|
|
Parameter optimization analysis of a nonlinear energy sink system under base harmonic excitation |
LIU Liangkun1,PAN Zhaodong1,TAN Ping2,YAN Weiming3,ZHOU Fulin2,3 |
1. School of Environment and Civil Engineering, Dongguan University of Technology, Dongguan 523808, China;
2. Earthquake Engineering Research & Test Center, Guangzhou University, Guangzhou 510405, China;
3. College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China |
|
|
Abstract In order to obtain the optimal stiffness parameter of a nonlinear energy sink (NES) system under base excitation, the complex-averaging method was employed to derive the equation of a corresponding slow dynamics system with 1∶1 resonance. The corresponding necessary condition of the strongly modulate response (SMR) and analytical equation of the fixed point were also obtained. Sequently, the lower limit and upper limit were solved based on the characteristics and analytical equation of the fixed point respectively. The numerical simulation results indicate that the fixed point solved by the analytical equation of the fixed point is in agreement with the counterpart directly calculated using Runge-Kutta method. Moreover, the former is also approximate to the stable response of the original dynamic system. Additionally, the slow dynamics system is convenient for computation and has rational results. The optimal stiffness areas for NES system trend to be larger with the increase of damping parameters. Compared with TMD system, NES system has broader frequency band for vibration attenuation but it is of lower efficiency at frequencies close to the inherent frequency and is also easily affected by the excitation magnitude.
|
Received: 31 May 2018
Published: 15 November 2019
|
|
|
|
[1] Gendelman O, Manevitch L I, Vakakis A F, et al. Energy Pumping in Nonlinear Mechanical Oscillators: Part I—Dynamics of the Underlying Hamiltonian Systems[J]. Journal of Applied Mechanics, 2001, 68(1):34-41.
[2] Vakakis A F, Gendelman O. Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture[J]. Journal of Applied Mechanics, 2001, 68(1):42-48.
[3] Quinn D D, Gendelman O, Kerschen G, et al. Efficiency of TET in coupled oscillators associated with 1: resonance: Part 1[J]. Journal of Sound & Vibration, 2008, 311:2028-2048.
[4] Sapsis T P, Vakakis A F. Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures:Part II, analytical study[J]. Journal of Sound & Vibration, 2009, 311(3):297-320.
[5] Vakakis A F, Gendelman O V, Bergman L A, et al. Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems[J]. Solid Mechanics & Its Applications, 2009, 156.
[6] Gendelman O V, Gourdon E, Lamarque C H. Quasiperiodic energy pumping in coupled oscillators under periodic forcing[J]. Journal of Sound & Vibration, 2006, 294(4–5):651-662.
[7] Gendelman O V, Starosvetsky Y. Quasi-Periodic Response Regimes of Linear Oscillator Coupled to Nonlinear Energy Sink Under Periodic Forcing[J]. Journal of Applied Mechanics, 2007, 74(2):325-331.
[8] Starosvetsky Y, Gendelman O V. Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry[J]. Physica D Nonlinear Phenomena, 2008, 237(13):1719-1733.
[9] Starosvetsky Y, Gendelman O V. Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning[J]. Journal of Sound & Vibration, 2008, 315(3):746-765.
[10] Gendelman O V, Starosvetsky Y, Feldman M. Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: Description of response regimes[J]. Nonlinear Dynamics, 2007, 51(1):31-46.
[11] Starosvetsky Y, Gendelman O V. Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber[J]. Nonlinear Dynamics, 2008, 51(1-2):47-57.
[12] Nguyen T A, Pernot S. Design criteria for optimally tuned nonlinear energy sinks—part 1: transient regime[J]. Nonlinear Dynamics, 2012, 69(1-2):1-19.
[13] Vaurigaud B, Savadkoohi A T, Lamarque C H. Targeted energy transfer with parallel nonlinear energy sinks. Part I: Design theory and numerical results[J]. Nonlinear Dynamics, 2011, 66(66):763-780.
[14] Savadkoohi A T, Vaurigaud B, Lamarque C H, et al. Targeted energy transfer with parallel nonlinear energy sinks, part II: theory and experiments[J]. Nonlinear Dynamics, 2012, 67(1):37-46.
[15] Gourc E, Michon G, Seguy S, et al. Experimental Investigation and Design Optimization of Targeted Energy Transfer Under Periodic Forcing[J]. Journal of Vibration & Acoustics, 2014, 136(2):858-862.
[16] Viguié R, Kerschen G Design Procedure of a Nonlinear Vibration Absorber: Enhancement of the Amplitude Robustness[C]// ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2010:711-720.
[17] Viguié R, Kerschen G. Design Procedure of a Nonlinear Vibration Absorber Using Bifurcation Analysis[C]// 27th International Modal Analysis Conference. 2009:381-389.
[18] 孔宪仁, 张也弛. 两自由度非线性吸振器在简谐激励下的振动抑制[J]. 航空学报, 2012, 33(6):1020-1029.
KONG X R, ZHANG Y C. Vibration suppression of a two-degree-of-freedom nonlinear energy sink under harmonic excitation[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(6):1020-1029. (in Chinese)
[19] 李海勤. 带有阻尼非线性的能量阱振动抑制效果研究[D]. 哈尔滨:哈尔滨工业大学, 2015:16-19
LI Haiqing. Research on energy sink with geometrically nonlinear damping for vibration suppression[D]. Harbin Institute of Technology, 2015: 16-19. (in Chinese)
[20] 楼京俊, 唐斯密, 朱石坚, 等. 改进的本质非线性吸振器宽频吸振参数域研究[J]. 振动与冲击,2011, 30(6):218-222.
LOU Jingjun, TANG Simi, ZHU Shijian, et al. Study on parameter range of improved essentially nonlinear absorber on broad frequency range[J]. Journal of Vibration and Shock, 2011, 30(6):218-222. (in Chinese)
[21] 王菁菁,浩文明,吕西林. 轨道非线性能量阱阻尼对其减振性能的影响[J]. 振动与冲击,2017,36(24):30-34+50.
Wang Jingjing, Hao Wenming, Lv Xilin. Influence of track nonlinear energy sink damping on its vibration reduction performance[J]. Journal of Vibration and Shock, 2017,36(24):30-34+50. (in Chinese)
[22] Den Hartog JP. Mechanical Vibrations[M].4thed. NY: McGraw Hill 1956.
[23] Gourdon E, Lamarque C H, Pernot S. Contribution to efficiency of irreversible passive energy pumping with a strong nonlinear attachment[J]. Nonlinear Dynamics, 2007, 50(4):793-808.
|
|
|
|