摘要
功能梯度材料(Functionally Graded Material,简写FGM)是一种特殊的非均匀材料。自从1984年日本科学家首次提出其设计概念以来,FGM在制造、设计和应用方面引起了广大学者的极大关注。虽然提出FGM的最初设想是作为热隔栅应用于航空航天领域,但目前发现它在电子、化学、核能、光学、声学、生物医学、土木工程和机械工程(例如汽车的发动机、高速机车的刹车盘和车轮)等诸多领域,都有十分广阔的应用前景。对FGM结构声学问题的研究,既有声学理论的需要,也有实际工程应用的需要。
本文首先建立了镶嵌在无限障板中功能梯度材料矩形板和无限长板条声辐射模型。根据功能梯度复合材料矩形板的基本动力方程,利用模态叠加法求出不同激励载荷作用下功能梯度材料矩形板和无限长板条横向振动位移,然后对振动位移进行傅立叶变换,根据Rayleigh积分公式求解,最终得到功能梯度材料矩形板和无限长板条远场辐射声压近似解析解。由于功能梯度材料矩形板近场辐射声压无法利用积分得到解析解,只能利用数值积分进行研究,因此本文利用数值积分方法分析了功能梯度材料矩形板近场辐射声压频率特性。
其次,本文建立了敷设阻尼层功能梯度材料圆柱壳在径向点激励载荷作用下的声辐射模型,研究了在阻尼层和圆柱壳不同参数下的振动和声辐射特性。研究时通过功能梯度材料圆柱壳的动力方程、流场Helmholtz方程、壳体表面边界条件和对有限长圆柱壳声压的傅氏积分变换来求解耦合声场中声压的表达式,其中阻尼层的运动采用Navier方程来描述。最后通过阻尼层与壳体的边界条件求解流固耦合振动方程,进而解得功能梯度材料圆柱壳在外流场的辐射声场表达式,并计算了表征壳体振动与声辐射的两个物理量:辐射声功率级和振动均方速度级。
再次,本文建立了旋转载荷作用下功能梯度材料圆柱壳的声辐射模型,研究了不同旋转速度下功能梯度材料圆柱壳在空气和水两种流场中的振动和声辐射特性。旋转载荷采用频率域表示,这种基于频率域的方法便于解释振动及声辐射响应与功能梯度材料圆柱壳模态之间的关系。
最后,本文还研究了功能梯度材料圆柱壳的声散射特性。首先将材料参数沿厚度方向连续变化的功能梯度材料圆柱壳,简化成多层横观各向同性柱状复合结构。然后利用传递矩阵法研究功能梯度材料圆柱壳声散射特性。
研究发现,通过改变板和壳的几何参数、材料参数和梯度指数等,可以改变FGM板壳结构的动力响应和声学特性。本文的研究对FGM板壳结构的声学设计具有重要的指导意义。
Functionally graded material (FGM) is special nonhomogeneous material. And it was first introduced by Japanese scientists in 1984. Since then, FGM has received more and more attention. Nowadays, FGM has extended their first applications in aerospace to electronics, chemistry, optics, biomedicine, acoustics, nuclear engineering, civil engineering, mechanical engineering (auto-engine, brake and wheel of bullet train) and the like. Research on the behavior of FGM structures acoustic problen not only benefits the needs of acoustic theory, but also satisfies the needs of practice.
First, the models of radiated sound of baffled functionally graded material rectangular plate and infinite length plate strip are set up and investigated theoretically in this dissertation. By basic dynamic equation of FGM rectangular plate, the flexural displacement is obtained by modal analysis method that they are excited by various excitation forces. And using Fourier transform and Rayleigh's formula, a far-field approximation solution of the radiated sound field is derived in a closed form. And the near acoustic field is investigated by a numerical integral method.
Second, the sound radiation model of a finite FGM cylindrical shell driven by a harmonious point force with the outer shell coated with compliant layer is set up, and the vibroacoustic characteristics of different FGM shell's and damping layer's parameters are systematically studied. The acoustic pressure expression is attained by the FGM shell's dynamic equation, the Helmholtz equation, the boundary conditions of the FGM shell surface and the Fourier integral transform of finite shell, where the layer motion is described by means of the three-dimensional Navier equations. Lastly, through the boundary conditions of the damping layer combined with the shell the coupled oscillation equation was solve, and radiation sound field expression was shown using the shell displacements. In the end, the parameters of the acoustic radiated power level and the radial quadratic velocity level are calculated. And these two parameters indicate the general characteristics of the FGM shell vibration and sound radiation.
Third, a theoretical model is developed to evaluate the vibration and sound radiation of a FGM cylindrical shell excited by a constant point load continuously traveling along the circumferential direction at a rotational speedΩ, and the FGM shell is immersed in two different fluids of air and water. The present approach is based rather on a frequency-domain solution of the vibratory and acoustic responses of the FGM shell, and such a frequency-domain solution is convenient to interpret the vibratory and acoustic responses in terms of shell modes.
Finally, the sound scattering by functionally graded material cylindrical shell is investigated in this dissertation. The original inhomogeneous shell with the material parameters's change along the thickness is approximated by a laminate modal. So the FGM shell is turned into a cylindrical layered structure with transversely isotropic symmetry. The transfer matrix solution is expected to gradually involves a system global transfer matrix formed as the product of the individual transfer matrices by applying continuity of the displacement and stress components at the interfaces of neighbouring layers, is employed to solve for the scattering coefficients.
We find that geometric parameters, material paratemers and power law index of the plate and shell affect the responses of FGM structures's vibroacoustic behaviour. This dissertation hopes to bring some insights on the acoustic designing of the FGM structures.
引文
[1]Yamanouchi M,Koizumi M,Hirai T,Shiota I.Proceedings of the First International Symposium on Functionally Gradient Materials.Japan,1990.
[2]Koizumi M.Functionally gradient materials the concept of FGM.Ceramic Transactions 1993;34:3-10.
[3]庞建超,高福宝,曹晓明.功能梯度材料的发展与制备方法的研究.金属制品,2005,31(4):4-9.
[4]Koizumi M..FGM activities in Japan.Composites B,1997,28:1-4.
[5]Hirai T,Chen L.Recent and prospective development of functionally graded materials in Japan.Materials Science Forum,1999,308-311,509-514.
[6]郭成,维斗,金志浩.功能梯度材料的研究现状与展望.稀有金属材料与工程,1995,24:19-25.
[7]李永,宋健,张志民.梯度功能力学.北京:清华大学出版社,2003.
[8]郑慧雯,克也木·沙吾提,章娴君.功能梯度材料的研究进展.西南师范大学学报(自然科学版),2002,27:788-793.
[9]王保林,韩杰才,张幸红.非均匀材料力学.北京:科学出版社,2003.
[10]李永,张志民,马淑雅.耐热梯度功能材料的热应力研究进展.力学进展,2000,30:571-580.
[11]Zavaliangos A.Challenges and opportunities for PM in functionally graded materials.Metal Powder Report,1999,54:37-38.
[12]Kieback B,Neubrand A,Riedel H.Processing techniques for functionally graded materials.Materials Science and Engineering:A,2003,362:81-106.
[13]Tanigawa Y.Some basic thermoelastic problems for nonhomogeneous structural materials.Applied Mechanics Reviews,1995,48:287-300.
[14]王保林,杜善义,韩杰才.功能梯度材料的热/械耦合分析研究进展.力学进展,1999,29:528-548.
[15]Survey for application of FGM,(Eds by FGM Forum).The Society of Non-Traditional Technology,Tokyo,1991.
[16]Mohamed Maalej,Shaikh,F.U.Ahmed,P.Paramasivam.Corrosion durability and structural response of functionally-graded concrete beams.Journal of Advanced Concrete Technology,2003,3:307-316.
[17]何祚镛,赵玉芳.声学理论基础.北京:国防工业出版社,1981.
[18]马大猷.现代声学理论基础.北京:科学出版社,2004.3.
[19][美]P.M.莫尔斯,K.U.英格特.理论声学.北京:科学出版社,1984.
[20]盛美萍,王敏庆.噪声与振动控制技术基础.北京:科学出版社,2001.
[21]周健.板结构的声辐射与隔声性能研究[学位论文].武汉:华中科技大学,2002.
[22]赵键,谢壮宁,黄幼玲.自由场结构体声辐射研究.声学学报,1994,19(1):22-31.
[23]Seybet A.F.,Soenark B,Rizzo F J,Shippy D J.Application of the BIE method to sound radiation problems using an iso-parametric element.ASME Transactions.J.Vib.Acoust.Stress Reliab.Design,1984,106:414-420.
[24]Seybet A.F.,Soenark B,Rizzo F J,Shippy D J.An advanced computational method for radiation and scattering of acoustic waves in three dimensions.J.Acoust.Soc.Am.,1985,77(2):362-368.
[25]M.P.诺顿著,盛元生等译.工程噪声和振动分析基础.北京:航空工业出版社,1993.
[26]姚德源,王其政.统计能量分析及其应用.北京:北京理工大学出版社,1995.
[27]黎胜.水下结构声辐射和声传输的数值分析及主动控制模拟研究[学位论文].大连:大连理工大学,2001.
[28]黎胜,赵德有.用边界元计算机构振动辐射声场.大连理工大学学报,2000,40(4):391-394.
[29]赵翔,汪鸿振,朱物华.边界元法计算已知振速封闭面的声辐射.声学学报,1989,14(4):250-257.
[30]Hunt J T,Knittel M R,Nichols C S,Don Barach.Finite Element Approch to Acoustic Radiation from Elastic Structure.Journal of the Acoustical Society of America,1974,55(2):269-280.
[31]沈壕,孙洪生.工程声学中的有限元法.声学学报,1981,4:249-259.
[32]P.Filippi Springer.Theoretical Acoustics and Numerical Techniques.Verlag,NewYork,1983.
[33]Junger M C.Sound Scattering by Thin Elastic Shells,Journal of the Acoustical Society of America.1952,24(4):366-373.
[34]G.Maidanik.Response of ribbed panels.Journal of the Acoustical Society of America,1962,34:809-835.
[35]C.E.Wallace.Radiation resistance of rectangular panels.Journal of the Acoustical Society of America,1972,53:946-952.
[36]G.Maidanik.Vibrational and radiative classification of modes of a baffled finite panel.Journal of Sound and Vibration,1974,34:447-455.
[37]E.G.Williams,J.D.Maynard.Numerical evaluation of the Rayleigh integral for planar radiators using the FFT.Journal of the Acoustical Society of America,1982,72(6):2020-2030.
[38]S.Schedin,C.Lambourge,A.Chaigne.Transient sound fields from impacted plates:comparison between numerical simulations and experiments.Journal of Sound and Vibration,1999,221(3):471-490.
[39]H.G.Davies.Low frequency random excitation of water-loaded rectangular plates.Journal of Sound and Vibration,1971,15:107-126.
[40]L.D.Pope and R.C.Leibowitz.Intermodal coupling coefficients for a fluid-loaded rectangular plate.Journal of the Acoustical Society of America,1974,56(2):408-415.
[41]B.E.Sandman.Motion of three-layered elastic-viscoelastic plate under fluid loading.Journal of the Acoustical Society of America,1975,57(5):1097-1107.
[42]C.E.Wallace,Radiation resistance of a rectangular panel.Journal of the Acoustical Society of America,1972,51(3):946-952.
[43]Zuo-Yong He.Scattering near field of a rectangular composite plate immersed in water.Chinese Journal of Acoustics,1985,4:26-43.
[44]Junger M.C.and Feit D..Sound,Structures and Their Interaction.MIT Press,Cambridge,MA,1972.
[45]Fahy F..Sound and Structural Vibration —Radiation,Transmission and Response.Academic Press,London,1985.
[46]Leppington F.G..Scattering of sound waves by finite membranes and plates near resonances.Q.J.Mech.Appl.Math.,1976,29:527-546.
[47]Sakagami K.,Morimoto M.and Takahashi D..Acoustic reflection of an elastic plate strip of finite width and infinite length in a rigid baffle.Mem.Grad.Sch.Sci.Tech.,Kobe Univ,1995,13-B:61-76(in Japanese).
[48]Kimihiro Sakagami,Kazutoshi Michishita,Masayuki Morimoto,Yasutoshi Kitamura.Sound radiation from a baffled elastic plate strip of infinite length with various concentrated excitation forces.Applied Acoustics,1998,55(3):181-202.
[49]N.Atalla,J.Nicolas,C.Gauthier.Acoustic radiation of an unbaffled vibrating plate with general elastic boundary conditions.J.Aoust.Soc.Am,1996,99:1484-1494
[50]姜哲,郭骅.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.
[51]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.
[52]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.
[53]吴文伟,冷文浩,沈顺根.具有等间距加强筋板的声辐射.中国造船,1999,146:72-81.
[54]毛崎波,姜哲.对声辐射模态的讨论.振动工程学报,2000,13(4):633-637.
[55]毛崎波,徐柏龄,姜哲.对声辐射模态法的改进.振动工程学报,2002,15(3):262-266.
[56]林书玉.弯曲振动矩形薄板的辐射声场研究.声学与电子工程,2000,59(3):13-18.
[57]Junger M C.Radiation loading of cylindrical and spherical surfaces.J.Acoust.Soc.Am.,1952,24:288-289.
[58]Junger M C.Vibrations of elastic shells in a fluid medium and the associated radiation of sound.J.Appl.Mech.,1952,74:439-445.
[59]Junger M C.The physical interpretation of the expression for an outgoing wave in cylindrical coordinates.J.Acoust.Soc.Am.,1953,25(1):40-47.
[60]Koval L R.On sound transmission into a thin cylindrical shell under "flight conditions".J.Sound Vib.,1976,48(2):265-275.
[61]Koval L R.Effects of cavity resonances on sound transmission into a thin cylindrical shell.J.Sound Vib.,1978,59(1):23-33.
[62]Manning J E,Maidanik G.Radiation properties of cylindrical shells.J.Acoust.Soc.Am.,1964,36(9):1691-1698.
[63]Scott J F M.The free modes of propagation of an infinite fluid-loaded thin cylindrical shell.J.Sound Vib.,1988,125(2):241-280.
[64]Guo Y P.Acoustic radiation from cylindrical shells due to internal forcing.J.Acoust.Soc.Am.,1996,99(3):1495-1505.
[65]Stepanishen Peter R.Radiated power and radiation loading of cylindrical surfaces with nonuniform velocity distributions.J.Acoust.Soc.Am.,1978,63(2):328-338.
[66]Keltie R F.The effect of hydrostatic pressure fields on the structural and acoustic response of cylindrical shells.J.Acoust.Soc.Am.,1986,79(3):595-603.
[67]石焕文,盛美萍,孙进才.圆柱壳水中平面振动和声辐射的导纳法研究.西北大学学报(自然科学版),2006,36(3):359-363.
[68]李洪亮,吴成军,黄协清.无限长FFS圆柱壳体远场辐射声压的参数研究.农业工程学报,2003,19(3):41-45.
[69]Stepanishen Peter R.Modal coupling in the vibration of fluid-loaded cylindrical shells.J.Acoust.Soc.Am.,1982,71(4):813-823.
[70]Sandman B E.Fluid-loading influence coefficients for a finite cylindrical shell.J.Acoust.Soc.Am.,1976,60(6):1256-1264.
[71]Laulagnet B,Guyader J L.Modal analysis of a shell's acoustic radiation in light an heavy fluids.J.Sound Vib.,1989,131(3):397-415.
[72]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.
[73]Mead D J.A comparison of some equations for the flexural vibration of damped sandwich beams.Journal of Sound and Vibration,1982,83(3):363-377.
[74]Kerwin E M.Damping of flexural waves by a constrained viscoelastic layer.Journal of the Acoustical Society of America,1959,31(7):952-962.
[75]Ross D,Ungar E E,Kerwin E M..Damping of flexural vibrations by means of viscoelastic laminate.Structural Damping,ASME,1959,23(1):12-18.
[76]Yu.Y.Y..Vibration of Elastic Sandwich Cylindrical Shells.Journal of Applied Mechanics,1960,27:653-662.
[77]Markus.S..Damping Properties of Layered Cylindrical Shells Vibration in Axially Symmetric Modes.Journal of Sound and vibration,1976,48(4):511-524.
[78]Alam N.Vibration and damping analysis of a multilayered cylindrical shells,part Ⅰ:Theoretical analysis.AIAA Journal,1984,22(6):803-810.
[79]Alam N.Vibration and damping analysis of a multilayered cylindrical shells,part Ⅱ:Numerical results.AIAA Journal,1984,22(7):975-981.
[80]Y.N.Liu and Tucker.A.J..The Distribution of Radiated and Vibrationary Powers of A Point-Driven Infinite Cylindrical Shell with a Compliant Layer.Noise-Con,West Lafayette,Indiana,1988.
[81]Laulagnet B.and Guyader J.L..Sound Radiation from A Finite Cylindrical Shell Covered With A Compliant Layer.Journal of Vibration and Acoustics,1991,113:267-274.
[82]Laulagnet B.and Guyader J.L..Sound radiation from finite cylindrical coated shells,by means of asymptotic expansion of three-dimensional equations for coating.J.Acoust.Soc.Am,1994,96(1):277-286.
[83]Laulagnet B.and Guyader J.L..Sound radiation from finite cylindrical shells,partially covered with longitudinal strips of compliant layer.Journal of Sound and Vibration,1995,186(5):723-742.
[84]Y.P.Guo.Attenuation of helical wave radiation from cylindrical shells by viscoelastic layer.The Journal of the Acoustical Society of America,1995,97(1):298-308.
[85]Ruzzene M,Baz A..Finite element modeling of vibration and sound radiation and sound radiation from fluid-loaded damped shells.Thin-Walled Structures,2000,36(1):21-46.
[86]Saravanan C,Ganesan N,Ramamurti V.Vibration and damping analysis of multilayered fluid filled cylindrical shells with constrained viscoelastic damping using modal strain energy method.Computers and Structures,2000,75(4):395-417.
[87]Boily S,Charron F.The vibroacoustic response of a cylindrical shell structure with viscoelastic and poroelastic materials.Applied Acoustics,1999,58(2):131-152.
[88]谢官模.粘弹性阻尼材料对环肋圆柱壳声辐射的影响.武汉工业大学学报,1995,17(2):97-99.
[89]谢官模.环肋圆柱壳在流场中的动力响应和声辐射[学位论文].武汉:华中理工大学,1994.
[90]陈炜.敷设自由阻尼层的环肋圆柱壳在流场中的声辐射[学位论文].1998.4.
[91]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(Ⅰ).西安交通大学学报,1998,32(7):76-79.
[92]陈美霞,骆东平,陈小宁,蔡敏波,周锋.有限长双层壳体声辐射理论及数值分析.中国造船.2003,44(4):59-67.
[93]陈美霞,骆东平,彭旭,罗斌.敷设阻尼材料的双层圆柱壳声辐射性能分析.声学学报,2003,28(6):486-493.
[94]周锋.部分敷设阻尼材料有限长圆柱壳在流场中声辐射性能分析[学位论文].武汉:华中科技大学,2004.4.
[95]毛云,谢官模.水下部分覆盖阻尼材料圆柱壳的声辐射性能.武汉理工大学学报,2005,27(5):21-23.
[96]郝承智,王敏庆,胡卫强.阻尼处理对水下弹性壳体振动声辐射影响分析.噪声与振动控制,2006,3:49-51.
[97]E.N.K.Liao and P.G.Kessel.Response of pressurized cylindrical shells subjected to moving loads.J.Appl.Mech.1972,39:227-234.
[98]D.B.Bogy,H.J.Greenberg and F.E.Talke.Steady solution for circumferentially moving loads on cylindrical shells.IBM J.Res.Develop,1974,395-400.
[99]K.Shirakawa.Response of cylindrical shells to circumferentially moving load.Solid Mech.Arch.,1984,9(3):335-351.
[100]S.C.Huang and W.Soedel.On the forced vibration of simply supported rotating cylindrical shells.J.Acoust.Soc.Am.,1988,84:275-285.
[101]W.Soedel.On the dynamic response of the rolling tire,Proceedings of the Eight International Congress on Acoustics(London,England,1974),July,23-31.
[102]Raymond Panneton,Alain Berry,and Frederic Laville.Vibration and sound radiation of a cylindrical shell under a circumferentially moving load.J.Acoust.Soc.Am,1995,98(4):2165-2173.
[103]C.J.Wu,H.L.Chen and X.Q.Huang.Vibroacoustic analysis of a fluid-loaded cylindrical shell excited by a rotating load.Journal of Sound and Vibration,1999,225(1):79-94.
[104]Hoppmann W.H.Flexual Vibration of Orthogonally Stiffened Cylindrical Shells,Proc.9th Intl.Cong.Appl.Mech.,Brukelles,1956,225-237.
[105]Galletly G.D.On the In-vacuo Vibration of Simply Supported Ring-Stiffened Cylindrical Shell,Proc of second U.S.A.national congress of applied mechanics,1954.
[106]Sewall J.L.,Clary R.R,Leadbetter S.A..An Experimental and Analytical Vibration Study of Ring-Stiffened Cylindrical Shell Structure with Various Support Conditions.NASA TN D-2398,1964,52-53.
[107]Sewall J.L.,Naumann,E.C..An Experimental and Analytical Vibration Study of Ring-Stiffened Cylindrical Shell Structure with Various Support Conditions,NASA TN D-4075,1968,54-55.
[108]Garnet H.,Goldberg M.A..Free Vibration of Ring-Stiffened Shells.Grumann Aircraft Engrg.Cor.Res.Dept.Mech.1962,Rept.21,156-157.
[109]Evseev V.N..Sound Radiation from A Shell Reinforced with Longitudinal Stiffeners.Sov. Phys.Acoust.,1989,35(6):624-627.
[110]Bernblit M.V..Sound Radiation by A Thin Elastic Cylindrical Shell with Reinforce Ribs.Sov.Phys.Acoust.,1975,20(5):414-418.
[111]Laulagnet B.,Guyader J.L..Sound radiation by finite cylindrical ring stiffened shells.J.Sound Vib.,1990,138(2):173-191.
[112]Burroughs B.C..Acoustic radiation from fluid-loaded infinite circular cylinders with doubly periodic ring supports.J.Acoust.Soc.Am,1984,75(3):714-722.
[113]Yoshikawa S.,Willams E.G.,Washburn K.B..Vibration of two concentric submerged cylindrical shells coupled by the contained fluid.J.Acoust.Soc.Am,1994,95(6):3273-3286.
[114]谢官模,骆东平.环肋圆柱壳在流场中辐射声场压力的解析解.应用数学和力学,1995,16(12):1061-1066.
[115]谢官模,骆东平.环肋柱壳在流场中声辐射性能分析.中国造船,1995,131(4):37-45.
[116]汤渭霖,何兵蓉.水中有限长加肋圆柱壳振动和声辐射近似解析解.声学学报,2001,26(3):1-5.
[117]曾革委,黄玉盈,马运义.舱壁和环肋加强的无限长圆柱壳声弹耦合模型及其声特性.固体力学学报,2002,23(3):269-279.
[118]赵翔,徐建学,江俊.双层壳-流耦合系统的频散方程.声学学报,1996,21(3):217-223.
[119]赵翔,徐建学,江俊.载流双层壳的声振特性研究.声学学报,1996,21(5):790-797.
[120]陈美霞,骆东平,陈小宁,沈瑞喜.双层柱壳在流场中辐射声场压力的解析解.应用数学和力学,2002,23(4):415-421.
[121]吴文伟,吴崇健,沈顺根.双层加肋圆柱壳振动和声辐射研究.船舶力学,2002,6(1):44-51.
[122]Bofilios D.A.,Lyrintzis C.S..Structure-borne noise transmission into cylindrical enclosures of finite extent.AIAA.1991,39(8):1193-1201.
[123]L.Cheng.Fluid-Structural Coupling of a plate-ended cylindrical shell:Vibtation and internal sound field.J.Sound Vib.,1994,174(5):641-654.
[124]肖邵予,骆东平,朱显明.两端用圆板封口的环肋柱壳振动声辐射性能分析.噪声与振动控制,2005,6:15-18.
[125]肖邵予.两端用圆板封口的环肋柱壳振动声辐射性能分析[学位论文].武汉:华中科技大学,2004.5.
[126]Veksler,N.,Izbicki,J.L.,Conoir,J.M..Elastic wave scattering by a cylindrical shell.Wave Motion,1999,29(3):195-209.
[127]Rayleigh L..On waves propagated among the plane surface of an elastic solid.Proceedings of the London Mathematic Soceity,1887,17:4-11.
[128]Sezawa K.Scattering of elastic waves and some allied problems.Bull Earthquake Res.Inst.Tokyo Imerial Univ,1927,3-19.
[129]Faran J.J..Sound scattering solid cylinders and spheres.J.Acoust.Soc.Am.,1951,23(4):405-418.
[130]White R.M..Elastic Wave scattering at a cylindrical discontinuity in a solid.J.Acoust.Soc.Am.1958,30(8):405-418.
[131]Hampton L.D.,McKinney,C.M..Experimental study of the scattering of acoustic energy from solid metal spheres in water,J.Acoust.Soc.Am.1961,33(5):664-673.
[132]Baron M.L.,Parmes R..Displacements and velocities produced by the diffraction of a pressure wave by a cylindrical cavity in an elastic medium.J.Appl.Mech.,1962,29:385-395.
[133]Hickling R..Analysis of echoes from a solid elastic sphere in water.J.Acoust.Soc.Am.,1962,34(10):1582-1592.
[134]Dragonette L.R.,Vogt R.H.,Flax L.,et al.Acoustic reflection from elastic spheres and rigid spheres and spheroids.Ⅱ.Transient analysis.J.Acoust.Soc.Am.,1974,55(6):1130-1137.
[135]Neubauer W.G,Vogt R.H.,Dragonette L.R..Acoustic reflection from elastic spheres.Ⅰ.Steady-state signals.J.Acoust.Soc.Am.,1974,55(6):1123-1129.
[136]Sachse W..Ultrasonic spectroscopy of a fluid-filled cavity in an elastic solid.J.Acoust.Soc.Am.,1974,56(3):891-896.
[137]Pao Y.H.,Mow C.C..Diffraction of elastic waves and dynamic stress concentrations[M],Crane and Russak,New York,1973.
[138]Frisk G.V,(U|¨)berall H..Creeping waves and lateral waves in acoustic scattering by large elastic cylinders.J.Acoustic.Soc.Am,1976,59(1):46-54.
[139]Hasegawa T.,Kitagawa Y.,Watanabe Y..Sound reflection from an absorbing sphere.J.Acoust.Soc.Am.,1977,62(5):1298-1300.
[140]Schuetz L.S.,Neubauer W.G..Acoustic reflection from cylinders-nonabsorbing and absorbing.J.Acoust.Soc.Am.1977,62(3):513-517.
[141]Mitri F.G.,Fellah Z.E.A.,Chapelon J.Y..Acoustic backscattering form function of absorbing cylinder targets(L).J.Acoust.Soc.Am.,2004,115(4):1411-1413.
[142]Diarmuid Murphy J.,Breitenbach,Edward D.,(U|¨)berall,Herbert.Resonance scattering of acoustic waves from cylindrical shells.J.Acoust.Soc.Am.1978,64(2):677-683.
[143]Lawrence Flax,V.K.Varadan and V.V.Varadan.Scattering of an obliquely incident acoustic wave by an infinite cylinder.J.Acoust.Soc.Am.,1980,68(6):1832-1835.
[144]Wen H.Lin and A.C.Raptis.Acoustic scattering by elastic solid cylinders and spheres in viscous fluids.J.Acoust.Soc.Am.,1982,73(3):736-748.
[145]Zhen Ye.A novel approach to sound scattering by cylindrical of finite length.J.Acoust.Soc.Am.,1997,102(2):877-884.
[146]Young-Sang Joo,Jeong-Guon Ih,Myoung-Seon Choi.Inherent background coefficients for acoustic resonance scattering from submerged,multilayered,cylindrical structures.J.Acoust.Soc.Am.,1998,103(2):900-910.
[147]S.M.Hasheminejad,N.Safari.Acoustic scattering from viscoelastically coated spheres and cylinders in viscous fluids.Journal of Sound and Vibration,2005,280:101-125.
[148]汤渭霖.可分离变量的水下弹性体的纯弹性共振散射.声学学报,1995,20(6):456-465.
[149]汤渭霖,范军.水中弹性球壳的共振声辐射理论.声学学报,2000,25(4):308-312.
[150]刘国利,汤渭霖.平面声波斜入射到水中无限长圆柱壳体的纯弹性共振散射.声学学报,1996,21(5):805-814.
[151]范军,刘涛,汤渭霖.水中双层无限长圆柱壳体声散射.声学学报,2003,28(4):345-350.
[152]张小凤,赵俊渭,王荣庆,韩静.非入射方向水下弹性目标声散射特性.声学与电子工程,2001,64:4-8.
[153]张小凤,赵俊渭.非入射方向有限长弹性柱声散射特性研究.陕西师范大学学报(自然科学版),2002,30(3):57-61.
[154]陆鹏,王耀俊.考虑界面状况时柱状弹性固体的声波散射.物理学报,2001,50(4):697-703.
[155]刘胜兴,王耀俊.横向各向同性柱状复合结构对超声波的散射.声学学报,2002,27(2):149-156.
[156]郭新毅,马力,吴国清.水下加筋圆柱壳结构声散射特性研究.海洋技术,2007,26(3):36-41.
[157]Noda N.,Tsuji T..Steady thermal stresses in a plate of functionally gradient material.Transactions of Japan Society of Mechanical Engineers,Series A,1991,57(533):98-103.
[158]Obata Y.,Noda N.,Tsuji T..Steady thermal stresses in a plate of functionally gradient material (influence of boundary conditions).Transactions of Japan Society of Mechanical Engineers,Series A,1992,58(553):1689-1695.
[159]Noda N.,Tsuji T..Steady thermal stresses in a plate of functionally gradient material with temperature-dependent properties.Transactions of Japan Society of Mechanical Engineers,Series A,1991,57(535):625-631.
[160]Cheng Z Q,Batra R C.Three-dimensional thermoelastic deformations of a functionally graded ellipic plate.Composites Part B:Engineering,2000,31:97-106.
[161]Tanigawa Y,et al.Optimization problem of material composition for nonhomogeneous plate to minimize thermal stresses when subjected to unsteady heat supply.Transactions of Japan Society of Mechanical Engineers,Series A,1996,62(593):115-122.
[162]Tanigawa Y,Akai T,Kawamura R,Oka N.Transient heat conduction and thermal stress problems of a nonhomogeneous plate with temperature-dependent material properties.Journal of Thermal Stresses,1996,19(1):77-102.
[163]Tanigawa Y,Ootao Y,Kawamura R.Thermal bending of laminated composite rectangular plates and nonhomogeneous plates due to partial heating.Journal of Thermal Stresses,1991,14(3):285-308.
[164]Ootao Y,Tanigawa Y.Three-dimensional transient thermal stresses of functionally graded rectangular plate due to partial heating.Journal of Thermal Stresses,1999,22(1):35-55.
[165]Reddy J N,Wang C M,Kitipomchai S.Axisymmetric bending of functionally grade circular and annular plates,European Journal of Mechanics-A/Solids,1999,18:185-199.
[166]Cheng Z Q,Batra R C.Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories.Archives Mechanics,2000,52(2):143-158.
[167]Cheng Z Q,Kitipomchai S.Exact bending solution of inhomogeneous plates from homogeneous thin-plate deflection.AIAA Journal,2000,38:1289-1291.
[168]Feldman E,Aboudi J.Buckling analysis of functionally graded plates subjected to uniaxial loading.Composite Structures,1997,38:29-36.
[169]Wu Lanhe.Thermal buckling of a simply supported moderately thick rectangular FGM plate.Composite Structures,2004,64(2):211-218.
[170]Y.Li,K.T.Ramesh,E.S.C.Chin.Dynamic characterization of layered and graded structures under impulsive loading.International Journal of Solids and Structures,2001,38:6045-6061.
[171]J.Yang,Hui-Shen Shen.Dynamic response of initially stressed functionally graded rectangular thin plates.Composite Structures,2001,54(4):497-508.
[172]Michael H.Santarea,Priya Thamburaj,George A.Gazonas.The use of graded finite elements in the study of elastic wave propagation in continuously nonhomogeneous materials.International Journal of Solids and Structures,2003,40(21):5621-5634.
[173]Serge Abrate.Free vibration,buckling,and static deflections of functionally graded plates.Composites Science and Technology,2006,66(14):2383-2394
[174]Ritesh Samadhiya,Abhijit Mukherjee,Siegfried Schmauder.Characterization of discretely graded materials using acoustic wave propagation.Computational Materials Science,2006,37:20-28.
[175]J.Woo,S.A.Meguida,L.S.Ong.Nonlinear free vibration behavior of functionally graded plates.Journal of Sound and Vibration,2006,289(3):595-611.
[176]曹志远.不同边界条件功能梯度矩形板固有频率解的一般表达式.复合材料学报,2005,22(5):172-177.
[177]曹志远.各种边界条件平行四边形功能梯度板的动力特性解析解.力学季刊,2006,27(2):255-261.
[178]曹志远.功能梯度板的非线性动力分析.固体力学学报,2006,27(1):21-25.
[179]Reddy J N,Chin C D.Thermoelastical analysis of functionally graded cylinders and plates.Journal of Thermal Stresses,1998,21:593-626.
[180]Obata Y,Noda N.Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material.Journal of Thermal Stresses,1994,17:471-487.
[181]Ootao Y.,Akai T,Tanigawa Y.Three-dimensional transient thermal stress analysis of a nonhomogenous hollow circular cylinder.Transactions of Japan Society of Mechanical Engineers,Series A.1993,59(563):1684-1690.
[182]Ootao Y.,Tanigawa Y,Kasai T,Nakanishi N.Inverse problem analysis of transient thermal stresses in a nonhomogenous solid hollow circular cylinder due to asymmetric heating.Transactions of Japan Society of Mechanical Engineers,Series A.1992,58(548):567-573.
[183]Takezono S,Tao K,Inamura E,Inoue M.Thermal stress and deformation in functionally graded material shells of revolution under thermal loading due to fluid.International Journal of Japan Society of Mechanical Engineers,Series A.1996,39(4):573-581.
[184]Praveen G N,Chin C D,Reddy J N.Thermoelastic analysis of functionally graded ceramic-metal cylinder.Journal of Engineering Mechanics ASCE,1999,125(11):1259-1267.
[185]Loy C T,Lain K Y,Reddy J N.Vibration of functionally graded cylindrical shells.International Journal of Mechanical Sciences,1999,41(3):309-324.
[186]S.C.Pradhan,C.T.Loya,K.Y.Lam,J.N.Reddy.Vibration characteristics of functionally graded cylindrical shells under various boundary conditions.Applied Acoustics,2000,61(1):111-129.
[187]Gong S W,Lam K Y,Reddy J N.The elastic response of functionally graded cylindrical shells to low-velocity impact.International Journal of Impact Engineering,1999,22(4):397-417.
[188]Seyyed M.Hasheminejad,M.Rajabi.Acoustic resonance scattering from a submerged functionally graded cylindrical shell.Journal of Sound and Vibration,2007,302:208-228.
[189]曹志远.功能梯度复合材料圆柱壳固有频率解.地震工程与工程振动,2005,25(6):38-42.
[190]曹志远.功能梯度复合材料圆柱壳基本理论及长壳固有振动解.玻璃钢/复合材料,2006,4:3-6.
[191]王素,倪春阳,朱心雄.功能梯度材料活塞三维温度场分析.北京航空航天大学学报, 2005,32(12):1299-1302.
[192]王素,倪春阳,朱心雄.一种功能梯度材料活塞的材料梯度方程选择.机械科学与技术,2006,25(2):133-138.
[193]冯忆艰,桂长林,王虎,孙军.功能梯度材料研究及其在内燃机中的应用.合肥工业大学学报(自然科学版),2004,27(6):597-601.
[194]冯忆艰,杜双松,程继贵,胡献国.活塞顶部功能梯度涂层的有限元模拟热分析.农业机械学报,2008,39(11):30-34.
[195]邢世凯.梯度功能材料及其在内燃机上的应用研究.汽车工艺与材料,2004,10:6-8.
[196]Yoshihiro Sugano,Ryoichi Chiba,Koichi Hirose,and Kazuhiro Takahashi.Material Design for reduction of thermal stress in a functionally graded material rotating disk.JSME International Journal,Series A,2004,47(2):189-197.
[197]李海波,王桂兰,张海鸥.等成分轮廓线的FGM零件直接成形路径规划方法.机电产品开发与创新,2007,20(2):76-78.
[198]Prakash T,Ganapathi M.Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method.Composites Part B:engineering,2006,37:642-649.
[199]Williamson R L,Rabin B H,Drake J T.Finite element analysis of thermal residual stresses at graded ceramic-metal interfaces Part Ⅰ:Model description and geometrical effects.Journal of Applied Physics,1993,74(2):1310-1320.
[200]Drake J T,Willamson R L,Rabin B H.Finite element analysis of thermal residual stresses at graded ceramic-metal interfaces Part Ⅱ:Interface optimization for residual stress reduction.Journal of Applied Physics,1993,74(2):1321-1326.
[201]Tanigawa Y,et al.One-dimensional transient thermal stress problem for nonhomogeneous hollow circular cylinder and its application.Transactions of Japan Society of Mechanical Engineers,Series A,1996,62(599):1656-1664.
[202]Tanaka K et al.An improved solution to thermoelastic material design in functionally gradient materials:scheme to reduce thermal stresses.Computer Methods in Applied Mechanics and Engineering,1993,109:377-389.
[203]Aboudi J,Pindera M J,Arnold S M.Response of functionally graded composites to thermal gradients.Composite Engineering,1994,4(1):4-18.
[204]Pindera M J,Aboudi J,Arnold S M.Limitations of the uncoupled,RVE-based micromechanical approach in the analysis of functionally graded materials.Mechanics of Materials,1995,20(1):77-94.
[205]Aboudi J,Pindera M J,Arnold S M.Higher-order theory for functionally graded materials.Composites Part B:Engineering,1999,30(8):777-832.
[206]L.Shuyu.Study on the radiation acoustic field of rectangular radistions in flexural vibration.Journal of Sound and Vibration,2002,254(3):469-479.
[207]田宝晶.敷设阻尼层的加肋圆柱壳辐射性能及噪声特性分析[学位论文].哈尔滨:哈尔滨工程大学,2006.5.
[208]B.E.Sandman.Numerical fluid loading coefficients for the modal velocities of a cylindrical shell.Computers & Structures,1976,6:467-473.
[209]李学斌.正交各向异性圆柱壳静动态特性分析及比较研究[学位论文].武汉:华中科技大学,2004.3.
[210]张华.水下环肋圆柱壳的自由振动特性分析[学位论文].哈尔滨:哈尔滨工程大学,2006.2.
[211]王耀俊.柱状分层固体媒质的声散射.物理学进展,2003,23(2):125-144.
[212]陈光敬,赵锡宏,于立.传递矩阵法求解成层横观各向同性弹性体轴对称问题.岩土工程学报,1998,20(5):105-108.
[213]陈伟球,边祖光,丁皓江.功能梯度矩形厚板的三维热弹性分析.力学季刊,2002,23(4):443-449.
[214]丁皓江,陈伟球,徐荣桥.横观各向同性层合矩形板弯曲、振动和稳定的三维精确分析.应用数学和力学,2001,22(1):16-22.
[215]杨正光,仲政,戴瑛.功能梯度矩形板的三维弹性分析.力学季刊,2004,25(1):15-20.
[216]刘杰斌.功能梯度材料厚板的三维弹性分析.安徽建筑工业学院学报(自然科学版),2006,14(3):4-7.
[217]刘杰斌.功能梯度材料厚板的弯曲、屈曲及振动分析[学位论文].合肥:合肥工业大学,2006.6.
[218]贺晨.圆柱壳体全频段振动声辐射特性研究[学位论文].西安:西北工业大学,2006.3.
[219]徐平.弹性波的多重散射在工程中的应用[学位论文].杭州:浙江大学,2006.6.
[220]王晓峰.水下加肋双层弹性壳体散射声场分析[学位论文].哈尔滨:哈尔滨工程大学,2007.3.
[221]张靖华.功能梯度材料梁、壳结构的静态力学响应[学位论文].兰州:兰州理工大学,2004.5.
[222]杨杰.功能梯度复合材料板结构的非线性力学行为与动力特性[学位论文].上海:上海交通大学,2001.12.
[223]边祖光.功能梯度材料板壳结构的耦合问题研究[学位论文].杭州:浙江大学,2005.5.
[224]胡世猛.板壳结构强度与声学特性分析[学位论文].武汉:武汉理工大学,2006.4.
[225]李林凌.计及气固耦合声辐射理论与应用研究[学位论文].武汉:华中科技大学,2005.4.
[226]邹元杰.水中阻尼复合壳体结构声振特性的数值分析[学位论文].大连:大连理工大学,2004.4.
[227]郝承智.水下加肋壳体振动与声辐射特性研究[学位论文].西安:西北工业大学,2006.3.
[228]杨娜娜.环肋圆柱壳水下辐射噪声有限元分析[学位论文].哈尔滨:哈尔滨工程大学,2004.2.
[229]周锋.部分敷设阻尼材料有限长圆柱壳在流场中声辐射性能分析[学位论文].武汉:华中科技大学,2004.5.
[230]曹志远.板壳振动理论(第一版).北京:中国铁道出版社,1989.4.
[231]Wihelm Fl(u|¨)gge.Stresses in Shells.Springer-Verlag,1960
[232]R.Szilard著,陈太平等译.板的理论和分析.北京:中国铁道出版社,1984.
[233]达奇纳著,王统,张尧弼译.数值分析及其程序应用手册,上海:上海科学技术文献出版社,1988 12.