|
|
基于杠杆型非线性能量阱的复合材料层合梁横向振动抑制
|
Abstract:
本文将杠杆型非线性能量阱(Lever-Type Nonlinear Energy Sink, LNES)耦合到复合材料层合梁的中点位置，研究了LNES对梁的横向振动抑制性能。结合牛顿第二运动定律和广义哈密顿原理，推导了耦合系统的动力学方程。采用伽辽金截断法离散耦合系统的偏微分控制方程，并通过龙格–库塔法获得近似数值解，验证了谐波平衡法得到的近似解析解。对比在相同幅值激励下耦合NES系统的响应曲线，发现LNES对系统的振动抑制效果更为优越。此外，讨论了LNES单一参数变化对系统幅频响应曲线的影响。根据结果确定，LNES对复合材料层合梁的横向振动有着显著的振动抑制效果。
The research explores the efficacy of transverse vibration suppression in a laminated composite beam. A lever-type nonlinear energy sink (LNES) is positioned at the beam’s midpoint to facilitate this suppression. The dynamic equations of the coupled system are derived in conjunction with Newton’s second law of motion and generalized Hamilton’s principle. The governing partial differential equations of the coupled system are truncated by the Galerkin method. The approximate numerical solutions obtained by the Runge-Kutta method verify the approximate analytical solution obtained by the harmonic balance method. The transient responses and steady-state responses of the coupled system were observed. It was found that the LNES exhibits a significant vibration suppression effect. Comparing the amplitude-frequency response curves of the coupled NES system reveals. The LNES exhibits a superior vibration suppression effect than NES under the same amplitude excitation. Furthermore, the impact of a single parameter change of the LNES on the amplitude-frequency response curve of the system is demonstrated. The results indicate that the LNES has a significant effect on suppressing transverse vibration in laminated composite beams.
| [1] | Nguyen, T., Nguyen, N., Vo, T.P. and Thai, H. (2017) Trigonometric-series Solution for Analysis of Laminated Composite Beams. Composite Structures, 160, 142-151. https://doi.org/10.1016/j.compstruct.2016.10.033 |
| [2] | Mohammad-Abadi, M. and Daneshmehr, A.R. (2015) Modified Couple Stress Theory Applied to Dynamic Analysis of Composite Laminated Beams by Considering Different Beam Theories. International Journal of Engineering Science, 87, 83-102. https://doi.org/10.1016/j.ijengsci.2014.11.003 |
| [3] | 徐鉴. 振动控制研究进展综述[J]. 力学季刊, 2015, 36(4): 547-565. |
| [4] | Ding, H. and Chen, L. (2020) Designs, Analysis, and Applications of Nonlinear Energy Sinks. Nonlinear Dynamics, 100, 3061-3107. https://doi.org/10.1007/s11071-020-05724-1 |
| [5] | Lee, Y.S., Vakakis, A.F., Bergman, L.A., McFarland, D.M., Kerschen, G., Nucera, F., et al. (2008) Passive Non-Linear Targeted Energy Transfer and Its Applications to Vibration Absorption: A Review. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 222, 77-134. https://doi.org/10.1243/14644193jmbd118 |
| [6] | Vakakis, A.F., Gendelman, O.V., Bergman, L.A., Mcfarland, D.M., Kerschen, G. and Lee, Y.S. (2008) Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems. Springer Science & Business Media. |
| [7] | Kopidakis, G., Aubry, S. and Tsironis, G.P. (2001) Targeted Energy Transfer through Discrete Breathers in Nonlinear Systems. Physical Review Letters, 87, Article ID: 165501. https://doi.org/10.1103/physrevlett.87.165501 |
| [8] | 钟锐, 陈建恩, 葛为民, 刘军. 串联非线性能量阱的高分支响应研究[J]. 动力学与控制学报, 2019, 17(3): 251-257. |
| [9] | Zhang, Z., Ding, H., Zhang, Y. and Chen, L. (2021) Vibration Suppression of an Elastic Beam with Boundary Inerter-Enhanced Nonlinear Energy Sinks. Acta Mechanica Sinica, 37, 387-401. https://doi.org/10.1007/s10409-021-01062-6 |
| [10] | 李继伟, 赵泽福. 冲击减振器与非线性能量阱耦合系统的振动抑制研究[J]. 动力学与控制学报, 2020, 18(2): 76-81. |
| [11] | Zang, J., Yuan, T., Lu, Z., Zhang, Y., Ding, H. and Chen, L. (2018) A Lever-Type Nonlinear Energy Sink. Journal of Sound and Vibration, 437, 119-134. https://doi.org/10.1016/j.jsv.2018.08.058 |
| [12] | Cao, R., Wang, Z., Zang, J. and Zhang, Y. (2022) Resonance Response of Fluid-Conveying Pipe with Asymmetric Elastic Supports Coupled to Lever-Type Nonlinear Energy Sink. Applied Mathematics and Mechanics, 43, 1873-1886. https://doi.org/10.1007/s10483-022-2925-8 |
| [13] | Rahmani, B. and Shenas, A.G. (2017) Robust Vibration Control of Laminated Rectangular Composite Plates in Hygrothermal and Thermal Environment. Composite Structures, 179, 665-681. https://doi.org/10.1016/j.compstruct.2017.07.058 |
| [14] | Ghayesh, M.H. and Amabili, M. (2013) Steady-state Transverse Response of an Axially Moving Beam with Time-Dependent Axial Speed. International Journal of Non-Linear Mechanics, 49, 40-49. https://doi.org/10.1016/j.ijnonlinmec.2012.08.003 |
| [15] | Ding, H. (2015) Periodic Responses of a Pulley？belt System with One-Way Clutch under Inertia Excitation. Journal of Sound and Vibration, 353, 308-326. https://doi.org/10.1016/j.jsv.2015.05.023 |
| [16] | Zang, J. and Zhang, Y. (2019) Responses and Bifurcations of a Structure with a Lever-Type Nonlinear Energy Sink. Nonlinear Dynamics, 98, 889-906. https://doi.org/10.1007/s11071-019-05233-w |
