| Citation: | HUANG Xingrong, LIU Jiuzhou, LI Linet al. Dynamic characteristics analysis method of complex systems based on nonlinear mode[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(7): 1337-1348. doi: 10.13700/j.bh.1001-5965.2018.0643(in Chinese)
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Nonlinear problem has always been an obstacle in dynamic analysis domain due to its complexity and high computational cost. This paper aims to present a simple, accurate and efficient nonlinear modal analysis method which can be applied to some common nonlinear systems, including Duffing system, dry friction, nonlinear material and so on. The kernel technique of this numerical method lies in establishing the variation law of the nonlinear modal parameters in function of modal amplitude:on the one hand, the steady-state problem is simplified into one-dimensional algebraic nonlinear problem, resulting in a significant simplification in numerical computation; on the other hand, the analysis of nonlinear modal parameters in function of modal amplitude provides a modal overview for the comprehension of system's nonlinear dynamic behavior. Following a description of the theoretical aspects and numerical simulation process of this method, it has been proven to be efficient in analyzing a Duffing system with real nonlinear mode, a dry friction system with complex nonlinear mode and a multi-physics system integrating piezoelectric material. A reduction method based on the proposed strategy is then presented, which is simple in mathematical form and efficient in numerical computations for analyzing large complex nonlinear systems. It has significant advantages in computational efficiency when combined with the mode synthesis method to solve the dynamic behavior of large complex nonlinear systems.
| [1] |
JIANG D, PIERRE C, SHAW S W.Nonlinear normal modes for vibratory systems under harmonic excitation[J].Journal of Sound and Vibration, 2005, 288(4-5):791-812. doi: 10.1016/j.jsv.2005.01.009
|
| [2] |
TOUZÉ C, AMABILI M.Nonlinear normal modes for damped geometrically nonlinear systems:Application to reduced-order modelling of harmonically forced structures[J].Journal of Sound and Vibration, 2006, 298(4-5):958-981. doi: 10.1016/j.jsv.2006.06.032
|
| [3] |
RENSON L, KERSCHEN G, COCHELIN B.Numerical computation of nonlinear normal modes in mechanical engineering[J].Journal of Sound and Vibration, 2016, 364:177-206. doi: 10.1016/j.jsv.2015.09.033
|
| [4] |
HUANG X R, JÉZÉQUEL L, BESSET S, et al.Nonlinear hybrid modal synthesis based on branch modes for dynamic analysis of assembled structure[J].Mechanical Systems and Signal Processing, 2018, 99:624-646. doi: 10.1016/j.ymssp.2017.07.002
|
| [5] |
LIU J Z, LI L, HUANG X R, et al.Dynamic characteristics of the blisk with synchronized switch damping based on negative capacitor[J].Mechanical Systems and Signal Processing, 2017, 95:425-445. doi: 10.1016/j.ymssp.2017.03.049
|
| [6] |
ROSENBERG R M.The normal modes of nonlinear n-degrees-of-freedom systems[J].Journal of Applied Mechanics, 1962, 29(1):595-611.
|
| [7] |
SZEMPLINSKA-STUPNICKA W. The resonant vibration of homogeneous non-linear systems[J].International Journal of Non-Linear Mechanics, 1980, 15(4-5):407-415. doi: 10.1016/0020-7462(80)90026-8
|
| [8] |
JÉZÉQUEL L, LAMARQUE C.Analysis of non-linear dynamical systems by the normal form theory[J].Journal of Sound and Vibration, 1991, 149(3):429-459. doi: 10.1016/0022-460X(91)90446-Q
|
| [9] |
SETIO H D, SETIO S, JÉZÉQUEL L.A method of non-linear modal identification from frequency response tests[J].Journal of Sound and Vibration, 1992, 158(3):497-515. doi: 10.1016/0022-460X(92)90421-S
|
| [10] |
CHONG Y H, IMREGUN M.Development and application of a nonlinear modal analysis technique for mdof systems[J].Journal of Vibration and Control, 2001, 7(2):167-179. doi: 10.1177/107754630100700202
|
| [11] |
GIBERT C.Fitting measured frequency response using non-linear modes[J].Mechanical Systems and Signal Processing, 2003, 17(1):211-218.
|
| [12] |
郑兆昌.关于线性和非线性系统内在的本质联系——多自由度非线性系统的定量和定性分析[J].振动与冲击, 2008, 27(1):4-8. doi: 10.3969/j.issn.1000-3835.2008.01.001
ZHENG Z C.Intrinsic and simple connection of linear systems with non-linear ones:Quantitative and qualitative analysis of large scale multiple DOF nonlinear systems[J].Journal of Vibration and Shock, 2008, 27(1):4-8(in Chinese). doi: 10.3969/j.issn.1000-3835.2008.01.001
|
| [13] |
HUANG X R, JÉZÉQUEL L, BESSET S, et al.Nonlinear modal synthesis for analyzing structures with a frictional interface using a generalized Masing model[J].Journal of Sound and Vibration, 2018, 434:166-191. doi: 10.1016/j.jsv.2018.07.027
|
| [14] |
LIU J Z, LI L, FAN Y, et al.A modified nonlinear modal synthesis scheme for mistuned blisks with synchronized switch damping[J].International Journal of Aerospace Engineering, 2018, 2018:8517890.
|
| [15] |
DUFFING G.Elastizität und Reibung beim Riementrieb[J].Forschung Auf Dem Gebiet Des Ingenieurwesens A, 1931, 2(3):99-104.
|
| [16] |
李琳, 刘久周, 李超.航空发动机中的干摩擦阻尼器及其设计技术研究进展[J].航空动力学报, 2016, 31(10):2305-2317.
LI L, LIU J Z, LI C.Review of the dry friction dampers in aero-engine and their design technologies[J].Journal of Aerospace Power, 2016, 31(10):2305-2317(in Chinese).
|
| [17] |
CHIANG D Y.The generalized Masing models for deteriorating hysteresis and cyclic plasticity[J].Applied Mathematical Modelling, 1999, 23(11):847-863. doi: 10.1016/S0307-904X(99)00015-3
|
| [18] |
BAMPTON M C C, CRAIG R R.Coupling of substructures for dynamic analyses[J].AIAA Journal, 1968, 6(7):1313-1319. doi: 10.2514/3.4741
|
| [19] |
KRYLOV N M, BOGOLYUBOV N N.Introduction to non-linear mechanics[M].Princeton:Princeton University Press, 1947.
|
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HUANG Xingrong, LIU Jiuzhou, LI Linet al. Dynamic characteristics analysis method of complex systems based on nonlinear mode[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(7): 1337-1348. doi: 10.13700/j.bh.1001-5965.2018.0643(in Chinese)
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