随机激励时多介质耦合型减振器求解的一种近似方法
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摘要
有关文献结合流体、橡胶、非线性弹性元件设计了一种多介质耦合减振器,获得较好的工作特性;在此基础上基于衰减随机振动的工程应用要求,提出了一种多介质耦合型非线性减振器的数学模型,该模型考虑了平方阻尼、线性阻尼、库伦阻尼及非线性弹性元件的耦合,在外部激励为随机振动激励时,通过FPK变换并结合等效原理对模型进行了理论上近似求解,具体讨论了非线性特性参数变化引起的系统特性变化,为进一步研究奠定了基础。
A new type of isolator with multi-types of damping and nonlinear stiffness through oil,air,rubber and spring coupling by ingenious tactics is presented in references.In this paper,a mathematical model of a multi-medium coupling isolator is developed for attenuating wide-band random vibration for practical applications.The model considers the coupling of quadratic damping,viscosity damping,coulomb damping and nonlinear spring.The approximate theoretical calculating formulae are deduced by combining FPK transform and equivalent principle method.By conducting parametric analysis,it is shown that changes in the nonlinear characteristic parameters would induce changes in the system characteristics.The solution establishes a theoretical basis for further research.
A new type of isolator with multi-types of damping and nonlinear stiffness through oil,air,rubber and spring coupling by ingenious tactics is presented in references.In this paper,a mathematical model of a multi-medium coupling isolator is developed for attenuating wide-band random vibration for practical applications.The model considers the coupling of quadratic damping,viscosity damping,coulomb damping and nonlinear spring.The approximate theoretical calculating formulae are deduced by combining FPK transform and equivalent principle method.By conducting parametric analysis,it is shown that changes in the nonlinear characteristic parameters would induce changes in the system characteristics.The solution establishes a theoretical basis for further research.
引文
[1]朱位秋.随机振动[M].北京:科学出版社,1998.Zhu Weiqiu.Random vibration[M].Beijing:Science Press,1998.(in Chinese)
[2]庄表中,陈乃立.随机振动的理论及应用[M].北京:地震出版社,1985.Zhuang Biaozhong,Chen Naili.The application and theory of random vibration[M].Beijing:Earthquake Press,1985.(in Chinese)
[3]Harris C M,Crede C E.Shock and vibration handbook[M].MC-Graw-Hill,1990.
[4]Chandra N,Shekhar,Hatwal H.Response of non-linear dissipative shock isolators[J].J.of Sound and Vibration,1998,214(4):589～603.
[5]Dunne J F.Extreme-value prediction for non-linear stochastic oscillators via numerical solutions of the stationary FPK equation[J].Journal of Sound and Vibration,1997,206(5):697～724.
[6]Liu X B,Liew K M.The Lyapunov exponent for a codimension two bifurcation system that is driven by a real noise[J].International Journal of Non-Linear Mechanics,2003,38(10);1495～1511.
[7]Ni Y Q,Ying Z G,Ko J M,Zhu W Q.Random response of integrable Duhem hysteretic systems under non-white excitation[J].International Journal of Non-Linear Mechanics,2002,37(8):1407～1419.
[8]Ulyanov S V,Feng M.Stochastic analysis of time-variant nonlinear dynamic systems.Part1:The Fokker-Planck-Kolmogorov equation approach in stochastic mechanics[J].Probabilistic Engineering Mechanics,1998,13(3):183～203.
[9]Er Guo-Kang.Exponential closure method for some randomly excited non-linear systems[J].International Journal of Non-Linear Mechanics,2000,35(1):69～78.
[10]Banik A K,Datta T K.Stochastic response and stability analysis of single leg articulated tower[C].Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering-OMAE,2003,2:21～28.
[11]Wang Rubin,Yasuda,Kimihiko.Generalized analysis technique of the stationary FPK equation in nonlinear systems under Gaussian white noise excitations[J].International Journal of Engineering Science,2000,38(12):1315～1330.
[12]Yang Ping.Experimental and mathematical evaluation for dynamic behavior of an oil-air coupling shock absorber[J].Mechanical Systems and Signal Processing,2003,17(6):1367～1379.
[13]Yang Ping,Zhong Yifang,Zhou Ji.CAD/CAE of the working characteristics of a new type of fluid coupling shock absorber[J].Chinese Journal of Mechanical Engineering,2002,15(3):222～227.
[2]庄表中,陈乃立.随机振动的理论及应用[M].北京:地震出版社,1985.Zhuang Biaozhong,Chen Naili.The application and theory of random vibration[M].Beijing:Earthquake Press,1985.(in Chinese)
[3]Harris C M,Crede C E.Shock and vibration handbook[M].MC-Graw-Hill,1990.
[4]Chandra N,Shekhar,Hatwal H.Response of non-linear dissipative shock isolators[J].J.of Sound and Vibration,1998,214(4):589～603.
[5]Dunne J F.Extreme-value prediction for non-linear stochastic oscillators via numerical solutions of the stationary FPK equation[J].Journal of Sound and Vibration,1997,206(5):697～724.
[6]Liu X B,Liew K M.The Lyapunov exponent for a codimension two bifurcation system that is driven by a real noise[J].International Journal of Non-Linear Mechanics,2003,38(10);1495～1511.
[7]Ni Y Q,Ying Z G,Ko J M,Zhu W Q.Random response of integrable Duhem hysteretic systems under non-white excitation[J].International Journal of Non-Linear Mechanics,2002,37(8):1407～1419.
[8]Ulyanov S V,Feng M.Stochastic analysis of time-variant nonlinear dynamic systems.Part1:The Fokker-Planck-Kolmogorov equation approach in stochastic mechanics[J].Probabilistic Engineering Mechanics,1998,13(3):183～203.
[9]Er Guo-Kang.Exponential closure method for some randomly excited non-linear systems[J].International Journal of Non-Linear Mechanics,2000,35(1):69～78.
[10]Banik A K,Datta T K.Stochastic response and stability analysis of single leg articulated tower[C].Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering-OMAE,2003,2:21～28.
[11]Wang Rubin,Yasuda,Kimihiko.Generalized analysis technique of the stationary FPK equation in nonlinear systems under Gaussian white noise excitations[J].International Journal of Engineering Science,2000,38(12):1315～1330.
[12]Yang Ping.Experimental and mathematical evaluation for dynamic behavior of an oil-air coupling shock absorber[J].Mechanical Systems and Signal Processing,2003,17(6):1367～1379.
[13]Yang Ping,Zhong Yifang,Zhou Ji.CAD/CAE of the working characteristics of a new type of fluid coupling shock absorber[J].Chinese Journal of Mechanical Engineering,2002,15(3):222～227.
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