基于声子晶体理论的潜艇推进轴系纵向减振技术研究
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摘要
声子晶体是由两种或两种以上弹性介质组成的具有弹性波带隙的周期复合材料或结构。其中,局域共振型声子晶体能够用尺寸远小于波长的复合结构形成带隙,从而抑制低频段弹性波传播。声子晶体局域共振带隙特性的发现为实际工程中的设备减振降噪提供了一种全新的思路。
本文在研究了潜艇轴系纵向振动传递问题的基础上,应用声子晶体局域共振带隙原理,在潜艇轴系上加装多个局域振子,利用遗传算法来优化振子力学参数,降低了轴系对螺旋桨脉动推力的传递。同时,本文对局域振子的结构设计进行了初步的探索,并利用有限元方法对上述工作进行了仿真验证。本文的主要研究内容和结论如下:
1.将四端参数法引入到潜艇推进轴系纵向振动特性计算中,建立了考虑螺旋桨、推力轴、推力轴承、基座、弹性壳体在内的较为完善的潜艇轴系纵向振动力学模型,并用有限元软件验证了所建模型的正确性。
2.选取了力传递率和功率流为振动传递的评价指标,对潜艇推进轴系纵向振动特性进行分析。结果表明,螺旋桨—轴的质量、轴—推力轴承的刚度是决定轴系纵向振动共振频率的主要因素;壳体弹性对轴系纵向振动有着重要影响,壳体纵向振动模态会引起轴系在低频段的共振,共振频率与壳体纵向振动固有频率相对应。
3.推导了附加多个局域振子的潜艇推进轴系四端参数传输矩阵,通过计算发现附加振子后特定频段内的功率流可以得到有效衰减,但亦会引起新的共振峰,故而需要对振子力学参数进行优化设计。结合遗传算法,以传递功率流最小为优化目标函数,建立了局域振子力学参数优化方案。
4.在满足适合轴系安装的前提下,对局域振子的结构设计方案进行了初步探索,确定了振子结构形式。按照优化后的振子力学参数和设计的振子结构形式,四端参数法与有限元仿真计算结果相吻合,两者均验证了优化后的振子对潜艇推进轴系纵向振动的传递有较好的抑制作用。
5.对附加局域振子的潜艇推进轴系进行了纵向振动校核,校核结果满足潜艇纵向振动校核标准。
总之,本文是声子晶体理论研究和减振降噪工程实践相结合的一次尝试,本文的研究有望拓宽人们解决振动和噪声问题的技术思路,对其他减振降噪问题的解决具有一定的参考价值。
The periodic composite materials and/or structure, known as phononic crystals (PCs), may exhibit elastic band gaps. The elastic wave in the frequency range of the band gaps will not propagate in the phononic crystal. The locally resonant band gap can restrain the propagation of the low frequency vibration, where the wave length is much longer than the periodic structures. The band gaps of locally resonant phononic crystal provide a new idea for vibration and noise reduction.
Propagation of axial vibration in submarine propelling shafts is investigated in this paper. According to the theory of locally resonant phononic crystal, the locally resonators are installed on the shafts to enhance axial vibration attenuation. The main contents and results are as follows:
Based on the theory of four-pole parameters method, we build a model of axial vibration of submarine propelling shafts, which includes the shafts, thrust bearing, foundation, and elastic hull. The axial vibration can be accurately simulated by the model, which is verified by finite element method (FEM) analyzing in Msc/Nastran software.
Axial force transmissibility and power flow are selected to evaluate the propagation of the axial vibration in the shafts. It is found that the resonance peak is determined by the mass of shafts and the stiffness of thrust bearing. More importantly, many resonances are arisen while taking the elasticity of the hull into account.
Four-pole parameters transfer matrix of propelling shafts with locally resonators is proposed. It is found that by attaching locally resonators on shafts we can attenuate the axial force transmission and power flow significantly. However, it also should be noted that new resonance peak are also arisen. In order to enhance the attenuation and avoid inducing large resonance peak, parameters optimization of the locally resonators is necessary. Genetic algorithm is used for optimizing the locally resonators to minimize the power flow of the shaft system.
The structure scheme of the locally resonators is provided in this paper. The optimization results are validated with the popular FEM software Msc/Nastran, which are in good agreement with the results of the four-pole parameters method. Both results confirm us that the axial transmissibility of submarine shafts could be substantially attenuated by periodically attaching locally resonators on the shaft.
It is also presented that the axial vibration of propelling shafts with locally resonators meets the requirement of criterions.
In summary, PC theory is introduced in the axial vibration reduction in the propelling shafts of submarine. The results of this thesis indicate that periodically installing locally resonators on the shaft is a feasible cure of the axial vibration transmission of submarine.
本文在研究了潜艇轴系纵向振动传递问题的基础上,应用声子晶体局域共振带隙原理,在潜艇轴系上加装多个局域振子,利用遗传算法来优化振子力学参数,降低了轴系对螺旋桨脉动推力的传递。同时,本文对局域振子的结构设计进行了初步的探索,并利用有限元方法对上述工作进行了仿真验证。本文的主要研究内容和结论如下:
1.将四端参数法引入到潜艇推进轴系纵向振动特性计算中,建立了考虑螺旋桨、推力轴、推力轴承、基座、弹性壳体在内的较为完善的潜艇轴系纵向振动力学模型,并用有限元软件验证了所建模型的正确性。
2.选取了力传递率和功率流为振动传递的评价指标,对潜艇推进轴系纵向振动特性进行分析。结果表明,螺旋桨—轴的质量、轴—推力轴承的刚度是决定轴系纵向振动共振频率的主要因素;壳体弹性对轴系纵向振动有着重要影响,壳体纵向振动模态会引起轴系在低频段的共振,共振频率与壳体纵向振动固有频率相对应。
3.推导了附加多个局域振子的潜艇推进轴系四端参数传输矩阵,通过计算发现附加振子后特定频段内的功率流可以得到有效衰减,但亦会引起新的共振峰,故而需要对振子力学参数进行优化设计。结合遗传算法,以传递功率流最小为优化目标函数,建立了局域振子力学参数优化方案。
4.在满足适合轴系安装的前提下,对局域振子的结构设计方案进行了初步探索,确定了振子结构形式。按照优化后的振子力学参数和设计的振子结构形式,四端参数法与有限元仿真计算结果相吻合,两者均验证了优化后的振子对潜艇推进轴系纵向振动的传递有较好的抑制作用。
5.对附加局域振子的潜艇推进轴系进行了纵向振动校核,校核结果满足潜艇纵向振动校核标准。
总之,本文是声子晶体理论研究和减振降噪工程实践相结合的一次尝试,本文的研究有望拓宽人们解决振动和噪声问题的技术思路,对其他减振降噪问题的解决具有一定的参考价值。
The periodic composite materials and/or structure, known as phononic crystals (PCs), may exhibit elastic band gaps. The elastic wave in the frequency range of the band gaps will not propagate in the phononic crystal. The locally resonant band gap can restrain the propagation of the low frequency vibration, where the wave length is much longer than the periodic structures. The band gaps of locally resonant phononic crystal provide a new idea for vibration and noise reduction.
Propagation of axial vibration in submarine propelling shafts is investigated in this paper. According to the theory of locally resonant phononic crystal, the locally resonators are installed on the shafts to enhance axial vibration attenuation. The main contents and results are as follows:
Based on the theory of four-pole parameters method, we build a model of axial vibration of submarine propelling shafts, which includes the shafts, thrust bearing, foundation, and elastic hull. The axial vibration can be accurately simulated by the model, which is verified by finite element method (FEM) analyzing in Msc/Nastran software.
Axial force transmissibility and power flow are selected to evaluate the propagation of the axial vibration in the shafts. It is found that the resonance peak is determined by the mass of shafts and the stiffness of thrust bearing. More importantly, many resonances are arisen while taking the elasticity of the hull into account.
Four-pole parameters transfer matrix of propelling shafts with locally resonators is proposed. It is found that by attaching locally resonators on shafts we can attenuate the axial force transmission and power flow significantly. However, it also should be noted that new resonance peak are also arisen. In order to enhance the attenuation and avoid inducing large resonance peak, parameters optimization of the locally resonators is necessary. Genetic algorithm is used for optimizing the locally resonators to minimize the power flow of the shaft system.
The structure scheme of the locally resonators is provided in this paper. The optimization results are validated with the popular FEM software Msc/Nastran, which are in good agreement with the results of the four-pole parameters method. Both results confirm us that the axial transmissibility of submarine shafts could be substantially attenuated by periodically attaching locally resonators on the shaft.
It is also presented that the axial vibration of propelling shafts with locally resonators meets the requirement of criterions.
In summary, PC theory is introduced in the axial vibration reduction in the propelling shafts of submarine. The results of this thesis indicate that periodically installing locally resonators on the shaft is a feasible cure of the axial vibration transmission of submarine.
引文
[1].王国治.舰艇机械结构的耦合振动及水下噪声控制.第十届船舶水下噪声学术讨论会,中国烟台,2005
[2].魏以迈.潜艇低噪声推进器技术研究与进展.第十届船舶水下噪声学术讨论会,中国烟台,2005
[3].王光荣.潜艇纵向振动计算及振动特性[J].海军工程大学学报,17(2):59-62,2005
[4].Liu Z Y,Zhang X X,Mao Y W,et al.Locally Resonant Sonic Materials[J],Science 289,1734-1736,2000
[5].郁殿龙.基于声子晶体理论的梁板类周期结构振动带隙特性研究.[博士学位论文].国防科技大学.长沙,2006
[6].李黎.基于带隙原理的梁类结构振动传播抑制技术研究.[硕士学位论文].国防科技大学.长沙,2006
[7].陈国钧,曾凡明.现代舰船轮机工程[M].长沙:国防科技大学出版社,2001,5
[8].陈锡恩.船舶轴系扭振计算和测试实例分析[J].船舶工程,2002,(1):10-13
[9].王璋奇.扭转固有振型分析传递矩阵法的改进[J].华北电力大学学报,2001,(7):66-68
[10].张洪田,张敬秋.大型船舶轴系纵扭耦合振动理论与试验研究[J].黑龙江工程学院学报,2004,18(4):1-6
[11].Magazinovic G.Shaftline design considerations of five-cylinder low-speed propulsion plants[D].13th Symposium on theory and practice of shipbuilding,1998
[12].王宏志,魏海军,关德林,陈椿芳.中间轴承对船舶轴系力学状态影响的数字模拟[J].船舶力学,2006,10(1):98-105
[13].Davor Sverko.Torsional-axial Coupling In The Line Shafting Vibrations In Merchant Ocean Going Ships[D].Concordia,Concordia University,1999
[14].张勇、蒋滋康.旋转轴系弯曲振动与扭转振动耦合的分析[J].清华大学学报(自然科学版),2000,40(6):114-117
[15].Rules and Regulations for the Classification of Ships,Part 5,Main and Auxiliary Machinery[M].Lioyd's Register(劳氏船级社),chap8,sec3 pp5,2006,7
[16].中华人民共和国船舶检验局.钢质海船建造与入级检验规范IS].北京:中华人民共和国船舶检验局,1989.
[17].Mouritz A P,Gellert E,Burchill P,Challis K.Review of advanced composite structures for naval ships and submarines[J].Composite Structures,2001,53:21-41
[18].Forrest J A.Measured dynamics of a thin cylindrical shell subject to axial excitation Acoustics[J].Western Australia,2005,11
[19].Dylejko P G,Kessissoglou N J.Minimization of the vibration transmission through the propeller-shafting system in a submarine[J].Journal of the Acoustical Society of America,2004,116(4):25-69
[20].Dylejko P G,Kessissoglou N J,Tso Y,Norwood C J.Active tuning of a resonance changer to minimise the vibration transmission in a submarine[M].ACTIVE2006,Adelaide,Australia,2006
[21].Pan X X,Tso Y,Juniper R R.Active Modal Control of Radiated Noise of a Submarine Hull[M].ACTIVE2006,Adelaide,Australia,2006
[22].Yablonovitch E.Inhibited spontaneous emission in solid-state physics and electronics.Phys.Rev.Lett.,1987,58(20):2059-2062
[23].John S.Strong locallyization of photons in certain disordered dielectric superlattices.Phys.Rev.Lett.,1987,58(23):2486-2489
[24].Sigalas M M and Economou E N.Elastic and acoustic wave band structure.J.Sound Vib.,1992,158(2):377-382
[25].Kushwaha M S,Halevi P,Dobrzynski Let al.Acoustic band structure of periodic elastic composites.Phys.Rev.Lett.,1993,71(13):2022-2025
[26].Martinez-Sala R,Sancho J,Sanchez J V et al.Sound attenuation by sculpture.Nature(London),1995,378:241
[27].Wang G,Wen X S,Wen J H et al.Two dimensional locally resonant phononic crystals with binary structures.Phys.Rev.Lett.2004,93(15):154302
[28].赵宏刚.固/固和固/气二维声子晶体的声波禁带研究[硕士学位论文].长沙:国防科技大学,2003
[29].温激鸿.声子晶体振动带隙及减振特性研究[博士学位论文].长沙:国防科技大学,2005
[30].Kushwaha M S,Halevi P,Martinez G et al.Theory of acoustic band structure of periodic elastic composites.Phys.Rev.B,1994,49(4):2313-2322
[31].Dowling J P.Sonic Band Structure In Fluids Exhibiting Periodic Density Variations.J.Acoust.Soc.Am..1992,91(5):2539-2543
[32].Economou B N and Sigalas M M.Classical wave propagation in periodic structures:Cermet versus network topology.Phys.Rev.B,1993,48(18):13434-13438
[33].管荣根,张瑞宏等.机械隔振装置的振动特性分析[J].机械设计与制造工程,2002,(31)4
[34].张志华.动力装置振动数值计算[M].哈尔滨:哈尔滨工程大学出版社,1994,12
[35].Paul G.Dylejko,Nicole J.Kessissoglou.Optimization of a resonance changer to minimize the vibration transmission in marine vessels[J].Journal of Sound and Vibration.300(2007) 101-116
[36].W.C.L.Hu,D.D.Kana.Four-pole parameters for impedance analysis of conical and cylindrical shells under axial excitations[J].Journal of the Acoustical Society of America.43(1968)683-690.
[37].严济宽,柴敏,陈小琳.振动隔离效果的评定[J].噪声与振动控制,1997,6:22-30
[38].朱石坚,何琳.船舶机械振动控制[M].国防工业出版社:北京:2006,1
[39].GOYDER H G D,WHITE R G.Vibration power flow from machines into built up structures.Part Ⅲ:Power flow through isolation systems[J].Journal of sound and vibration.1980,68(1):97-117.
[40].CUSCHIERI J M.Structural power flow analysis using a mobility approach of an L2shaped plate [J].Journal of the Acoustical Society of America.1990(87):1159-1165.
[41].KON Y K,WHITE R G.Analysis and control of vibrational power transmission to machinery supporting structures subjected to a multi2excitation system,Part Ⅰ:Driving point mobility matrix of beams and rectangular plates[J].Journal of Sound and Vibration.1996,196(4):469-493.
[42].KON Y K,WHITE R G.Analysis and control of vibrational power transmission to machinery supporting structures subjected to a multi2excitation system,Part Ⅱ:Vibrational power analysis and control schemes[J].Journal of Sound and Vibration,1996,196(4):495-508.2
[43].LANGL EY R S.On the vibrational conductivity approach to high frequency dynamics for tow2dimensional structural components[J].Journal of Sound and Vibration,1995,182(4):637-657.
[44].SIGNORELL I,FLOTOW A H V.Wave propagation Power flow and resonance in a truss beam[J].J.S.V,1988,126:127-144.
[45].张效慈,李国华等.Calculation of power flow transmission for a common floating raft shared by several ship machines[J].船舶力学(英文版),2001,5(3):89-94.
[46].Jie Pan,Nabil Parag.Propeller induced structural vibration through the thrust beating.Conference of the Australian Acoustical Society.Australia,2002,12
[47].马军建,董增川.蚁群算法研究进展[J].河海大学学报(自然科学版),2005,(33)2:19-143
[48].周勇,陈洪亮.蚁群算法的研究现状及其展望[J].微型电脑应用,2002,(18)2:5-7
[49].黎锁平,张秀媛.人工蚁群算法理论及其在经典TSP问题中的实现[J].交通运输系统工程与信息,2002,(2)1:55-57
[50].杨维,李歧强.粒子群优化算法综述[J].中国工程科学,2004,(6)5:34-36
[51].张荣沂.一种新的集群优化方法—粒子群优化算法[J].黑龙江工程学院学报(自然科学版),2004.(18)4:87-89
[52].侯志荣,吕振肃.基于MATLAB的粒子群优化算法及其应用[J].计算机仿真,2003,10(20):68-70
[53].朱丽莉,杨志鹏.粒子群优化算法分析及研究进展[J].计算机工程与应用,2007,(43)5:24-28
[54].徐宁,李春光.几种现代优化算法的比较研究[J].系统工程与电子技术,2004,(24)12:100-104
[55].魏燕定.两级振动隔振系统参数优化设计[J].浙江大学学报,2006,5(40)5
[56].D.A.RADE.Optimizations of dynamic vibration absorbers over a frequency bands[J].Mechanical Systems and Signal Processing.2000,14(5):679-690
[57].M.Moshrefi-Torbati.Passive vibration control of a satellite boom structure by geometric optimization using genetic algorithm[J].Journal of Sound and Vibration.267(2003):879-892
[58].张庆雅,汪亮,孙东.遗传算法在固体发动机结构可靠性计算中的应用[J].固体火箭技术,2002,25(2)
[59].刘琼荪,周声华.基于自适应惩罚函数法的混合遗传算法[J].重庆大学学报(自然科学版),2006,29(6):78-81
[60].雷英杰,张善文等.Matlab遗传算法工具箱及应用[M].西安电子科技大学出版社:西安,2005,4
[2].魏以迈.潜艇低噪声推进器技术研究与进展.第十届船舶水下噪声学术讨论会,中国烟台,2005
[3].王光荣.潜艇纵向振动计算及振动特性[J].海军工程大学学报,17(2):59-62,2005
[4].Liu Z Y,Zhang X X,Mao Y W,et al.Locally Resonant Sonic Materials[J],Science 289,1734-1736,2000
[5].郁殿龙.基于声子晶体理论的梁板类周期结构振动带隙特性研究.[博士学位论文].国防科技大学.长沙,2006
[6].李黎.基于带隙原理的梁类结构振动传播抑制技术研究.[硕士学位论文].国防科技大学.长沙,2006
[7].陈国钧,曾凡明.现代舰船轮机工程[M].长沙:国防科技大学出版社,2001,5
[8].陈锡恩.船舶轴系扭振计算和测试实例分析[J].船舶工程,2002,(1):10-13
[9].王璋奇.扭转固有振型分析传递矩阵法的改进[J].华北电力大学学报,2001,(7):66-68
[10].张洪田,张敬秋.大型船舶轴系纵扭耦合振动理论与试验研究[J].黑龙江工程学院学报,2004,18(4):1-6
[11].Magazinovic G.Shaftline design considerations of five-cylinder low-speed propulsion plants[D].13th Symposium on theory and practice of shipbuilding,1998
[12].王宏志,魏海军,关德林,陈椿芳.中间轴承对船舶轴系力学状态影响的数字模拟[J].船舶力学,2006,10(1):98-105
[13].Davor Sverko.Torsional-axial Coupling In The Line Shafting Vibrations In Merchant Ocean Going Ships[D].Concordia,Concordia University,1999
[14].张勇、蒋滋康.旋转轴系弯曲振动与扭转振动耦合的分析[J].清华大学学报(自然科学版),2000,40(6):114-117
[15].Rules and Regulations for the Classification of Ships,Part 5,Main and Auxiliary Machinery[M].Lioyd's Register(劳氏船级社),chap8,sec3 pp5,2006,7
[16].中华人民共和国船舶检验局.钢质海船建造与入级检验规范IS].北京:中华人民共和国船舶检验局,1989.
[17].Mouritz A P,Gellert E,Burchill P,Challis K.Review of advanced composite structures for naval ships and submarines[J].Composite Structures,2001,53:21-41
[18].Forrest J A.Measured dynamics of a thin cylindrical shell subject to axial excitation Acoustics[J].Western Australia,2005,11
[19].Dylejko P G,Kessissoglou N J.Minimization of the vibration transmission through the propeller-shafting system in a submarine[J].Journal of the Acoustical Society of America,2004,116(4):25-69
[20].Dylejko P G,Kessissoglou N J,Tso Y,Norwood C J.Active tuning of a resonance changer to minimise the vibration transmission in a submarine[M].ACTIVE2006,Adelaide,Australia,2006
[21].Pan X X,Tso Y,Juniper R R.Active Modal Control of Radiated Noise of a Submarine Hull[M].ACTIVE2006,Adelaide,Australia,2006
[22].Yablonovitch E.Inhibited spontaneous emission in solid-state physics and electronics.Phys.Rev.Lett.,1987,58(20):2059-2062
[23].John S.Strong locallyization of photons in certain disordered dielectric superlattices.Phys.Rev.Lett.,1987,58(23):2486-2489
[24].Sigalas M M and Economou E N.Elastic and acoustic wave band structure.J.Sound Vib.,1992,158(2):377-382
[25].Kushwaha M S,Halevi P,Dobrzynski Let al.Acoustic band structure of periodic elastic composites.Phys.Rev.Lett.,1993,71(13):2022-2025
[26].Martinez-Sala R,Sancho J,Sanchez J V et al.Sound attenuation by sculpture.Nature(London),1995,378:241
[27].Wang G,Wen X S,Wen J H et al.Two dimensional locally resonant phononic crystals with binary structures.Phys.Rev.Lett.2004,93(15):154302
[28].赵宏刚.固/固和固/气二维声子晶体的声波禁带研究[硕士学位论文].长沙:国防科技大学,2003
[29].温激鸿.声子晶体振动带隙及减振特性研究[博士学位论文].长沙:国防科技大学,2005
[30].Kushwaha M S,Halevi P,Martinez G et al.Theory of acoustic band structure of periodic elastic composites.Phys.Rev.B,1994,49(4):2313-2322
[31].Dowling J P.Sonic Band Structure In Fluids Exhibiting Periodic Density Variations.J.Acoust.Soc.Am..1992,91(5):2539-2543
[32].Economou B N and Sigalas M M.Classical wave propagation in periodic structures:Cermet versus network topology.Phys.Rev.B,1993,48(18):13434-13438
[33].管荣根,张瑞宏等.机械隔振装置的振动特性分析[J].机械设计与制造工程,2002,(31)4
[34].张志华.动力装置振动数值计算[M].哈尔滨:哈尔滨工程大学出版社,1994,12
[35].Paul G.Dylejko,Nicole J.Kessissoglou.Optimization of a resonance changer to minimize the vibration transmission in marine vessels[J].Journal of Sound and Vibration.300(2007) 101-116
[36].W.C.L.Hu,D.D.Kana.Four-pole parameters for impedance analysis of conical and cylindrical shells under axial excitations[J].Journal of the Acoustical Society of America.43(1968)683-690.
[37].严济宽,柴敏,陈小琳.振动隔离效果的评定[J].噪声与振动控制,1997,6:22-30
[38].朱石坚,何琳.船舶机械振动控制[M].国防工业出版社:北京:2006,1
[39].GOYDER H G D,WHITE R G.Vibration power flow from machines into built up structures.Part Ⅲ:Power flow through isolation systems[J].Journal of sound and vibration.1980,68(1):97-117.
[40].CUSCHIERI J M.Structural power flow analysis using a mobility approach of an L2shaped plate [J].Journal of the Acoustical Society of America.1990(87):1159-1165.
[41].KON Y K,WHITE R G.Analysis and control of vibrational power transmission to machinery supporting structures subjected to a multi2excitation system,Part Ⅰ:Driving point mobility matrix of beams and rectangular plates[J].Journal of Sound and Vibration.1996,196(4):469-493.
[42].KON Y K,WHITE R G.Analysis and control of vibrational power transmission to machinery supporting structures subjected to a multi2excitation system,Part Ⅱ:Vibrational power analysis and control schemes[J].Journal of Sound and Vibration,1996,196(4):495-508.2
[43].LANGL EY R S.On the vibrational conductivity approach to high frequency dynamics for tow2dimensional structural components[J].Journal of Sound and Vibration,1995,182(4):637-657.
[44].SIGNORELL I,FLOTOW A H V.Wave propagation Power flow and resonance in a truss beam[J].J.S.V,1988,126:127-144.
[45].张效慈,李国华等.Calculation of power flow transmission for a common floating raft shared by several ship machines[J].船舶力学(英文版),2001,5(3):89-94.
[46].Jie Pan,Nabil Parag.Propeller induced structural vibration through the thrust beating.Conference of the Australian Acoustical Society.Australia,2002,12
[47].马军建,董增川.蚁群算法研究进展[J].河海大学学报(自然科学版),2005,(33)2:19-143
[48].周勇,陈洪亮.蚁群算法的研究现状及其展望[J].微型电脑应用,2002,(18)2:5-7
[49].黎锁平,张秀媛.人工蚁群算法理论及其在经典TSP问题中的实现[J].交通运输系统工程与信息,2002,(2)1:55-57
[50].杨维,李歧强.粒子群优化算法综述[J].中国工程科学,2004,(6)5:34-36
[51].张荣沂.一种新的集群优化方法—粒子群优化算法[J].黑龙江工程学院学报(自然科学版),2004.(18)4:87-89
[52].侯志荣,吕振肃.基于MATLAB的粒子群优化算法及其应用[J].计算机仿真,2003,10(20):68-70
[53].朱丽莉,杨志鹏.粒子群优化算法分析及研究进展[J].计算机工程与应用,2007,(43)5:24-28
[54].徐宁,李春光.几种现代优化算法的比较研究[J].系统工程与电子技术,2004,(24)12:100-104
[55].魏燕定.两级振动隔振系统参数优化设计[J].浙江大学学报,2006,5(40)5
[56].D.A.RADE.Optimizations of dynamic vibration absorbers over a frequency bands[J].Mechanical Systems and Signal Processing.2000,14(5):679-690
[57].M.Moshrefi-Torbati.Passive vibration control of a satellite boom structure by geometric optimization using genetic algorithm[J].Journal of Sound and Vibration.267(2003):879-892
[58].张庆雅,汪亮,孙东.遗传算法在固体发动机结构可靠性计算中的应用[J].固体火箭技术,2002,25(2)
[59].刘琼荪,周声华.基于自适应惩罚函数法的混合遗传算法[J].重庆大学学报(自然科学版),2006,29(6):78-81
[60].雷英杰,张善文等.Matlab遗传算法工具箱及应用[M].西安电子科技大学出版社:西安,2005,4
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