Nonlinear Dynamics

, Volume 95, Issue 1, pp 151–174 | Cite as

Nonlinear dynamic responses of rotating pretwisted cylindrical shells

  • Minghui YaoEmail author
  • Yan Niu
  • Yuxin Hao
Original Paper


A rotating pretwisted cylindrical shell model with a presetting angle is established to investigate nonlinear dynamic responses of the aero-engine compressor blade. The centrifugal force and the Coriolis force are considered in the model. The aerodynamic pressure is obtained by the first-order piston theory. The strain–displacement relationship is derived by the Green strain tensor. Based on the first-order shear deformation theory and the isotropic constitutive law, nonlinear partial differential governing equations are derived by using the Hamilton principle. Discarding the Coriolis force effect, Galerkin approach is utilized to reduce nonlinear partial differential governing equations into a two-degree-of-freedom nonlinear system. According to nonlinear ordinary differential equations, numerical simulations are performed to explore nonlinear transient dynamic responses of the system under the effect of the single point excitation and nonlinear steady-state dynamic responses of the system under the effect of the uniform distribution excitation. The effects of the excitation parameter, damping coefficient, rotating speed, presetting angle and pretwist angle on nonlinear dynamic responses of the system are fully discussed.


Nonlinear dynamics Pretwisted cylindrical shell Rotating speed Single point excitation Uniform distribution excitation 



The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NNSFC) through Grant No. 11372015.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.College of Mechanical EngineeringBeijing University of Technology, Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical StructuresBeijingPeople’s Republic of China
  2. 2.College of Mechanical EngineeringBeijing Information Science and Technology UniversityBeijingPeople’s Republic of China

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