柔性隔振系统的功率流传递特性与控制研究
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摘要
振动隔离是许多工程结构需要解决的难点问题之一,如航天器上精密仪器的隔振、潜艇中动力机械的消声减噪、大型旋转机械引发的振动消除等。随着轻质、薄化结构在工程领域中的广泛应用,振动隔离中基础的非刚性问题日益突出,如何正确建立隔振系统的动力学模型和研究系统动力学特性的分析手段,对上述工程系统具有重要的理论意义和实际应用价值。
从振动能量传递的观点看,研究柔性基础上复杂机械系统的动力传递特性及控制策略,是上述工程系统的研究热点问题之一,分析方法主要是采用功率流方法。本文紧密围绕柔性隔振系统功率流传递及控制两个核心问题,运用机械阻抗/导纳法,建立了柔性基础隔振系统的动力学模型,分析了被动和主动隔振系统的功率流传递规律。
本文在国家自然科学基金(编号:10772112,10472065)、教育部重点项目(编号:107043)、教育部博士点基金(编号:20070248032)、上海市教委科研重点项目(编号:09ZZ17)和海洋工程国家重点实验室自主研究课题(编号:GKZD010807)的资助下,对柔性隔振系统的动力学建模、功率流传递、被动与主动控制策略等问题进行了深入研究,主要研究内容和成果总结如下:
(1)在大量阅读文献的基础上,较为全面地综述了柔性隔振系统的功率流传递特性与控制问题的研究进展。
(2)研究了单层柔性被动隔振系统的功率流传递特性问题。在考虑基础柔性的前提下,建立了单层隔振系统的理论模型,运用机械导纳法推导了系统的功率流传递函数。研究中,柔性基础分别考虑了有限板和无限板,隔振器分别讨论了竖直和倾斜放置两种情况。研究结果显示,橡胶隔振器对隔离高频振动具有很好的效果,无限板比有限板的隔振效果好。在低频域,机器共振以刚体模态振动为主;在中低频段内,纵向功率流分量对功率流的传递起着主要作用,可以忽略其它的功率流成分;在高频域,横向和旋转的功率流分量的作用逐渐加强,呈现出隔振器的内共振。对于有限板,在中高频域隔振系统表现出多个共振峰,对于无限板则表现为少量的共振峰。基础的厚度对隔振系统有影响,随着基础的厚度由厚变薄,系统在低频阶段的三个刚性模态振动逐渐变得不明显,峰值也变得越来越扁平。对于隔振器倾斜放置的情况,当基础较薄时,基础的功率流随隔振器倾斜角度的增大而略有增加,有限板的共振峰数量大大多于无限板的情况。机器与基础上同时作用有激励时,对于无限板,在低频阶段基础激励以及基础激励位置对基础上的总功率流的影响不大,在中高频阶段基础激励会导致总功率流有所增大,系统的隔振效果变差;而对于有限板,传到基础上的功率流受薄板激励影响很小,可以忽略不计,基础的运动特性与仅有机器作用时几乎一样。
(3)研究了单层柔性主动隔振系统的功率流传递特性问题。推导了主动隔振系统的功率流传递函数,讨论了总功率流最小、力最小、速度最小等目标函数下的主动控制方法,并通过数值仿真对比了它们的控制效果。研究结果显示,主动隔振的隔振效果明显优于被动隔振。
(4)讨论了双层柔性隔振系统的功率流传递特性问题。在考虑基础柔性的前提下,建立了隔振系统的数学模型,推导了系统的功率流传递函数,讨论了总功率流最小控制策略下的控制效果。研究中,分别考虑了被动控制和主动控制。研究结果显示,双层隔振系统的振动功率流的传输主要集中在低频段;在高频段,机器输入到系统的功率流和通过上层隔振器传递到中间板的功率流随频率的增加呈指数衰减;主动隔振的隔振效果明显优于被动隔振;如果激励频率比较低,采用机器控制即能满足隔振要求,如果激振频率较高则要考虑浮筏控制。
减振与隔振的研究一直是国内外的前沿研究课题,目前在许多方面还需要进行进一步的深入研究与探讨,因此在论文的最后,对本文的研究工作和成果进行了全面总结,对未来的研究问题进行了展望。
Vibration isolation is one of the difficult problems faced by engineering structures, such as vibration isolation of precision equipment on space-plane, noise reduction of motive mechanics on submarines, vibration reduction of large rotor mechanics, etc. As the use of vibration isolation systems in the field of light, thin structures, the problem of non-rigid foundation of vibration isolation has been severe. It will be quite valuable in both theoretical research and practical use for these engineering systems.
In the view of vibration energy transmission, it is a hot subject of the above engineering systems to study the dynamic transmission characteristics and control strategies of complex mechanical systems on flexible foundation. In these studies, the power flow method is mostly selected. This paper focuses on transfer of power flow and vibration control. Mechanical mobility and impedance methods are used to establish dynamic model of vibration isolation system on flexible foundation. Transfer rules of power flow of both passive and active vibration control systems are analyzed.
This paper subjected on dynamic modeling of flexible vibration isolation system, power flow transmission, and passive/active control strategy. It is supported by the National Natural Science Foundation of China (Grant Nos. 10772112 and 10472065), the Key Project of Ministry of Education of China (Grant No. 107043), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20070248032), the Key Project of Education Committee of Shanghai (Grant No. 09ZZ17) and the Research Project of State Key Laboratory of Ocean Engineering of China (Grant No. GKZD010807). The main contents and conclusions are as follows:
(1) Based on a great deal of references, the development of transfer characteristics of power flow and control problems of vibration isolating systems on flexible foundation are summarized.
(2) The transmission characteristics of power flow of single-stage isolation systems with flexible foundation are discussed. With the consideration of flexibility of foundation, the theoretical model of single-stage isolation system is established, in which power flow transmission functions are induced using the method of mobility and impedance. Within this study, the flexible foundation is either finite or infinite, while the isolator is either vertical or inclined. The results show that rubber vibration isolator performs well at high frequencies and infinite plate is better than finite one.
At low frequencies, resonance appears in the form of rigid modes. At middle stage frequencies, vertical factor of the power flow has main effect on transmission, while other parts can be ignored. At high frequencies, horizontal and rotational factors of the power flow become more important and resonance within the vibration isolator systems appears.
For finite plate, there are several peaks of resonances, while fewer peaks for infinite plate. The thickness of foundation affects the systems, too. As the foundation becomes thinner, vibration around rigid modes at low frequencies becomes relaxed and peaks become flatter.
As for the case of inclined isolators with thin foundation, power flow of foundation increases slightly as the angle of inclination gets larger. Finite plate contains even more resonance peaks than infinite one.
When there are excitations on both foundation and vibration source, as for infinite plate, the excitation, when at low frequencies, and position of excitation don’t affect the total power flow much. If the frequencies are higher, the power flow transmitted will increase, and isolation efficiency becomes bad. For finite plate, the effect of force on power flow transmitted to thin foundation is so little that it can be omitted. The movement of the foundation is almost the same as when there nothing more than a machine.
(3) The transmission characteristics of power flow of single layer vibration isolation systems with active control are studied. Five different active control strategies have been discussed. Compared with numerous simulations, active control isolation system was overweighing its passive alternate.
(4) The transmission characteristics of power flow of two-stage isolation systems with flexible foundation are discussed. With consideration of flexibility of foundation, mathematic model of vibration isolating system is established. The transmission function of power flow is induced and effect of control is discussed when the minimum of total power flow energy is the object. Both passive and active controls are considered in this study. The results show that, the transmission of power flow of two-stage isolation systems concentrate at low frequencies. At high frequencies, the power flow transmitted from the actuators to the system decreases exponentially as the frequency. And so is the power flow transmitted from the upper isolator to the middle stage plate. It is obvious that active isolation is better than passive one. If the excitation frequency is low, machine-control is good enough for the purpose of vibration isolation, while raft-control should be considered at high frequencies.
The study on vibration reduction & isolation has been the frontier of research in domestic and overseas alike. Nowadays, further studies and discussions on some detail problems are still needed. At the end of this paper, the study and result are summarized and future research is prospected.
从振动能量传递的观点看,研究柔性基础上复杂机械系统的动力传递特性及控制策略,是上述工程系统的研究热点问题之一,分析方法主要是采用功率流方法。本文紧密围绕柔性隔振系统功率流传递及控制两个核心问题,运用机械阻抗/导纳法,建立了柔性基础隔振系统的动力学模型,分析了被动和主动隔振系统的功率流传递规律。
本文在国家自然科学基金(编号:10772112,10472065)、教育部重点项目(编号:107043)、教育部博士点基金(编号:20070248032)、上海市教委科研重点项目(编号:09ZZ17)和海洋工程国家重点实验室自主研究课题(编号:GKZD010807)的资助下,对柔性隔振系统的动力学建模、功率流传递、被动与主动控制策略等问题进行了深入研究,主要研究内容和成果总结如下:
(1)在大量阅读文献的基础上,较为全面地综述了柔性隔振系统的功率流传递特性与控制问题的研究进展。
(2)研究了单层柔性被动隔振系统的功率流传递特性问题。在考虑基础柔性的前提下,建立了单层隔振系统的理论模型,运用机械导纳法推导了系统的功率流传递函数。研究中,柔性基础分别考虑了有限板和无限板,隔振器分别讨论了竖直和倾斜放置两种情况。研究结果显示,橡胶隔振器对隔离高频振动具有很好的效果,无限板比有限板的隔振效果好。在低频域,机器共振以刚体模态振动为主;在中低频段内,纵向功率流分量对功率流的传递起着主要作用,可以忽略其它的功率流成分;在高频域,横向和旋转的功率流分量的作用逐渐加强,呈现出隔振器的内共振。对于有限板,在中高频域隔振系统表现出多个共振峰,对于无限板则表现为少量的共振峰。基础的厚度对隔振系统有影响,随着基础的厚度由厚变薄,系统在低频阶段的三个刚性模态振动逐渐变得不明显,峰值也变得越来越扁平。对于隔振器倾斜放置的情况,当基础较薄时,基础的功率流随隔振器倾斜角度的增大而略有增加,有限板的共振峰数量大大多于无限板的情况。机器与基础上同时作用有激励时,对于无限板,在低频阶段基础激励以及基础激励位置对基础上的总功率流的影响不大,在中高频阶段基础激励会导致总功率流有所增大,系统的隔振效果变差;而对于有限板,传到基础上的功率流受薄板激励影响很小,可以忽略不计,基础的运动特性与仅有机器作用时几乎一样。
(3)研究了单层柔性主动隔振系统的功率流传递特性问题。推导了主动隔振系统的功率流传递函数,讨论了总功率流最小、力最小、速度最小等目标函数下的主动控制方法,并通过数值仿真对比了它们的控制效果。研究结果显示,主动隔振的隔振效果明显优于被动隔振。
(4)讨论了双层柔性隔振系统的功率流传递特性问题。在考虑基础柔性的前提下,建立了隔振系统的数学模型,推导了系统的功率流传递函数,讨论了总功率流最小控制策略下的控制效果。研究中,分别考虑了被动控制和主动控制。研究结果显示,双层隔振系统的振动功率流的传输主要集中在低频段;在高频段,机器输入到系统的功率流和通过上层隔振器传递到中间板的功率流随频率的增加呈指数衰减;主动隔振的隔振效果明显优于被动隔振;如果激励频率比较低,采用机器控制即能满足隔振要求,如果激振频率较高则要考虑浮筏控制。
减振与隔振的研究一直是国内外的前沿研究课题,目前在许多方面还需要进行进一步的深入研究与探讨,因此在论文的最后,对本文的研究工作和成果进行了全面总结,对未来的研究问题进行了展望。
Vibration isolation is one of the difficult problems faced by engineering structures, such as vibration isolation of precision equipment on space-plane, noise reduction of motive mechanics on submarines, vibration reduction of large rotor mechanics, etc. As the use of vibration isolation systems in the field of light, thin structures, the problem of non-rigid foundation of vibration isolation has been severe. It will be quite valuable in both theoretical research and practical use for these engineering systems.
In the view of vibration energy transmission, it is a hot subject of the above engineering systems to study the dynamic transmission characteristics and control strategies of complex mechanical systems on flexible foundation. In these studies, the power flow method is mostly selected. This paper focuses on transfer of power flow and vibration control. Mechanical mobility and impedance methods are used to establish dynamic model of vibration isolation system on flexible foundation. Transfer rules of power flow of both passive and active vibration control systems are analyzed.
This paper subjected on dynamic modeling of flexible vibration isolation system, power flow transmission, and passive/active control strategy. It is supported by the National Natural Science Foundation of China (Grant Nos. 10772112 and 10472065), the Key Project of Ministry of Education of China (Grant No. 107043), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20070248032), the Key Project of Education Committee of Shanghai (Grant No. 09ZZ17) and the Research Project of State Key Laboratory of Ocean Engineering of China (Grant No. GKZD010807). The main contents and conclusions are as follows:
(1) Based on a great deal of references, the development of transfer characteristics of power flow and control problems of vibration isolating systems on flexible foundation are summarized.
(2) The transmission characteristics of power flow of single-stage isolation systems with flexible foundation are discussed. With the consideration of flexibility of foundation, the theoretical model of single-stage isolation system is established, in which power flow transmission functions are induced using the method of mobility and impedance. Within this study, the flexible foundation is either finite or infinite, while the isolator is either vertical or inclined. The results show that rubber vibration isolator performs well at high frequencies and infinite plate is better than finite one.
At low frequencies, resonance appears in the form of rigid modes. At middle stage frequencies, vertical factor of the power flow has main effect on transmission, while other parts can be ignored. At high frequencies, horizontal and rotational factors of the power flow become more important and resonance within the vibration isolator systems appears.
For finite plate, there are several peaks of resonances, while fewer peaks for infinite plate. The thickness of foundation affects the systems, too. As the foundation becomes thinner, vibration around rigid modes at low frequencies becomes relaxed and peaks become flatter.
As for the case of inclined isolators with thin foundation, power flow of foundation increases slightly as the angle of inclination gets larger. Finite plate contains even more resonance peaks than infinite one.
When there are excitations on both foundation and vibration source, as for infinite plate, the excitation, when at low frequencies, and position of excitation don’t affect the total power flow much. If the frequencies are higher, the power flow transmitted will increase, and isolation efficiency becomes bad. For finite plate, the effect of force on power flow transmitted to thin foundation is so little that it can be omitted. The movement of the foundation is almost the same as when there nothing more than a machine.
(3) The transmission characteristics of power flow of single layer vibration isolation systems with active control are studied. Five different active control strategies have been discussed. Compared with numerous simulations, active control isolation system was overweighing its passive alternate.
(4) The transmission characteristics of power flow of two-stage isolation systems with flexible foundation are discussed. With consideration of flexibility of foundation, mathematic model of vibration isolating system is established. The transmission function of power flow is induced and effect of control is discussed when the minimum of total power flow energy is the object. Both passive and active controls are considered in this study. The results show that, the transmission of power flow of two-stage isolation systems concentrate at low frequencies. At high frequencies, the power flow transmitted from the actuators to the system decreases exponentially as the frequency. And so is the power flow transmitted from the upper isolator to the middle stage plate. It is obvious that active isolation is better than passive one. If the excitation frequency is low, machine-control is good enough for the purpose of vibration isolation, while raft-control should be considered at high frequencies.
The study on vibration reduction & isolation has been the frontier of research in domestic and overseas alike. Nowadays, further studies and discussions on some detail problems are still needed. At the end of this paper, the study and result are summarized and future research is prospected.
引文
[1]丁文镜.减振理论.清华大学出版社, 1988.
[2]牛军川.基于多模型柔性隔振系统的振动机理和主动控制研究.山东大学博士学位论文, 2003.
[3] Plunkett R. Interaction between a vibratory machine and its foundation. Noise Control, 1958, 4: 18~22.
[4]陈树勋.基础柔性对传递率的影响.振动与冲击, 1984, 1: 23~25.
[5]严济宽.隔振降噪技术的新进展.嗓声与振动控制, 1991, 5(6): 11~16.
[6] Goyder HGD, White RG. Vibration power flow from machine into built-up structures, Part I: Introduction and approximate analyses of beam and plate-like foundations. Journal of sound and vibration, 1980, 68(1): 59~75.
[7] Goyder HGD, White RG. Vibration power flow from machine into built-up structures, Part II: wave propagation and power flow in beam-stiffened plates. Journal of sound and vibration, 1980, 68(1): 77~96.
[8] Goyder HGD, White RG. Vibration power flow from machine into built-up structures, Part III: power flow through isolation systems. Journal of sound and vibration, 1980, 68(1): 97~117.
[9] Pan J, Pan JQ, Hansen CH. Total power flow from a vibrating rigid body to a flexible panel through multiple elastic mounts. Journal of the Acoustical Society of America, 1992, 92(2): 895~907.
[10] Petersson B, Plunt J. On effective mobility in the prediction of structure-borne sound transmission between a source structure and a receiving structure. Part I: theoretical back ground and basic experimental studies. Journal of Sound and Vibration, 1982, 82(4): 517~529.
[11] Petersson B, Plunt J. On effective mobility in the prediction of structure-borne sound transmission between a source structure and a receiving structure. Part II: procedure for the estimation of mobilities. Journal of Sound and Vibration, 1982, 82(4): 531~540.
[12] Pinnington RJ. Vibrational power flow transmission to a seating of a vibration isolated motor. Journal of Sound and Vibration, 1987, 118(3): 515~530.
[13] Pinnington RJ, White RG, Power flow through machine isolators to resonant and non-resonant beam. Journal of Sound and Vibration, 1981, 75: 179~197.
[14] Cuschieri JM. Vibration transmission through periodic structures using a mobility power flow approach. Journal of Sound and Vibration, 1990, 143(1): 65~74.
[15] Gardonio P, Elliot SJ, Pinnington RJ. Active isolation of structure vibration on a multiple-degree-of-freedom system. Part I: dynamics of the system. Journal of Sound and Vibration, 1997, 207(1): 61~93.
[16] Gardonio P, Elliot SJ, Pinnington RJ. Active isolation of structure vibration on a multiple-degree-of-freedom system. Part II: effectiveness of active control strategies. Journal of Sound and Vibration, 1997, 207(1): 95~121.
[17]顾仲权.振动控制评述.噪声与振动控制, 1988, 1: 5~13.
[18]施引.双层隔振及其初步计算方法.海工科技, 1987, 4: 1~23.
[19]朱石坚.双层隔振系统的运动响应的分析.海军工程学院学报, 1985, 3: 1~5.
[20]王孚懋,宋孔杰.小中间质量对复杂系统隔振效果的影响及最优设计.振动工程学报, 1991, 4(3): 10~17.
[21]王光,董邦宜.小中间质量双层隔振实验研究.噪声与振动控制, 1989, 4: 38~43.
[22] Sciulli D. Isolation design for a flexible system. Journal of Sound and Vibration, 1998, 216(2): 251~267.
[23] Sciulli D. Isolation design for a full flexible system. Journal of Intelligent Material Systems and Structures, 1999, 10: 813~824.
[24]宋孔杰.考虑基础弹性影响的实用隔振设计探讨.噪声与振动控制, 1988, 2: 3~7.
[25]熊冶平,宋孔杰.柔性隔振系统中驻波效应的研究.山东工业大学学报, 1995, 25(2): 108~113.
[26] Harison CM, Sykes AO, Martin M. Wave effects in isolation mounts. Journal of the Acoustical Society of America, 1952, 24: 62~70.
[27] Harris CM. Handbook of Noise Control. McGraw-Hill, 1957.
[28] Ungar EE, Dietrich CW. High-frequency vibration isolation. Journal of Sound and Vibration, 1966, 4(2): 224~241.
[29]董邦宜.船体固体声控制技术综述.噪声与振动控制, 1883, 2: 15~21.
[30]马永涛,周炎,张泉南,童宗鹏,尹立国.浮筏隔振系统的一种新隔振效果建模方法.振动与冲击, 2009, 7: 28~32.
[31]沈荣瀛.浮筏系统工程应用设计方法研究.中国国防科学技术报告, 2000.
[32] Niu Junchuan, Song Kongjie, Lim CW. On active vibration isolation of floating raft system. Journal of Sound and Vibration, 2005, 285(6): 391~406.
[33] Snowton JC. Mechanical four-pour parameters and their application. Journal of the Acoustical Society of America, 1971, 15(3): 307~323.
[34] Snowton JC. Reduction of the response to vibration of structures processing finite mechanical impedance. Journal of the Acoustical Society of America, 1961, 33(11): 1466~1475.
[35]霍睿.复杂隔振系统的功率流传递特性与控制策略研究.山东工业大学博士学位论文, 1998.
[36]孙玉国.柔性多维耦合系统功率流传递及控制研究.山东大学博士学位论文, 2001.
[37]张春红,汤炳新.主动隔振技术的回顾与展望.河海大学机电工程学院.河海大学常州分校学报. 2002, 16(2): 1~5.
[38]王永岩.动态子结构方法理论与应用.科学出版社, 1999.
[39]黄欢.柔性机械臂的模态综合建模及其动力学分析.浙江工业大学研究生学位论文, 2005.
[40]丁文镜.振动主动控制当前的主要研究课题.力学进展, 1994, 2(2): 173~180.
[41]马扣根,顾仲权.结构振动主动控制技术的现状与发展趋向.南京航空学院学报, 1991, 23(2): 97~108.
[42]潘继,陈龙祥,蔡国平.压电柔性板主动控制中作动器优化位置的粒子群方法.振动与冲击(已录用,待发表).
[43]章敏,蔡国平.柔性板的模态价值降阶及其主动控制研究.动力学与控制学报, 2008, 6(4): 348~352.
[44]伍先俊,朱石坚.振动反馈主动控制的功率流计算方法研究.船舶力学, 2009, 2: 298~304.
[45] Huang X, Elliot SJ, Brennan MJ. Active isolation of a flexible structure form base vibration. Journal of Sound and Vibration, 2004, 271: 323~337.
[46]董兴建.实验模态综合法若干问题的研究.上海交通大学博士后研究工作报告, 2008.
[47] Ha JY, Kim KJ. Analysis of mimo mechanical systems using the vectorial four pole parameter method. Journal of Sound and Vibration, 1995, 180(2): 333~350.
[48]严济宽,宋孔杰.四端参数法在振动隔离中的应用.噪声与振动控制, 1985, 6: 3~11.
[49]朱宏平,唐家祥.高层建筑结构的波传播及其振动功率流.华中理工大学学报, 1995, 3: 78~81.
[50] Song Kong-jie, Ji Lin, Huo Rui, Zhu Chuan-min. Power flow transmission of an asymmertrical flexible system excited by an off-center force. Chinese Journal of Mechanical Engineering, 1999, 12(3): 183~187.
[51] Xiong YP, Xing JT, Price WG. Power flow analysis of complex coupled systems by progressive approaches. Journal of Sound and Vibration, 2001, 239(2): 275~295.
[52] Xiong YP, Song KJ. Influence of flexible foundation on isolator wave effects. Shock and Vibration, 1996, 3(1): 61~67.
[53]毛映红,牛军川,宋孔杰.连续隔振浮筏系统功率流研究.声学学报. 2001, 26(3): 272~276.
[54]张雪冰,饶柱石,塔娜,邵宇鹰.变压器油箱振动功率流研究.振动与冲击, 2009, 5: 188~191.
[55]谢基榕,吴文伟,沈顺根.基于有限元的功率流分析方法及实现.船舶力学, 2009, 1: 144~149.
[56] Jungmin Seo, Seung-Jong Yi.采用汽车功率流一般算法设计任意功率流的汽车变速装置(II).传动技术, 2009, 2: 21~31.
[57] Jungmin Seo, Seung-Jong Yi.采用汽车功率流一般算法设计任意功率流的汽车变速装置.传动技术, 2009, 1: 29~38.
[58]赵群,张义民,赵晋芳.频域内振动路径的功率流传递度排序.航空动力学报, 2009, 5: 1177~1181.
[59] Mitchell LD, West RL, Wicks AL. An emergineg trend in experimental dynamics: merging of laser-based three-dimensional structural imaging and modal analysis. Journal of Sound and Vibration, 1998, 211(3): 323~333.
[60]王文亮,杜作润.结构振动与动态子结构方法.复旦大学出版社, 1985.
[61] Orefice G, Cacciolati C, Guyader JL. The energy mobility. Journal of Sound and Vibration. 2002, 254(2): 269~295.
[62] Langley RS. Analysis of power flow in beams and frame works using the direct-dynamic stiffness method. Journal of Sound and Vibration, 1990, 136(3): 439~452.
[63] Hussein MFM, Hunt HEM. A power flow method for evaluating vibration from underground railways. Journal of Sound and Vibration, 2006, 293(3–5): 667~679.
[64] Sutton, TJ, Elliott SJ, Brennan MJ, Heron KH, Jessop DAC. Active isolation of multiple structural waves on a helicopter gearbox support structures. Journal of Sound and Vibration, 1997, 205(7): 81~101.
[65] Gavies HG. Ensemble averages of power in randomly excited coupled beams. Journal of Sound and vibration, 1981, 77(3): 311~321.
[66] Mondot, Petersson. Characterization of structure-borne sound sources: the source descriptor and the coupling function. Journal of Sound and Vibration, 1987, 114(3): 507~518.
[67]明端森.结构声强技术测量墙体结构中弯曲波耦合功率流.应用声学, 1996, 15(1): 9~15.
[68] Langley RS. A wave intensity technique for the analysis of high frequency vibrations. Journal of Sound and Vibration, 1992, 159(3): 483~502.
[69]吴广明,沈荣瀛.舰船复杂隔振系统建模及其功率流研究.上海交通大学博士学位论文, 2004.
[70]沈荣瀛,卢峥. MTU柴油发电机组隔装置振动固有特性分析.噪声与振动控制, 1994, 3: 2~7.
[71]徐张明,沈荣瀛,华宏星.潜艇动力舱浮筏隔振参数对振动与声辐射的影响.船舶工程, 2002, 6: 22~26.
[72]张满满,骆冬平,骆子夜等.船用辅机浮筏动态特性有限元分析.噪声与振动控制. 2002, 22(4): 24~26.
[73]李良碧,王国治,温华兵.舰船浮筏隔振特性有限元分析及试验研究.华东船舶工业学院学报(自然科学板), 2001, 15(2): 72~76.
[74]左鹤声.机械阻抗方法与应用.机械工业出版社, 1987.
[75]牛军川,葛培琪,林志华,梁以德,宋孔杰, Lim CW, Leung AYT.评估内燃机隔振系统功率流传递的一种新模型(英文).内燃机学报, 2009, 1: 74~80.
[76]宋孔杰.大功率柴油机隔振实验台设计探讨及其实践.内燃机学报, 1987, 2(5): l80~186.
[77] Leissa A. Vibration of Plates. Acoustical Society of America, New York, USA, 1993.
[78] Xie Shilin. Analysis of vibration power flow from a vibrating machinery to a floating elastic panel. Mechanical Systems and Signal Processing, 2007, 21: 389~404.
[79]冯德振,宋孔杰,张洪安.浮筏弹性对复杂隔振系统振动传递的影响.山东建材学院学报,1997,11(3):219~224.
[80]张效慈,李国华,潘建强. Calculation of power flow transmission for a common floating raft shared by several ship machines.船舶力学(英文版), 2001, 5(3): 89~94.
[81] Levy R. Guyan reduction solutions recycled for improved accuracy. NASTRAN Users Experimences, NASA, Sept, 1971: 201~202.
[82] Ramsden JN, Stoker JR. Mass condensation– a semi-automatic method for reducing the size of vibration problems. International Journal for Numerical Methods in Engineering, 1969, 1(4): 333~349.
[83] Henshell RD, Ong JH. Automatic maters for eigenvalue economization. Earthquake Engineering and Structural Dynamics, 1975, 3(4): 375~383.
[84] Guyan RJ. Reduction of stiffness and mass matrices. AIAA Journal, 1965, 3(2): 380.
[85] Irons B. Structural eigenvalue problems: elimination of unwanted variables. AIAA Journal, 1965, 3(5): 961~962.
[86]瞿祖清.结构动力缩聚技术:理论与应用.上海交通大学博士学位论文, 1998.
[87] MSC/NASTRAN, Handbook for Dynamic Analysis. Las Angeles(CA): The MacNeal-Schwendler Corporation, 1983.
[88] ANSYS, Dynamics User Guider for Revision 5.0, 1993.
[89] Sauer G. Iterative improvement of eigensolution form reduced matrices. Communications in Applied Numerical Methods, 1989, 5: 329~335.
[90] Blair MA, Camino TS, Dickens JM. An iterative approach to a reduced mass matrix. In: Proceedings of the 9th Internatoinal Modal Analysis Conference, (Florence, Italy), Union College, Schenectady, NY, 1991, 621~626.
[91]张德文.结构动力分析中的逐级近似缩聚法.固体力学学报, 1992, 15(4): 360~364.
[92]张德文.改进Guyan~递推减缩技术.计算结构力学及其应用, 1996, 13(1): 90~94.
[93] Choi D, Kim H, Cho M. Iterative method for dynamic condensation combined with substructuring scheme. Journal of Sound and Vibration, 2008, 317: 199~218.
[94] Qu ZQ, Fu ZF. New structural dynamic condensation method for finite element models. AIAA Journal, 1998, 36(7): 1320~1324.
[95] Qu ZQ, Selvam RP. Efficient method for dynamic condensation of nonclassically damped vibration systems. AIAA Journal, 2002, 40(2): 368~375.
[96] Qu ZQ, Selvam RP. Dynamic superelement modeling method for compound dynamic systems. AIAA Journal, 2000, 38(6): 1078~1083.
[97] Shah VN, Raymond M. Analytial selection of masters for the reduced eigenvalue problem. International Journal for Numerical Methods in Engineering, 1982, 18(1): 89~98.
[98] Wu CJ, White RG. Vibrational power transmission in a finite multi-supported beam. Journal of Sound and Vibration, 1995, 181(1): 99~114.
[99] Wu CJ, White RG. Reduction of vibrational power in periodically supported beams by use of a neutralizer. Journal of Sound and Vibration, 1995, 187(2): 329~328.
[100] Bishop RED. The Mechanics of Vibrations. London: Cambridge University Press, 1960.
[101] Graff KF. Wave Motion in Elastic Solids. Oxford University Press, 1975.
[102] Cremer L, Heckel M, Ungar EE. Structure-Borne Sound (second edition). Berlin: Springer-Verlag, 1988.
[103] Junchuan Niu, Kongjie Songa, Limb CW. On active vibration isolation of floating raft system. Journal of Sound and Vibration, 2005, 285: 391~406.
[104] Choi WJ, Xiong YP, Shenoi RA. Power flow analysis for a floating sandwich raft isolation system using a higher-order theory. Journal of Sound and Vibration, 2009, 319: 228~246.
[2]牛军川.基于多模型柔性隔振系统的振动机理和主动控制研究.山东大学博士学位论文, 2003.
[3] Plunkett R. Interaction between a vibratory machine and its foundation. Noise Control, 1958, 4: 18~22.
[4]陈树勋.基础柔性对传递率的影响.振动与冲击, 1984, 1: 23~25.
[5]严济宽.隔振降噪技术的新进展.嗓声与振动控制, 1991, 5(6): 11~16.
[6] Goyder HGD, White RG. Vibration power flow from machine into built-up structures, Part I: Introduction and approximate analyses of beam and plate-like foundations. Journal of sound and vibration, 1980, 68(1): 59~75.
[7] Goyder HGD, White RG. Vibration power flow from machine into built-up structures, Part II: wave propagation and power flow in beam-stiffened plates. Journal of sound and vibration, 1980, 68(1): 77~96.
[8] Goyder HGD, White RG. Vibration power flow from machine into built-up structures, Part III: power flow through isolation systems. Journal of sound and vibration, 1980, 68(1): 97~117.
[9] Pan J, Pan JQ, Hansen CH. Total power flow from a vibrating rigid body to a flexible panel through multiple elastic mounts. Journal of the Acoustical Society of America, 1992, 92(2): 895~907.
[10] Petersson B, Plunt J. On effective mobility in the prediction of structure-borne sound transmission between a source structure and a receiving structure. Part I: theoretical back ground and basic experimental studies. Journal of Sound and Vibration, 1982, 82(4): 517~529.
[11] Petersson B, Plunt J. On effective mobility in the prediction of structure-borne sound transmission between a source structure and a receiving structure. Part II: procedure for the estimation of mobilities. Journal of Sound and Vibration, 1982, 82(4): 531~540.
[12] Pinnington RJ. Vibrational power flow transmission to a seating of a vibration isolated motor. Journal of Sound and Vibration, 1987, 118(3): 515~530.
[13] Pinnington RJ, White RG, Power flow through machine isolators to resonant and non-resonant beam. Journal of Sound and Vibration, 1981, 75: 179~197.
[14] Cuschieri JM. Vibration transmission through periodic structures using a mobility power flow approach. Journal of Sound and Vibration, 1990, 143(1): 65~74.
[15] Gardonio P, Elliot SJ, Pinnington RJ. Active isolation of structure vibration on a multiple-degree-of-freedom system. Part I: dynamics of the system. Journal of Sound and Vibration, 1997, 207(1): 61~93.
[16] Gardonio P, Elliot SJ, Pinnington RJ. Active isolation of structure vibration on a multiple-degree-of-freedom system. Part II: effectiveness of active control strategies. Journal of Sound and Vibration, 1997, 207(1): 95~121.
[17]顾仲权.振动控制评述.噪声与振动控制, 1988, 1: 5~13.
[18]施引.双层隔振及其初步计算方法.海工科技, 1987, 4: 1~23.
[19]朱石坚.双层隔振系统的运动响应的分析.海军工程学院学报, 1985, 3: 1~5.
[20]王孚懋,宋孔杰.小中间质量对复杂系统隔振效果的影响及最优设计.振动工程学报, 1991, 4(3): 10~17.
[21]王光,董邦宜.小中间质量双层隔振实验研究.噪声与振动控制, 1989, 4: 38~43.
[22] Sciulli D. Isolation design for a flexible system. Journal of Sound and Vibration, 1998, 216(2): 251~267.
[23] Sciulli D. Isolation design for a full flexible system. Journal of Intelligent Material Systems and Structures, 1999, 10: 813~824.
[24]宋孔杰.考虑基础弹性影响的实用隔振设计探讨.噪声与振动控制, 1988, 2: 3~7.
[25]熊冶平,宋孔杰.柔性隔振系统中驻波效应的研究.山东工业大学学报, 1995, 25(2): 108~113.
[26] Harison CM, Sykes AO, Martin M. Wave effects in isolation mounts. Journal of the Acoustical Society of America, 1952, 24: 62~70.
[27] Harris CM. Handbook of Noise Control. McGraw-Hill, 1957.
[28] Ungar EE, Dietrich CW. High-frequency vibration isolation. Journal of Sound and Vibration, 1966, 4(2): 224~241.
[29]董邦宜.船体固体声控制技术综述.噪声与振动控制, 1883, 2: 15~21.
[30]马永涛,周炎,张泉南,童宗鹏,尹立国.浮筏隔振系统的一种新隔振效果建模方法.振动与冲击, 2009, 7: 28~32.
[31]沈荣瀛.浮筏系统工程应用设计方法研究.中国国防科学技术报告, 2000.
[32] Niu Junchuan, Song Kongjie, Lim CW. On active vibration isolation of floating raft system. Journal of Sound and Vibration, 2005, 285(6): 391~406.
[33] Snowton JC. Mechanical four-pour parameters and their application. Journal of the Acoustical Society of America, 1971, 15(3): 307~323.
[34] Snowton JC. Reduction of the response to vibration of structures processing finite mechanical impedance. Journal of the Acoustical Society of America, 1961, 33(11): 1466~1475.
[35]霍睿.复杂隔振系统的功率流传递特性与控制策略研究.山东工业大学博士学位论文, 1998.
[36]孙玉国.柔性多维耦合系统功率流传递及控制研究.山东大学博士学位论文, 2001.
[37]张春红,汤炳新.主动隔振技术的回顾与展望.河海大学机电工程学院.河海大学常州分校学报. 2002, 16(2): 1~5.
[38]王永岩.动态子结构方法理论与应用.科学出版社, 1999.
[39]黄欢.柔性机械臂的模态综合建模及其动力学分析.浙江工业大学研究生学位论文, 2005.
[40]丁文镜.振动主动控制当前的主要研究课题.力学进展, 1994, 2(2): 173~180.
[41]马扣根,顾仲权.结构振动主动控制技术的现状与发展趋向.南京航空学院学报, 1991, 23(2): 97~108.
[42]潘继,陈龙祥,蔡国平.压电柔性板主动控制中作动器优化位置的粒子群方法.振动与冲击(已录用,待发表).
[43]章敏,蔡国平.柔性板的模态价值降阶及其主动控制研究.动力学与控制学报, 2008, 6(4): 348~352.
[44]伍先俊,朱石坚.振动反馈主动控制的功率流计算方法研究.船舶力学, 2009, 2: 298~304.
[45] Huang X, Elliot SJ, Brennan MJ. Active isolation of a flexible structure form base vibration. Journal of Sound and Vibration, 2004, 271: 323~337.
[46]董兴建.实验模态综合法若干问题的研究.上海交通大学博士后研究工作报告, 2008.
[47] Ha JY, Kim KJ. Analysis of mimo mechanical systems using the vectorial four pole parameter method. Journal of Sound and Vibration, 1995, 180(2): 333~350.
[48]严济宽,宋孔杰.四端参数法在振动隔离中的应用.噪声与振动控制, 1985, 6: 3~11.
[49]朱宏平,唐家祥.高层建筑结构的波传播及其振动功率流.华中理工大学学报, 1995, 3: 78~81.
[50] Song Kong-jie, Ji Lin, Huo Rui, Zhu Chuan-min. Power flow transmission of an asymmertrical flexible system excited by an off-center force. Chinese Journal of Mechanical Engineering, 1999, 12(3): 183~187.
[51] Xiong YP, Xing JT, Price WG. Power flow analysis of complex coupled systems by progressive approaches. Journal of Sound and Vibration, 2001, 239(2): 275~295.
[52] Xiong YP, Song KJ. Influence of flexible foundation on isolator wave effects. Shock and Vibration, 1996, 3(1): 61~67.
[53]毛映红,牛军川,宋孔杰.连续隔振浮筏系统功率流研究.声学学报. 2001, 26(3): 272~276.
[54]张雪冰,饶柱石,塔娜,邵宇鹰.变压器油箱振动功率流研究.振动与冲击, 2009, 5: 188~191.
[55]谢基榕,吴文伟,沈顺根.基于有限元的功率流分析方法及实现.船舶力学, 2009, 1: 144~149.
[56] Jungmin Seo, Seung-Jong Yi.采用汽车功率流一般算法设计任意功率流的汽车变速装置(II).传动技术, 2009, 2: 21~31.
[57] Jungmin Seo, Seung-Jong Yi.采用汽车功率流一般算法设计任意功率流的汽车变速装置.传动技术, 2009, 1: 29~38.
[58]赵群,张义民,赵晋芳.频域内振动路径的功率流传递度排序.航空动力学报, 2009, 5: 1177~1181.
[59] Mitchell LD, West RL, Wicks AL. An emergineg trend in experimental dynamics: merging of laser-based three-dimensional structural imaging and modal analysis. Journal of Sound and Vibration, 1998, 211(3): 323~333.
[60]王文亮,杜作润.结构振动与动态子结构方法.复旦大学出版社, 1985.
[61] Orefice G, Cacciolati C, Guyader JL. The energy mobility. Journal of Sound and Vibration. 2002, 254(2): 269~295.
[62] Langley RS. Analysis of power flow in beams and frame works using the direct-dynamic stiffness method. Journal of Sound and Vibration, 1990, 136(3): 439~452.
[63] Hussein MFM, Hunt HEM. A power flow method for evaluating vibration from underground railways. Journal of Sound and Vibration, 2006, 293(3–5): 667~679.
[64] Sutton, TJ, Elliott SJ, Brennan MJ, Heron KH, Jessop DAC. Active isolation of multiple structural waves on a helicopter gearbox support structures. Journal of Sound and Vibration, 1997, 205(7): 81~101.
[65] Gavies HG. Ensemble averages of power in randomly excited coupled beams. Journal of Sound and vibration, 1981, 77(3): 311~321.
[66] Mondot, Petersson. Characterization of structure-borne sound sources: the source descriptor and the coupling function. Journal of Sound and Vibration, 1987, 114(3): 507~518.
[67]明端森.结构声强技术测量墙体结构中弯曲波耦合功率流.应用声学, 1996, 15(1): 9~15.
[68] Langley RS. A wave intensity technique for the analysis of high frequency vibrations. Journal of Sound and Vibration, 1992, 159(3): 483~502.
[69]吴广明,沈荣瀛.舰船复杂隔振系统建模及其功率流研究.上海交通大学博士学位论文, 2004.
[70]沈荣瀛,卢峥. MTU柴油发电机组隔装置振动固有特性分析.噪声与振动控制, 1994, 3: 2~7.
[71]徐张明,沈荣瀛,华宏星.潜艇动力舱浮筏隔振参数对振动与声辐射的影响.船舶工程, 2002, 6: 22~26.
[72]张满满,骆冬平,骆子夜等.船用辅机浮筏动态特性有限元分析.噪声与振动控制. 2002, 22(4): 24~26.
[73]李良碧,王国治,温华兵.舰船浮筏隔振特性有限元分析及试验研究.华东船舶工业学院学报(自然科学板), 2001, 15(2): 72~76.
[74]左鹤声.机械阻抗方法与应用.机械工业出版社, 1987.
[75]牛军川,葛培琪,林志华,梁以德,宋孔杰, Lim CW, Leung AYT.评估内燃机隔振系统功率流传递的一种新模型(英文).内燃机学报, 2009, 1: 74~80.
[76]宋孔杰.大功率柴油机隔振实验台设计探讨及其实践.内燃机学报, 1987, 2(5): l80~186.
[77] Leissa A. Vibration of Plates. Acoustical Society of America, New York, USA, 1993.
[78] Xie Shilin. Analysis of vibration power flow from a vibrating machinery to a floating elastic panel. Mechanical Systems and Signal Processing, 2007, 21: 389~404.
[79]冯德振,宋孔杰,张洪安.浮筏弹性对复杂隔振系统振动传递的影响.山东建材学院学报,1997,11(3):219~224.
[80]张效慈,李国华,潘建强. Calculation of power flow transmission for a common floating raft shared by several ship machines.船舶力学(英文版), 2001, 5(3): 89~94.
[81] Levy R. Guyan reduction solutions recycled for improved accuracy. NASTRAN Users Experimences, NASA, Sept, 1971: 201~202.
[82] Ramsden JN, Stoker JR. Mass condensation– a semi-automatic method for reducing the size of vibration problems. International Journal for Numerical Methods in Engineering, 1969, 1(4): 333~349.
[83] Henshell RD, Ong JH. Automatic maters for eigenvalue economization. Earthquake Engineering and Structural Dynamics, 1975, 3(4): 375~383.
[84] Guyan RJ. Reduction of stiffness and mass matrices. AIAA Journal, 1965, 3(2): 380.
[85] Irons B. Structural eigenvalue problems: elimination of unwanted variables. AIAA Journal, 1965, 3(5): 961~962.
[86]瞿祖清.结构动力缩聚技术:理论与应用.上海交通大学博士学位论文, 1998.
[87] MSC/NASTRAN, Handbook for Dynamic Analysis. Las Angeles(CA): The MacNeal-Schwendler Corporation, 1983.
[88] ANSYS, Dynamics User Guider for Revision 5.0, 1993.
[89] Sauer G. Iterative improvement of eigensolution form reduced matrices. Communications in Applied Numerical Methods, 1989, 5: 329~335.
[90] Blair MA, Camino TS, Dickens JM. An iterative approach to a reduced mass matrix. In: Proceedings of the 9th Internatoinal Modal Analysis Conference, (Florence, Italy), Union College, Schenectady, NY, 1991, 621~626.
[91]张德文.结构动力分析中的逐级近似缩聚法.固体力学学报, 1992, 15(4): 360~364.
[92]张德文.改进Guyan~递推减缩技术.计算结构力学及其应用, 1996, 13(1): 90~94.
[93] Choi D, Kim H, Cho M. Iterative method for dynamic condensation combined with substructuring scheme. Journal of Sound and Vibration, 2008, 317: 199~218.
[94] Qu ZQ, Fu ZF. New structural dynamic condensation method for finite element models. AIAA Journal, 1998, 36(7): 1320~1324.
[95] Qu ZQ, Selvam RP. Efficient method for dynamic condensation of nonclassically damped vibration systems. AIAA Journal, 2002, 40(2): 368~375.
[96] Qu ZQ, Selvam RP. Dynamic superelement modeling method for compound dynamic systems. AIAA Journal, 2000, 38(6): 1078~1083.
[97] Shah VN, Raymond M. Analytial selection of masters for the reduced eigenvalue problem. International Journal for Numerical Methods in Engineering, 1982, 18(1): 89~98.
[98] Wu CJ, White RG. Vibrational power transmission in a finite multi-supported beam. Journal of Sound and Vibration, 1995, 181(1): 99~114.
[99] Wu CJ, White RG. Reduction of vibrational power in periodically supported beams by use of a neutralizer. Journal of Sound and Vibration, 1995, 187(2): 329~328.
[100] Bishop RED. The Mechanics of Vibrations. London: Cambridge University Press, 1960.
[101] Graff KF. Wave Motion in Elastic Solids. Oxford University Press, 1975.
[102] Cremer L, Heckel M, Ungar EE. Structure-Borne Sound (second edition). Berlin: Springer-Verlag, 1988.
[103] Junchuan Niu, Kongjie Songa, Limb CW. On active vibration isolation of floating raft system. Journal of Sound and Vibration, 2005, 285: 391~406.
[104] Choi WJ, Xiong YP, Shenoi RA. Power flow analysis for a floating sandwich raft isolation system using a higher-order theory. Journal of Sound and Vibration, 2009, 319: 228~246.
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