基于增维精细积分法非线性能量陷减振系统分析
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摘要
通过线性减振弹簧构建具有非线性能量陷的Duffing振子,提出一种切实可行的非线性能量陷减振系统构建方法,利用增维精细积分法求解非线性能量陷减振系统,得到较高精度解。确定给定条件下,2自由度非线性能量陷减振系统和3自由度非线性能量陷减振系统的减振角频率范围,对非线性能量陷减振系统施加外部连续随机激励仿真,进一步确定所构建的非线性能量陷Duffing振子的可行性,为非线性能量陷减振方面的研究提供研究方向和理论基础。
The Duffing oscillator with a nonlinear energy sink is constructed by linear damping springs. A feasible method for constructing the damping system with the nonlinear energy sink is put forward. The magnified precise integration method is used to solve the nonlinear vibration control system and the high precision solution is obtained. Under the given conditions, the frequency range of the vibration attenuation angles of the 2-DOF and 3-DOF nonlinear energy sink vibration systems are obtained respectively. Then, the external continuous stochastic excitation is applied to the nonlinear energy sink system for simulation to verify the feasibility of constructing the nonlinear energy sink in Duffing oscillator. This paper may provide a research direction and theoretical basis for the study of nonlinear energy sinks.
The Duffing oscillator with a nonlinear energy sink is constructed by linear damping springs. A feasible method for constructing the damping system with the nonlinear energy sink is put forward. The magnified precise integration method is used to solve the nonlinear vibration control system and the high precision solution is obtained. Under the given conditions, the frequency range of the vibration attenuation angles of the 2-DOF and 3-DOF nonlinear energy sink vibration systems are obtained respectively. Then, the external continuous stochastic excitation is applied to the nonlinear energy sink system for simulation to verify the feasibility of constructing the nonlinear energy sink in Duffing oscillator. This paper may provide a research direction and theoretical basis for the study of nonlinear energy sinks.
引文
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[9]李渊印,金先龙,张晓云,等.非线性动力方程精细积分级数解的并行算法[J].上海交通大学学报,2006,40(10):809-1812.
[10]钟万勰.结构动力学方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-136.
[11]葛根,王洪礼,谭建国.多自由度非线性动力方程的改进增维精细积分法[J].天津大学学报,2009,42(2):113-117.
[12]靳晓雄,张立军,江浩.汽车振动分析[M].上海:同济大学出版社,2014.
[13]张继锋,邓子辰.机构动力方程的增维分块精细积分法[J].振动与冲击,2008,27(12):88-90.
[2]GOURDON E.LAMARQUE C H.Energy pumpingωith various nonlinear structures:numerical evidences[J].Nonlinear Dynamics,2005,40(3):281-307.
[3]KOPIDAKIS G,AUBRY S,TSIRONIS G P.Targeted energy transfer through discrete breathers in nonlinear systems[J].Physical RevieωLetters,2001:165-170.
[4]MANIADIS P,KOPIDAKIS G,AUBRY S.Classical and quantum targeted energy transfer betωeen nonlinear oscillators[J].Physica D,2004,188:153-177.
[5]张也弛,孔宪仁.非线性吸振器的靶能量传递及参数设计[J].振动工程学报,2011(4):111-117.
[6]AWREJCEWICZ J,PETROV A G.Nonlinear oscillations of an elastic two-degrees-of-freedom pendulum[J].Nonlinear Dynamics,2007,53:19-30.
[7]张也弛,孔宪仁.非线性耦合振子间产生靶能量传递的初始条件[J].哈尔滨工业大学学报,2012(7):21-26.
[8]KOVACIC I,BRENNAN M J.The Dufting equation:nonlinear oscillators and their behaviourlM].Wiley.2011.
[9]李渊印,金先龙,张晓云,等.非线性动力方程精细积分级数解的并行算法[J].上海交通大学学报,2006,40(10):809-1812.
[10]钟万勰.结构动力学方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-136.
[11]葛根,王洪礼,谭建国.多自由度非线性动力方程的改进增维精细积分法[J].天津大学学报,2009,42(2):113-117.
[12]靳晓雄,张立军,江浩.汽车振动分析[M].上海:同济大学出版社,2014.
[13]张继锋,邓子辰.机构动力方程的增维分块精细积分法[J].振动与冲击,2008,27(12):88-90.