Abstract
With rigorous dynamic performance of mechanical products, it is important to identify dynamic parameters exactly. In this paper, a response surface plotting method is proposed and it can be applied to identify the dynamic parameters of some nonlinear systems. The method is based on the principle of harmonic balance method (HBM). The nonlinear vibration system behaves linearly under the steady-state response amplitude, which presents the equivalent stiffness and damping coefficient. The response surface plot is over two-dimensional space, which utilizes excitation as the vertical axis and the frequency as the horizontal axis. It can be applied to observe the output vibration response data. The modal parameters are identified by the response surface plot as linearity for different excitation levels, and they are converted into equivalent stiffness and damping coefficient for each resonant response. Finally, the HBM with first-order expansion is utilized for identification of stiffness and damping coefficient of nonlinear systems. The classical nonlinear systems are applied in the numerical simulation as the example, which is used to verify its effectiveness and accuracy. An application of this technique for nonlinearity identification by experimental setup is also illustrated.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
NOËL J P, KERSCHEN G. Nonlinear system identification in structural dynamics: 10 more years of progress [J]. Mechanical Systems and Signal Processing, 2017, 83: 2–35.
LIU X, SUN B B, LI L, et al. Nonlinear identification and characterization of structural joints based on vibration transmissibility [J]. Journal of Southeast University (English Edition), 2018, 34(1): 36–42.
CHEN C Y, SONG H W, WANG D Y, et al. The natural frequency shift of satellite vibration test and parameter identification of nonlinear in satellite structure [J]. Journal of Shanghai Jiao Tong University, 2005, 39(7): 1197–1200 (in Chinese).
AGUIRRE L A, LETELLIER C. Modeling nonlinear dynamics and chaos: A review [J]. Mathematical Problems in Engineering, 2009, 2009: 238960.
LIU X, WANG L X, CHEN Q D, et al. Nonlinear modeling and identification of structural joint by response control vibration test [J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2019, 36(6): 964–976.
MAO K, LI B, WU J, et al. Stiffness influential factors-based dynamic modeling and its parameter identification method of fixed joints in machine tools [J]. International Journal of Machine Tools and Manufacture, 2010, 50(2): 156–164.
GÖGE D, SINAPIUS M, FÜLLEKRUG U, et al. Detection and description of non-linear phenomena in experimental modal analysis via linearity plots [J]. International Journal of Non-Linear Mechanics, 2005, 40(1): 27–48.
AHMADIAN H, ZAMANI A. Identification of nonlinear boundary effects using nonlinear normal modes [J]. Mechanical Systems and Signal Processing, 2009, 23(6): 2008–2018.
PRAWIN J, RAMA MOHAN RAO A, LAKSHMI K. Nonlinear identification of structures using ambient vibration data [J]. Computers & Structures, 2015, 154: 116–134.
NOEL J P, KERSCHEN G, FOLTETE E, et al. Greybox identification of a non-linear solar array structure using cubic splines [J]. International Journal of Non-Linear Mechanics, 2014, 67: 106–119.
ALEJO D,ISIDRO L,JESTJS R, et al. Parameter estimation of linear and nonlinear systems based on orthogonal series [J]. Procedia Engineering, 2012, 35: 67–76.
GOGE D, SINAPIUS M, FÜLLEKRUG U, et al. Detection and description of non-linear phenomena in experimental modal analysis via linearity plots [J]. International Journal of Non-Linear Mechanics, 2005, 40(1): 27–48.
SADATI SMS, NOBARI A S, NARAGHI T. Identification of a nonlinear joint in an elastic structure using optimum equivalent linear frequency response function [J]. Acta Mechanica, 2012, 223: 1507–1516.
ÖZER M B, ÖZGÜVEN H N, ROYSTON T J. Identification of structural non-linearities using describing functions and the Sherman-Morrison method [J]. Mechanical Systems and Signal Processing, 2009, 23(1): 30–44.
FELDMAN M, BRAUN S. Nonlinear vibrating system identification via Hilbert decomposition [J]. Mechanical Systems and Signal Processing, 2017, 84: 65–96.
JALALI H, AHMADIAN H, MOTTERSHEAD J E. Identification of nonlinear bolted lap-joint parameters by force-state mapping [J]. International Journal of Solids and Structures, 2007, 44(25/26): 8087–8105.
THOTHADRI M, CASAS R A, MOON F C, et al. Nonlinear system identification of multi-degree-of-freedom systems [J]. Nonlinear Dynamics, 2003, 32(3): 307–322.
AHMADIAN H, JALALI H. Generic element formulation for modelling bolted lap joints [J]. Mechanical Systems and Signal Processing, 2007, 21(5): 2318–2334.
ARSLAN Ö, AYKAN M, NEVZAT ÖZGÜVEN H. Parametric identification of structural nonlinearities from measured frequency response data [J]. Mechanical Systems and Signal Processing, 2011, 25(4): 1112–1125.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, X., Wang, L., Chen, Q. et al. Parameter Identification of Structural Nonlinearity by Using Response Surface Plotting Technique. J. Shanghai Jiaotong Univ. (Sci.) 26, 819–827 (2021). https://doi.org/10.1007/s12204-020-2242-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12204-020-2242-8
Key words
- structural nonlinearity
- parameter identification
- equivalent stiffness and damping
- response surface plot