Nonlinear Dynamics

, Volume 94, Issue 3, pp 2219–2241 | Cite as

A new nonlinear vibration model of fiber-reinforced composite thin plate with amplitude-dependent property

  • Hui LiEmail author
  • Pengcheng Xue
  • Zhongwei Guan
  • Qingkai Han
  • Bangchun Wen
Original Paper


In this paper, the material nonlinearity is introduced in the dynamic modeling of fiber-reinforced composite thin plates, and a new nonlinear vibration model of such composite plate structures with amplitude-dependent property is established with the consideration of the nonlinear stiffness and damping characteristics, which is observed and confirmed in the nonlinear vibration characterization experiment. In this new model, the elastic moduli and loss factors are expressed as the function of strain energy density on the basis of Jones–Nelson material nonlinear model. By using the identified parameters under different excitation amplitudes, these elastic moduli and loss factors are characterized as the function of the maximum dimensionless strain energy density. Then, the power function fitting technique is used to determine the nonlinear stiffness and damping parameters in the model, and the nonlinear natural frequencies, vibration responses and damping ratios of a TC300 carbon/epoxy composite thin plate are calculated and measured in a case study. The comparisons between the theoretical and experimental results show that the maximum calculation error of natural frequencies with consideration of amplitude-dependent property is less than 4.3%, and the maximum calculation errors of resonant response and damping results are no more than 12.5 and 9.6% in the 3rd mode and the 6th mode, respectively. Therefore, the practicability and reliability of the proposed model have been verified.


Nonlinear vibration model Fiber-reinforced composite thin plate Nonlinear vibration Amplitude-dependent property Strain energy density 



This study was supported by the National Natural Science Foundation of China granted No. 51505070, the Fundamental Research Funds for the Central Universities of China granted No. N150304011, N160313002 and N160312001, the Scholarship Fund of China Scholarship Council (CSC) granted No. 201806085032, and the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, granted No.VCAME201603.

Compliance with ethical standards

Conflict of interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangChina
  2. 2.School of EngineeringUniversity of LiverpoolLiverpoolUnited Kingdom

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