh. Active Control of Sound Power Using Acoustic Basis Function as Surface Velocity Filters.Journal of the Acoustical Society of America,1993,93(5):2749-2752
[58] Ellot S J, Johnson M E.Radiation Modes and the Active Control of Sound Power. Journal of the Acoustical Society of America,1993,94(4):2302-2312
[59]李增刚.SYSNOISE Res5.6详解.北京:国防工业出版社,2005,20-170
[60] Cui Weicheng. Buckling and Ultimate Strength Analysis of Stiffened Panels. Journal of Ship Mechanics,1998,2(3),41-61
[61]崔维成.加筋板格的屈曲强度和极限强度分析.船舶力学,1998,(2):41-61
[62]黎顺生.加筋板极限强度计算与分析:[武汉理工大学硕士学位论文].武汉:武汉理工大学,2005,1-6
[63]郭达,谢柞水,俞铭华.大型板架稳定性的有限元分析.华东船舶工业学院学报,14(2),200-205
[64]付立英,王维扬.四边形加筋版的拓扑研究.科学技术与工程, 2008,8(7):1926-1928
[65]江玮,郁鼎文,冯平法.加筋板结构静态性能分析及优化设计.机械设计与制造,2008,(2):4-6
[66]张军.声学-结构灵敏度及结构-声学优化设计研究:[大连交通大学博士学位论文].大连:大连交通大学,2005,28-36
[67] Lamancusa J S, Eschenauer H A. Design optimizationmethods for rectangular panels with minimal sound radiation. AIAAJ,1994,32(3):472-479
[68] Choi K K,Lee J H. Sizing design sensitivity analysis of dynamic frequency response of vibrating structures.Journal of Mechanical Design,1992,(114):166 -173
[69]白杨,汪鸿振.声学-结构设计灵敏度分析.振动与冲击,2003,22(3):43-45
[70]张军,兆文忠,张维英.结构声辐射有限元/边界元法-结构灵敏度研究.振动工程学报.2005,18(3):366-368
[71]王敏庆,盛美萍,孙进才等.板受力激励下加筋板结构振动功率流.声学学报,1997,22(4):323-329
[72]张升明,潘旭初.板架结构的振动噪声研究.噪声与振动控制,1995,(5):9-13
[73] Stepanishen P R. Model coupling in the vibration of fluid-loaded cylindrical shells. Journal of the Acoustical Society of America,1982,71(4):813-823
[74]石焕文,孙进才.加纵肋平底圆柱壳振动和声辐射地FEM/BEM研究.振动与冲击,2006,25(2):88-89
[2]胡家雄,伏同先.21世纪常规潜艇隐身技术发展动态.舰船科学技术, 2001,215-218
[3]吴成军,黄协清,陈花玲.复合圆柱形薄壳在重质流体中声辐射的建模与理论预估.西安交通大学学报,1998,32(9):321-326
[4]韩洪伟.加筋薄壁结构振动声辐射特性理论及应用研究:[西北工业大学硕士学位论文].西安:西北工业大学,2006,1-10
[5] Fabyy F.Sound and structural vibration.Cambridge:Academic Press,1985,112-121
[6]方同,薛璞.振动理论及应用.西安:西北工业大学出板社,1998,113-126
[7] G.Maidanik.Response of ribbed panels to Reverberant Acoustic Fields. Journal of the Acoustical Society of America,1962,(34):809-835
[8] C.E.Wallace.radiation resistance of rectangular panel. Journal of the Acoustical Society of America,1972,(53):946-952
[9] G.Maidanik.Vibrational and radiative classifications of modes of a baffled finite panel.Journal of Sound and Vibration,1974,(34):447-455
[10] H.G.Davies.Acoustic radiation from fluid loaded rectangular plates.MIT Report.1976,(76):52-56
[11] H.G.Davies.Sound from turbulent boundary layer excited panels. Journal of the Acoustical Society of America,1971,(49):878-889
[12] Takaaki.Evaluation of Acoustic Radiation Efficieney for Hull Plate Using the Reciprocity Method.JSME,1994,(3):114-120
[13] K.Renji,P.S.Nair,S.Narayanan.On Acoustic radiation of plates.Journal of Sound and Vibration,1998,212(4):583-598
[14]姜哲,郭骤.由试验模态分析确定振动物体的辐射效率.振动与冲击,1992, 44(4):45-49
[15]尹岗,陈花玲,陈天宁.薄板低频声辐射效率的研究.西安交通大学学报, 1999,(33):108-110
[16]吴文伟,冷文浩,沈顺根.具有等间距加筋板的声辐射.中国造船,1999, (146):72-81
[17]姚本炎,黄其柏.加筋薄板结构振动与声辐射特性研究.华中科技大学学报,2001,29(2):90-92
[18]黎胜,赵德有.结构声辐射的振动模态分析和声辐射模态分析研究.声学学报,2004,29(3):200-208.
[19]郭新毅,洪明.含损伤加筋板结构声辐射阻尼变异研究.船舶力学,2007,11(4):628-636
[20] J.A.Deruntz,T.L.Geerse.Added mass computation by the boundary integral method.IJNLM,1978,(12):531-550
[21] P.Orsero,J.L.Armand.A numerical determine:itian of the entrained in ship Vibration.IJNPM,1978,(13):358-361
[22] Melvyn,S.Marcus.A Finite Element Method Applied to the Vibration of Submerged Plates.Journal of Ship Research,1978,22(2):94-99
[23] G .P.Eatwell.The Response of a Fluid-loaded Beam-Stiffened Plate.Journal of Sound and Vibration,1982,84(3):450-456
[24]韩继文,汪摩宝,陆鑫森.Green函数法计算船底板振动的附连水质量.中国造船,1985,(3):42-46
[25]崔宏武,赵德有,罗志雍等.结构振动的水中声辐射计算.中国造船,1990,31(4):49-54
[26]郭兆璞,陈浩然,项晨.空间复合材料加筋板流固耦合振动分析.中国造船,1994,(3):50-59
[27]赵键.薄板和不可压流体藕合振动的边界元法研究.中山大学学报(自然科学版),1996,35(1):32-36
[28]刘连海.含损伤加筋板结构水中振动特性及声辐射研究:[大连理工大学硕士学位论文].大连:大连理工大学,2006,8-16
[29] Smith R R,Hunt J T,Barach D. Finite element analysis of acoustically radiating structures with application to sonar transducers. Journal of the Acoustical Societ -y of America,1974,(55):1277-1288
[30] Lamancusa J S.Acoustic finite element modeling using commercial structural analysis programs. Noise Control Engineering Journal,1988,30(2):65-71
[31] A stleyR J .Wave envelopand infinite elements cheme for acoustical radiation. International journal for numerical methods in engineering,1983,(3):507-526
[32] Astley R J, Eversman W.Finite element for mulation for acoustical radiation.Journal of Sound and Vibration,1983,(88):47-64
[33] Astley R J, Macaulay G J, Coyette J P. Mapped wave envelop elements for acoustic radiation and scattering.Journal of Sound and Vibration,1994, (170):97-118-envelope elements of variable order for acoustic radiation and scattering.Part1. Formulation in the frequency domain. Journal of the Acoustical Society of America,1998,103(1):49-63
[35] Zienkiewicz O C, Bando K, Bettess Petc.Mapped infinite element for exterior wave problems. International journal for numerical methods in engineering, 1985,(21):1229-1252
[36] Gorranson J P E, Davidsson C F.Three dimensional infinite element for wave propogation.Journal of Sound and Vibration,1987,(115):556-559
[37] Raveevdra S T. An efficient indirect boundary element technique for multi– Frequency acoustic analysis. International journal for numerical methods in engineering,1999,(44):59-76
[38]姚振汉,杜庆华.边界元法应用的若干近期研究及国际新进展.清华大学学报(自然科学版),2001,41(5):89-93
[39] Wang Y C, Liu Z, Wu Y. All particular solutions method in boundary element techniques. Proceedings of the 6th China-Japan symposium on BEM,Intern -ational Academic Publishers,1994,458-463
[40]王有成,刘钊,吴约.边界元结束中的全特解场方法.第四届全国工程中的边界元方法学术会议论文集,南京:河海大学出版社,1994,301-321
[41]王有成.边界元技术新探一边界点方法力学与实践,力学与实践,1997,19(4):12-16
[42]张胜勇,陈心昭.应用二次B样条函数插值的边界元法计算结构振动声辐射问题.声学技术,1998,17(1):20-23
[43]姚德源,王其政.统计能量分析原理及应用.北京:北京理工大学出版社,1995,1-6
[44] Price A J, Crocker M J. Sound transmission through double analysis. Journal of the Acoustical Society of America, 1970,47(3):688-693
[45]王兆骞.平均流流速对板振动声辐射特性影响的数值计算研究:[大连理工大学硕士学位论文].大连:大连理工大学,2006,6-9
[46]赵其昌,陈晓勇.薄板的弯曲振动.电声技术,2001,(11):23-27
[47]洪明.分层损伤复合材料层合板振动与声特性研究:[大连理工大学博士学位论文].大连:大连理工大学,2003,25-35
[48]艮田.损伤对板架结构动力特性影响:[大连理工大学硕士学位论文].大连:大连理工大学,2004.14-20
[49]付喜华.舰船加筋结构声辐射阻尼研究:[大连理工大学硕士学位论文].大连:大连理工大学,2007,10-20
[50]吴芳.板和加筋板附水质量算法研究:[大连理工大学硕士学位论文].大连:大连理工大学,2006,11-16
[51]邱菊,孙秦.基于MSC.Nastran优化梁元偏置的分析.飞机设计,2008,28(3):20-21
[52]胡海昌.多自由度结构固有振动理论.北京:科学出版社,1987,60-87
[53]何祚镛.结构振动与声辐射.哈尔滨:哈尔滨工程大学出版社,2001,80-86
[54]何琳,朱海潮,邱小军.声学理论与工程应用.北京:科学出版社,2006,213-226
[55]赵志高.结构声辐射的机理与数值方法研究:[华中科技大学博士学位论文].武汉:华中科技大学,2005,28-35
[56]潘仲麟,翟国庆.噪声控制技术.北京:化学工业出版社,2006,8-10
[57] Koorosh, Naglishinrh. Active Control of Sound Power Using Acoustic Basis Function as Surface Velocity Filters.Journal of the Acoustical Society of America,1993,93(5):2749-2752
[58] Ellot S J, Johnson M E.Radiation Modes and the Active Control of Sound Power. Journal of the Acoustical Society of America,1993,94(4):2302-2312
[59]李增刚.SYSNOISE Res5.6详解.北京:国防工业出版社,2005,20-170
[60] Cui Weicheng. Buckling and Ultimate Strength Analysis of Stiffened Panels. Journal of Ship Mechanics,1998,2(3),41-61
[61]崔维成.加筋板格的屈曲强度和极限强度分析.船舶力学,1998,(2):41-61
[62]黎顺生.加筋板极限强度计算与分析:[武汉理工大学硕士学位论文].武汉:武汉理工大学,2005,1-6
[63]郭达,谢柞水,俞铭华.大型板架稳定性的有限元分析.华东船舶工业学院学报,14(2),200-205
[64]付立英,王维扬.四边形加筋版的拓扑研究.科学技术与工程, 2008,8(7):1926-1928
[65]江玮,郁鼎文,冯平法.加筋板结构静态性能分析及优化设计.机械设计与制造,2008,(2):4-6
[66]张军.声学-结构灵敏度及结构-声学优化设计研究:[大连交通大学博士学位论文].大连:大连交通大学,2005,28-36
[67] Lamancusa J S, Eschenauer H A. Design optimizationmethods for rectangular panels with minimal sound radiation. AIAAJ,1994,32(3):472-479
[68] Choi K K,Lee J H. Sizing design sensitivity analysis of dynamic frequency response of vibrating structures.Journal of Mechanical Design,1992,(114):166 -173
[69]白杨,汪鸿振.声学-结构设计灵敏度分析.振动与冲击,2003,22(3):43-45
[70]张军,兆文忠,张维英.结构声辐射有限元/边界元法-结构灵敏度研究.振动工程学报.2005,18(3):366-368
[71]王敏庆,盛美萍,孙进才等.板受力激励下加筋板结构振动功率流.声学学报,1997,22(4):323-329
[72]张升明,潘旭初.板架结构的振动噪声研究.噪声与振动控制,1995,(5):9-13
[73] Stepanishen P R. Model coupling in the vibration of fluid-loaded cylindrical shells. Journal of the Acoustical Society of America,1982,71(4):813-823
[74]石焕文,孙进才.加纵肋平底圆柱壳振动和声辐射地FEM/BEM研究.振动与冲击,2006,25(2):88-89