Nonlinear Dynamical Responses of Rotary Cylindrical Shells with Internal Resonance

  • Yufei ZhangEmail author
  • Jintang Liu
  • Bangchun Wen


The nonlinear forced vibration response of a thin, elastic, rotary cylindrical shell to a harmonic excitation is investigated in this study. Nonlinearities due to the large-amplitude shell motion are considered by using Donnell’s nonlinear shallow-shell theory, with consideration of the effect of viscous structural damping. Different from the conventional Donnell’s nonlinear shallow-shell equations, an improved nonlinear model without employing the Airy stress function is utilized to study the nonlinear dynamics of thin shells. The system is discretized using the Galerkin method, while a model involving two degrees of freedom and allowing for the traveling wave response of the shell is adopted. The method of harmonic balance is applied to study the nonlinear dynamic responses of the two-degree-of-freedom system. In addition, the stability of steady-state solutions is analyzed in detail. Finally, results are given for exploring the effects of different parameters on the nonlinear dynamic response with internal resonance.


Cylindrical shells Rotary Nonlinear vibrations Internal resonance Dynamical response 



This research was supported by the National Natural Science Foundation of China (Project No. 11672188).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.School of Aerospace EngineeringShenyang Aerospace UniversityShenyangChina
  2. 2.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangChina

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