几何非线性摩擦阻尼隔振系统动力学行为研究
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摘要
非线性隔振系统由于具有较线性系统更优的隔振性能,因此在工程中应用广泛.本文通过配置与被隔振对象的运动方向相垂直的库伦摩擦阻尼器,构建了几何非线性摩擦阻尼模型.由于引入了几何非线性,因此其摩擦力与位移正相关,这与传统与位移无关摩擦力模型有显著不同.首先,建立了具有几何非线性摩擦阻尼的数学模型以及隔振系统的受迫振动方程;然后,使用谐波平衡法求解了动力学方程,并使用数值仿真方法验证了谐波平衡法求解的准确性;最后,研究了几何非线性摩擦阻尼隔振器的绝对位移传递率和相对位移传递率.研究结果表明,在库伦摩擦阻尼选择适当,非线性摩擦阻尼系统可以在保持高频振动衰减效果的前提下,显著降低系统共振峰,其性能优于传统的恒定摩擦阻尼隔振模型.同时,几何非线性摩擦阻尼系统能够避免传统摩擦阻尼系统中的"锁定"现象,从传递率角度来说,不利于共振峰控制;但从激励环境改变引发隔振系统失效的角度来看,几何非线性摩擦阻尼系统可以拓宽系统对激励幅值的适应范围,避免隔振系统失效.本文的研究结果对此类隔振系统的设计和摩擦阻尼参数的选择具有通用的指导意义.
In vibration isolation field, nonlinear vibration isolation system catch more attention than linear system because of the better vibration isolation performance. In this paper, a novel nonlinear vibration isolation system with geometric nonlinear friction damping is proposed by add two friction damper that perpendicular to the movement direction of the isolated object. The absolute and relative displacement transmissibility of such kind of vibration isolation system are studied in this paper. Different from the friction damper which usually assuming that the friction force is constant, the friction force studied in this paper is proportional to the displacement of the isolated mass by configuring two linear friction dampers perpendicular to the moving direction of the mass. The mathematical model of the friction damping and the forced vibration of the system are established. The dynamic equation is solved by using Harmonic Balance Method(HBM) subsequently by making some simplification. The result solved by HBM is verified numerically. The performance of the nonlinear vibration isolation system is compared with that of a linear one by the performance index defined by absolute and relative transmissibility. The geometric nonlinear friction can offer small or large friction damping depends on the relative displacement, therefore, the nonlinear friction force can improve the transmissibility for both absolute and relative displacement at resonance and the higher frequencies region if the damping values are chosen carefully which surpass a traditional Kevin vibration isolator model. Meanwhile, the nonlinear vibration isolation system can enlarge the application region for different excitation amplitude and avoid the system failure though the responses of the isolated mass is amplified at low frequency. The vibration isolation system with the configuration of the friction damper proposed is very suitable for both resonance and higher frequencies vibration control. The conclusions given are of importance when design and choosing the friction damping parameters.
In vibration isolation field, nonlinear vibration isolation system catch more attention than linear system because of the better vibration isolation performance. In this paper, a novel nonlinear vibration isolation system with geometric nonlinear friction damping is proposed by add two friction damper that perpendicular to the movement direction of the isolated object. The absolute and relative displacement transmissibility of such kind of vibration isolation system are studied in this paper. Different from the friction damper which usually assuming that the friction force is constant, the friction force studied in this paper is proportional to the displacement of the isolated mass by configuring two linear friction dampers perpendicular to the moving direction of the mass. The mathematical model of the friction damping and the forced vibration of the system are established. The dynamic equation is solved by using Harmonic Balance Method(HBM) subsequently by making some simplification. The result solved by HBM is verified numerically. The performance of the nonlinear vibration isolation system is compared with that of a linear one by the performance index defined by absolute and relative transmissibility. The geometric nonlinear friction can offer small or large friction damping depends on the relative displacement, therefore, the nonlinear friction force can improve the transmissibility for both absolute and relative displacement at resonance and the higher frequencies region if the damping values are chosen carefully which surpass a traditional Kevin vibration isolator model. Meanwhile, the nonlinear vibration isolation system can enlarge the application region for different excitation amplitude and avoid the system failure though the responses of the isolated mass is amplified at low frequency. The vibration isolation system with the configuration of the friction damper proposed is very suitable for both resonance and higher frequencies vibration control. The conclusions given are of importance when design and choosing the friction damping parameters.
引文
1 Harris C,Piersol A.Shock and Vibration Handbook.New York:McGraw-Hill,2002
2 Rivin E.Passive Vibration Isolation.New York:ASME Press,2003
3 Ibrahim R.Recent advances in nonlinear passive vibration isolators.Journal of Sound and Vibration,2008,314(3-5):371-452
4曹登庆,白坤朝,丁虎等.大型柔性航天器动力学与振动控制研究进展.力学学报,2019,51(1):1-13(Cao Dengqing,Bai Kunchao,Ding Hu,et al.Advances in dynamics and vibration control of large scale flexible spacecraft.Chinese Journal of Theoretical and Applied Mechanics,2019,51(1):1-13(in Chinese))
5 Carrella A,Brennan M,Waters T.Static analysis of a passive vibration isolator with quasi-zero stiffness characteristic.Journal of Sound and Vibration,2007,301(3-5):678-689
6 Kovacic I,Brennan M,Waters T.A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic.Journal of Sound and Vibration,2008,315(3):700-711
7 Mizuno T,Toumiya T,Takasaki M,Vibration isolation system using negative stiffness.Japan Society of Mechanical Engineers International Journal Series C,2003,46(3):807-812
8 Zhou N,Liu K.A tunable high-static-low-dynamic stiffness vibration isolator.Journal of Sound and Vibration,2010,329(9):1254-1273
9 Carrella A,Brennan M,Waters TP,et al.On the design of a highstatic-low-dynamic stiffness isolator using linear mechanical springs and magnets.Journal of Sound and Vibration,2008,315(3):712-720
10 Zhu T,Benjamin C,Robertson W,et al.Vibration isolation using six degree-of-freedom quasi-zero stiffness magnetic levitation.Journal of Sound and Vibration,2015,358:48-73
11 Le T,Kyoung K.Active pneumatic vibration isolation system using negative stiffness structures for a vehicle seat.Journal of Sound and Vibration,2014,333(5):1245-1268
12 Sun X,Jing X.A nonlinear vibration isolator achieving high-staticlow-dynamic stiffness and tunable anti-resonance frequency band.Mechanical Systems and Signal Processing,2016,80:166-188
13 Sun X,Jing X.Multi-direction vibration isolation with quasi-zero stiffness by employing geometrical nonlinearity.Mechanical Systems and Signal Processing,2015,62-63:149-163
14 Araki Y,Asai T,Masui T.Vertical vibration isolator having piecewise-constant restoring force.Earthquake Engineering and Structural Dynamics,2019,38(13):1505-1523
15高雪,陈前,刘先斌.一类分段光滑隔振系统的非线性动力学设计方法.力学学报,2016,48(1):192-200(Gao Xue,Chen Qian,Liu Xianbin.Nonlinear dynamics design for piecewise smooth vibration isolation system.Chinese Journal of Theoretical and Applied Mechanics,2016,48(1):192-200(in Chinese))
16陆泽琦,陈立群.非线性被动隔振的若干进展.力学学报,2017,49(3):550-564(Lu Zeqi,Chen Liqun.Some recent progresses in nonlinear passive isolations of vibrations.Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):550-564(in Chinese))
17 Lu Z,Yang T,Brennan M,et al.Experimental investigation of a two-stage nonlinear vibration isolation system with high-staticlow-dynamic stiffness.ASME Journal of Applied Mechanics,2017,84(2):021001
18 Ruzicka J,Derby T.Influence of damping in vibration isolation.Washington,DC:Shock and Vibration Information Center(Defense),1971
19 Ravindra B,Mallik A.Performance of non-linear vibration isolators under harmonic excitation.Journal of Sound and Vibration,1994,170(3):325-337
20 Ravindra B,Mallik A.Hard Duffing-type vibration isolator with combined coulomb and viscous damping.International Journal of Non-linear Mechanics,1993,28(4):427-440
21 Thaijaroen W,Harrison A.Nonlinear dynamic modelling of rubber isolators using six parameters based on parabolic spring,springpot,and smooth-slip friction element.Polymer Testing,2010,29(7):857-865
22 Yang P,Yang J,Ding J.Dynamic transmissibility of a complex nonlinear coupling isolator.Tsinghua Science and Technology,2006,11(5):538-542
23 Peng ZK,Lang ZQ,Jing XJ,et al.The transmissibility of vibration isolators with a nonlinear antisymmetric damping characteristic.Journal of Vibration and Acoustics,2010,132(1):014501
24彭志科,郎自强,孟光等.一类非线性隔振器振动传递特性分析.动力学与控制学报,2011,9(4):314-320(Peng Zhike,Lang Ziqiang,Meng Guang,et al.Analysis on transmissibility for a class of nonlinear vibration isolators.Journal of Dynamics and Control,2011,9(4):314-320(in Chinese))
25 Peng ZK,Meng G,Lang ZQ,et al.Study of the effects of cubic nonlinear damping on vibration isolations using Harmonic Balance Method.International Journal of Non-Linear Mechanics,2012,47(10):1073-1080
26 Kovacic I,Milovanovic Z,Brennan M.On the relative and absolute transmissibility of a vibration isolation system subjected to base excitation//XXI Conference with International Participation,Noise and Vibration,Serbia,Tara,2008
27 L′opez I,Busturia J,Nijmeijer H.Energy dissipation of a friction damper.Journal of Sound and Vibration,2003,278(3):539-561
28 Berger E.Friction modeling for dynamic system simulation.Applied Mechanics Review,2002,55(6):535-577
29 Stein G,Zahoransky R,Mucka P.On dry friction modelling and simulation in kinematically excited oscillatory systems.Journal of Sound and Vibration,2008,311(1-2):74-96
30 Zhao D,Zhang W,Ma R et al.Research on a new damper and its application in vibration control of a building.Industrial Construction,2006,36(2):1-5
31 Tadjbakhsh I,Lin B.Displacement-proportional friction(DPF)in base isolation.Earthquake Engineering and Structural Dynamics,1987,15(7):799-813
32 Ferri A.Friction Damping and Isolation Systems.Journal of Vibration and Acoustics,1995,117(B):196-206
33 Ferri A,Whiteman W.Free response of a system with negative viscous damping and displacement-dependent dry friction damping.Journal of Sound and Vibration,2007,306(3-5):400-418
34 Whiteman W,Ferri A.Displacement-dependent dry friction damping of a beam-like structure.Journal of Sound and Vibration,1996,198(3):313-329
35 Tang B,Brennan M.A comparison of two nonlinear damping mechanisms in a vibration isolator.Journal of Sound and Vibration,2013,332(3):510-520
2 Rivin E.Passive Vibration Isolation.New York:ASME Press,2003
3 Ibrahim R.Recent advances in nonlinear passive vibration isolators.Journal of Sound and Vibration,2008,314(3-5):371-452
4曹登庆,白坤朝,丁虎等.大型柔性航天器动力学与振动控制研究进展.力学学报,2019,51(1):1-13(Cao Dengqing,Bai Kunchao,Ding Hu,et al.Advances in dynamics and vibration control of large scale flexible spacecraft.Chinese Journal of Theoretical and Applied Mechanics,2019,51(1):1-13(in Chinese))
5 Carrella A,Brennan M,Waters T.Static analysis of a passive vibration isolator with quasi-zero stiffness characteristic.Journal of Sound and Vibration,2007,301(3-5):678-689
6 Kovacic I,Brennan M,Waters T.A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic.Journal of Sound and Vibration,2008,315(3):700-711
7 Mizuno T,Toumiya T,Takasaki M,Vibration isolation system using negative stiffness.Japan Society of Mechanical Engineers International Journal Series C,2003,46(3):807-812
8 Zhou N,Liu K.A tunable high-static-low-dynamic stiffness vibration isolator.Journal of Sound and Vibration,2010,329(9):1254-1273
9 Carrella A,Brennan M,Waters TP,et al.On the design of a highstatic-low-dynamic stiffness isolator using linear mechanical springs and magnets.Journal of Sound and Vibration,2008,315(3):712-720
10 Zhu T,Benjamin C,Robertson W,et al.Vibration isolation using six degree-of-freedom quasi-zero stiffness magnetic levitation.Journal of Sound and Vibration,2015,358:48-73
11 Le T,Kyoung K.Active pneumatic vibration isolation system using negative stiffness structures for a vehicle seat.Journal of Sound and Vibration,2014,333(5):1245-1268
12 Sun X,Jing X.A nonlinear vibration isolator achieving high-staticlow-dynamic stiffness and tunable anti-resonance frequency band.Mechanical Systems and Signal Processing,2016,80:166-188
13 Sun X,Jing X.Multi-direction vibration isolation with quasi-zero stiffness by employing geometrical nonlinearity.Mechanical Systems and Signal Processing,2015,62-63:149-163
14 Araki Y,Asai T,Masui T.Vertical vibration isolator having piecewise-constant restoring force.Earthquake Engineering and Structural Dynamics,2019,38(13):1505-1523
15高雪,陈前,刘先斌.一类分段光滑隔振系统的非线性动力学设计方法.力学学报,2016,48(1):192-200(Gao Xue,Chen Qian,Liu Xianbin.Nonlinear dynamics design for piecewise smooth vibration isolation system.Chinese Journal of Theoretical and Applied Mechanics,2016,48(1):192-200(in Chinese))
16陆泽琦,陈立群.非线性被动隔振的若干进展.力学学报,2017,49(3):550-564(Lu Zeqi,Chen Liqun.Some recent progresses in nonlinear passive isolations of vibrations.Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):550-564(in Chinese))
17 Lu Z,Yang T,Brennan M,et al.Experimental investigation of a two-stage nonlinear vibration isolation system with high-staticlow-dynamic stiffness.ASME Journal of Applied Mechanics,2017,84(2):021001
18 Ruzicka J,Derby T.Influence of damping in vibration isolation.Washington,DC:Shock and Vibration Information Center(Defense),1971
19 Ravindra B,Mallik A.Performance of non-linear vibration isolators under harmonic excitation.Journal of Sound and Vibration,1994,170(3):325-337
20 Ravindra B,Mallik A.Hard Duffing-type vibration isolator with combined coulomb and viscous damping.International Journal of Non-linear Mechanics,1993,28(4):427-440
21 Thaijaroen W,Harrison A.Nonlinear dynamic modelling of rubber isolators using six parameters based on parabolic spring,springpot,and smooth-slip friction element.Polymer Testing,2010,29(7):857-865
22 Yang P,Yang J,Ding J.Dynamic transmissibility of a complex nonlinear coupling isolator.Tsinghua Science and Technology,2006,11(5):538-542
23 Peng ZK,Lang ZQ,Jing XJ,et al.The transmissibility of vibration isolators with a nonlinear antisymmetric damping characteristic.Journal of Vibration and Acoustics,2010,132(1):014501
24彭志科,郎自强,孟光等.一类非线性隔振器振动传递特性分析.动力学与控制学报,2011,9(4):314-320(Peng Zhike,Lang Ziqiang,Meng Guang,et al.Analysis on transmissibility for a class of nonlinear vibration isolators.Journal of Dynamics and Control,2011,9(4):314-320(in Chinese))
25 Peng ZK,Meng G,Lang ZQ,et al.Study of the effects of cubic nonlinear damping on vibration isolations using Harmonic Balance Method.International Journal of Non-Linear Mechanics,2012,47(10):1073-1080
26 Kovacic I,Milovanovic Z,Brennan M.On the relative and absolute transmissibility of a vibration isolation system subjected to base excitation//XXI Conference with International Participation,Noise and Vibration,Serbia,Tara,2008
27 L′opez I,Busturia J,Nijmeijer H.Energy dissipation of a friction damper.Journal of Sound and Vibration,2003,278(3):539-561
28 Berger E.Friction modeling for dynamic system simulation.Applied Mechanics Review,2002,55(6):535-577
29 Stein G,Zahoransky R,Mucka P.On dry friction modelling and simulation in kinematically excited oscillatory systems.Journal of Sound and Vibration,2008,311(1-2):74-96
30 Zhao D,Zhang W,Ma R et al.Research on a new damper and its application in vibration control of a building.Industrial Construction,2006,36(2):1-5
31 Tadjbakhsh I,Lin B.Displacement-proportional friction(DPF)in base isolation.Earthquake Engineering and Structural Dynamics,1987,15(7):799-813
32 Ferri A.Friction Damping and Isolation Systems.Journal of Vibration and Acoustics,1995,117(B):196-206
33 Ferri A,Whiteman W.Free response of a system with negative viscous damping and displacement-dependent dry friction damping.Journal of Sound and Vibration,2007,306(3-5):400-418
34 Whiteman W,Ferri A.Displacement-dependent dry friction damping of a beam-like structure.Journal of Sound and Vibration,1996,198(3):313-329
35 Tang B,Brennan M.A comparison of two nonlinear damping mechanisms in a vibration isolator.Journal of Sound and Vibration,2013,332(3):510-520