Multi-frequency resonance capture and targeted vibration suppression mechanism in thin-walled casing-nonlinear energy sink
-
摘要:
引入具有非线性刚度特征的动力吸振器（非线性能量阱）至三自由度系统开展对主系统多阶频率振动抑制的研究，在此基础上扩展至具有连续介质特性的航空发动机真实机匣结构。在理论分析方面，基于复变量平均法揭示了三自由度非线性系统中非线性能量阱实现瞬态共振捕获和靶向能量传递的内在机理和必要条件，得到了多自由度系统中非线性能量阱的动力学响应特性。在规律分析方面，开展三自由度非线性系统中不同非线性刚度和阻尼参数对非线性能量阱能量耗散特性影响规律研究，得出了多自由度系统中非线性能量阱最优振动耗散特性。基于振动能量可视化分析方法，非线性能量阱设计方法扩展至真实航空发动机组合机匣结构，成功可视化捕捉到振动能量从机匣振源传递至非线性能量阱的过程，从振动能量的角度揭示了非线性能量阱对机匣结构的靶向能量吸收与耗散特性，单个非线性能量阱有效抑制机匣三阶模态振动，振幅分别降低25.1%、25.3%和25.2%，实现了非线性能量阱对薄壁机匣结构的宽频振动抑制。
Abstract:A dynamic absorber with nonlinear stiffness characteristics (nonlinear energy sink, NES) was introduced into a three-degree-of-freedom system to study the suppression of multi-frequency vibrations in the main system, and then extended to the real casing structure of an aero-engine with continuous medium characteristics. In terms of theoretical analysis, based on the complex variable averaging method, the intrinsic mechanism and necessary conditions for the nonlinear energy sink to achieve transient resonance capture and targeted energy transfer in a three-degree-of-freedom nonlinear system were revealed, and the dynamic response characteristics of the nonlinear energy sink in a multi-degree-of-freedom system were obtained. In terms of regularity analysis, the influences of different nonlinear stiffness and damping parameters on the energy dissipation characteristics of the nonlinear energy sink in a three-degree-of-freedom nonlinear system were studied, and the optimal vibration dissipation characteristics of the nonlinear energy sink in a multi-degree-of-freedom system were obtained. Based on the vibration energy visualization analysis method, the design method of the nonlinear energy sink was extended to the real engine combined casing structure, and the process of vibration energy transfer from the casing vibration source to the nonlinear energy sink was successfully visualized. From the perspective of vibration energy, the targeted energy absorption and dissipation characteristics of the nonlinear energy sink on the casing structure were revealed. A single nonlinear energy sink effectively suppressed the first three modal vibrations of the casing, reducing the amplitudes by 25.1%, 25.3%, and 25.2%, respectively, achieving broadband vibration suppression of the thin-walled casing structure by the nonlinear energy sink.
-
图 1 含NES的三自由度非线性系统示意图
Figure 1. Schematic diagram of a three-degree-of-freedom nonlinear system with NES
图 5 不同脉冲激励下NES能量耗散比例
Figure 5. Energy dissipation ratio of NES under different pulse excitations
图 7 各质点局部位移-时间响应结果（C点）
Figure 7. Local displacement-time response results of each particle （point C）
图 8 质点1位移傅里叶变换和系统能量耗散对比（C点）
Figure 8. Comparison of Fourier transform of displacement of m1 and system energy dissipation （point C）
图 11 不同参数下NES能量耗散特性
Figure 11. Energy dissipation characteristics of NES with different parameters
图 12 不同激励下不同参数NES能量耗散特性
Figure 12. Energy dissipation characteristics of NES with different parameters under various excitations
图 18 脉冲激励下机匣振动能量矢量云图
Figure 18. Vibration energy vector cloud map on the casing under pulse excitation
图 20 点Ⅰ位移响应傅里叶变换结果
Figure 20. Fourier transform results of displacement response at point Ⅰ
图 22 点Ⅰ位移响应傅里叶变换结果（初始阶段）
Figure 22. Fourier transform results of displacement response at point Ⅰ （initial stage）
图 24 点Ⅰ位移响应对比（初始阶段）
Figure 24. Comparison of displacement response at point Ⅰ （initial stage）
图 25 点Ⅰ位移响应傅里叶变换对比
Figure 25. Comparison of Fourier transform of displacement response at point Ⅰ
图 27 点Ⅱ位移响应对比（初始阶段）
Figure 27. Comparison of displacement response at point Ⅱ （initial stage）
图 29 点Ⅰ与NES质点位移响应（初始阶段）
Figure 29. Displacement response of point I and NES mass（initial stage）
图 31 点Ⅱ位移响应傅里叶变换对比
Figure 31. Comparison of Fourier transform of displacement response at point Ⅱ
表 1 不同模态分支下系统动力学特性
模态分支 各质点运动相位 振幅比变化趋势 NES靶向吸收振动能量 S111+++ 质点1与NES同相运动；
质点2与NES同相运动随着振动能量的耗散，An/A1绝对值
逐渐增加，An/A2绝对值逐渐增加NES实现了对质点1和质点2的瞬态共振捕获，靶向吸收其振动能量 S111++− 质点1与NES反相运动；
质点2与NES反相运动随着振动能量的耗散，An/A1绝对值
逐渐减小，An/A2绝对值逐渐减小NES未实现靶向吸收振动能量的功能 S111+−− 质点1与NES反相运动；
质点2与NES同相运动随着振动能量的耗散，An/A1绝对值
逐渐增加，An/A2绝对值逐渐增加NES实现了对质点1和质点2的瞬态共振捕获，靶向吸收其振动能量 S111+−+ 质点1与NES同相运动；
质点2与NES反相运动随着振动能量的耗散，An/A1绝对值
逐渐减小，An/A2绝对值逐渐减小NES未实现靶向吸收振动能量的功能 
下载: 导出CSV
-
[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. doi: 10.1115/1.1345524 [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. doi: 10.1115/1.1345525 [3] 张运法. 基于非线性能量阱的减振系统动力学特性研究[D]. 哈尔滨: 哈尔滨工业大学, 2023. Zhang Yunfa. Study on dynamic characteristics of vibration reduction systems based on nonlinear energy traps[D]. Harbin: Harbin Institute of Technology, 2023. (in ChineseZhang Yunfa. Study on dynamic characteristics of vibration reduction systems based on nonlinear energy traps[D]. Harbin: Harbin Institute of Technology, 2023. (in Chinese) [4] Lee Y S, Vakakis A F, Bergman L A, et al. Passive non-linear targeted energy transfer and its applications to vibration absorption: a review[J]. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2008, 222(2): 77-134. doi: 10.1243/14644193jmbd118 [5] Lu Zheng, Wang Zixin, Zhou Ying, et al. Nonlinear dissipative devices in structural vibration control: a review[J]. Journal of Sound and Vibration, 2018, 423: 18-49. doi: 10.1016/j.jsv.2018.02.052 [6] Nayfeh S A, Nayfeh A H. Energy transfer from high-to low-frequency modes in a flexible structure via modulation[J]. Journal of Vibration and Acoustics, 1994, 116(2): 203-207. doi: 10.1115/1.2930413 [7] Kerschen G, Mcfarland D M, Kowtko J J, et al. Experimental demonstration of transient resonance capture in a system of two coupled oscillators with essential stiffness nonlinearity[J]. Journal of Sound and Vibration, 2007, 299(4/5): 822-838. doi: 10.1016/j.jsv.2006.07.029 [8] Musienko A I, Lamarque C H, Manevitch L I. Design of mechanical energy pumping devices[J]. Journal of Vibration and Control, 2006, 12(4): 355-371. doi: 10.1177/1077546306062098 [9] Malatkar P, Nayfeh A H. Steady-State dynamics of a linear structure weakly coupled to an essentially nonlinear oscillator[J]. Nonlinear Dynamics, 2007, 47(1): 167-179. doi: 10.1007/s11071-006-9066-4 [10] Nayfeh A H. Perturbation methods in nonlinear dynamics[M]//Lecture Notes in Physics. Berlin, Germany: Springer, 2007: 238-314. [11] Nayfeh A H, Chin C, Nayfeh S A. On nonlinear normal modes of systems with internal resonance[J]. Journal of Vibration and Acoustics, 1996, 118(3): 340-345. doi: 10.1115/1.2888188 [12] Ding Hu, Chen Liqun. Designs, analysis, and applications of nonlinear energy sinks[J]. Nonlinear Dynamics, 2020, 100(4): 3061-3107. doi: 10.1007/s11071-020-05724-1 [13] Li Shuangbao, Zhou Xinxing, Chen Jianen. Hamiltonian dynamics and targeted energy transfer of a grounded bistable nonlinear energy sink[J]. Communications in Nonlinear Science and Numerical Simulation, 2023, 117: 106898. doi: 10.1016/j.cnsns.2022.106898 [14] 李双宝, 周新星. 周期激励下接地双稳态非线性能量阱的动力学[J]. 中国民航大学学报, 2023, 41(4): 51-57. Li Shuangbao, Zhou Xinxing. Dynamics of a grounded bistable nonlinear energy sink under periodic excitations[J]. Journal of Civil Aviation University of China, 2023, 41(4): 51-57. (in Chinese doi: 10.3969/j.issn.1674-5590.2023.04.009Li Shuangbao, Zhou Xinxing. Dynamics of a grounded bistable nonlinear energy sink under periodic excitations[J]. Journal of Civil Aviation University of China, 2023, 41(4): 51-57. (in Chinese) doi: 10.3969/j.issn.1674-5590.2023.04.009 [15] Qiu Donghai, Li Tao, Seguy S, et al. Efficient targeted energy transfer of bistable nonlinear energy sink: application to optimal design[J]. Nonlinear Dynamics, 2018, 92(2): 443-461. doi: 10.1007/s11071-018-4067-7 [16] 张运法, 孔宪仁. 具有组合非线性阻尼的非线性能量阱振动抑制响应分析[J]. 力学学报, 2023, 55(4): 972-981. Zhang Yunfa, Kong Xianren. Analysis on vibration suppression response of nonlinear energy sink with combined nonlinear damping[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 972-981. (in Chinese doi: 10.6052/0459-1879-22-563Zhang Yunfa, Kong Xianren. Analysis on vibration suppression response of nonlinear energy sink with combined nonlinear damping[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 972-981. (in Chinese) doi: 10.6052/0459-1879-22-563 [17] 莫帅, 黄祖瑞, 刘翊恒, 等. 具有几何非线性刚度的非线性能量阱振动抑制与动态特性研究[J/OL]. 工程力学, 1-11[2024-08-26]. Mo Shuai, Huang Zurui, Liu Saheng, et al. Study on vibration suppression and dynamic characteristics of nonlinear energy traps with geometric nonlinear stiffness[J/OL]. Engineering Mechanics, 1-11[2024-08-26]. (in ChineseMo Shuai, Huang Zurui, Liu Saheng, et al. Study on vibration suppression and dynamic characteristics of nonlinear energy traps with geometric nonlinear stiffness[J/OL]. Engineering Mechanics, 1-11[2024-08-26]. (in Chinese) [18] 李建玲, 陈建恩, 孙敏, 等. 非线性能量阱最优参数的变化规律研究[J]. 天津理工大学学报, 2024, 40(1): 133-139. Li Jianling, Chen Jian’en, Sun Min, et al. Study on variation of optimal parameters of nonlinear energy sink[J]. Journal of Tianjin University of Technology, 2024, 40(1): 133-139. (in Chinese doi: 10.3969/j.issn.1673-095X.2024.01.019Li Jianling, Chen Jian’en, Sun Min, et al. Study on variation of optimal parameters of nonlinear energy sink[J]. Journal of Tianjin University of Technology, 2024, 40(1): 133-139. (in Chinese) doi: 10.3969/j.issn.1673-095X.2024.01.019 [19] Zhang Yewei, Yuan Bin, Fang Bo, et al. Reducing thermal shock-induced vibration of an axially moving beam via a nonlinear energy sink[J]. Nonlinear Dynamics, 2017, 87(2): 1159-1167. doi: 10.1007/s11071-016-3107-4 [20] Noiseux D U. Measurement of power flow in uniform beams and plates[J]. The Journal of the Acoustical Society of America, 1970, 47(1B): 238-247. doi: 10.1121/1.1911472 [21] Williams E G. Structural intensity in thin cylindrical shells[J]. The Journal of the Acoustical Society of America, 1991, 89(4): 1615-1622. doi: 10.1121/1.400996 [22] 马英群, 徐蒙, 张锴, 等. 基于结构声强法的机匣振动能量传递特性[J]. 航空学报, 2019, 40(9): 222938. Ma Yingqun, Xu Meng, Zhang Kai, et al. Vibration energy transmission characteristics of casing based on structural intensity method[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(9): 222938. (in ChineseMa Yingqun, Xu Meng, Zhang Kai, et al. Vibration energy transmission characteristics of casing based on structural intensity method[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(9): 222938. (in Chinese) [23] 马英群, 张锴, 徐蒙, 等. 多重激励下机匣振动能量传递规律与耦合特性[J]. 推进技术, 2019, 40(6): 1389-1398. Ma Yingqun, Zhang Kai, Xu Meng, et al. Investigation on transmitting regularities and coupling characteristics of vibrational energy for casing structure under multiple excitations[J]. Journal of Propulsion Technology, 2019, 40(6): 1389-1398. (in Chinese doi: 10.13675/j.cnki.tjjs.180351Ma Yingqun, Zhang Kai, Xu Meng, et al. Investigation on transmitting regularities and coupling characteristics of vibrational energy for casing structure under multiple excitations[J]. Journal of Propulsion Technology, 2019, 40(6): 1389-1398. (in Chinese) doi: 10.13675/j.cnki.tjjs.180351 [24] Kim J, Yoon J C, Kang B S. Finite element analysis and modeling of structure with bolted joints[J]. Applied Mathematical Modelling, 2007, 31(5): 895-911. doi: 10.1016/j.apm.2006.03.020 [25] Pratt W. Advanced bolted joint modeling methodology for PW1000G engine fan case[R]. ASME GT2021-58932, 2021. [26] 马英群. 基于结构声强可视化的航空发动机转子-支承-机匣耦合系统振动能量传递特性研究[D]. 北京: 中国科学院大学, 2020. Ma Yingqun. Investigation on vibration energy transmission characteristics of aero-engine rotor-support-casing coupling system based on visualization of structural acoustic intensity[D]. Beijing: Chinese Academy of Sciences, 2020. (in ChineseMa Yingqun. Investigation on vibration energy transmission characteristics of aero-engine rotor-support-casing coupling system based on visualization of structural acoustic intensity[D]. Beijing: Chinese Academy of Sciences, 2020. (in Chinese) [27] 韩佳奇, 陈伟, 刘璐璐, 等. 基础冲击载荷作用下转子-机匣系统动力学响应试验研究[C]//第15届全国转子动力学学术大会摘要集. 沈阳: 中国振动工程学会转子动力学专业委员会, 2023. -
点击查看大图
计量
- 文章访问数: 239
- HTML浏览量: 93
- PDF量: 22
- 被引次数: 0