Nonlinear dynamic response and transmissibility of a flexible rotor system mounted on viscoelastic elements

Mohammed Khair Al-Solihat*, Kamran Behdinan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


In this paper, the three-dimensional nonlinear dynamics and force transmissibility characteristics of a flexible shaft-disk rotor system are investigated numerically. The rotor system is comprised of a flexible shaft supporting a rigid disk, and the shaft ends are mounted on viscoelastic elements (bearing/support). The dynamic model of the system is developed considering the coupled axial and bending–bending elastic motions of the shaft while the disk is modeled as a rigid body. The equations of motion (EOM) obtained using Lagrange’s equation are discretized using the assumed mode method utilizing large number of modes to examine the system dynamics accurately for multiple resonance regions. The EOM are then linearized to obtain the natural frequencies to construct the Campbell diagrams and investigate the influence of the bearing stiffness and disk location on critical speeds and whirling modes. The harmonic balance method combined with the pseudo-arclength continuation method is used to construct the nonlinear frequency response and force transmissibility curves due to disk unbalance force. The effects of the bearing stiffness and damping, unbalance force magnitude and disk location on the nonlinear multi-mode primary frequency response and force transmissibility are then thoroughly investigated.

Original languageEnglish
Pages (from-to)1581-1600
Number of pages20
JournalNonlinear Dynamics
Issue number2
StatePublished - 31 Jul 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature B.V.


  • Campbell diagram
  • Critical speeds
  • Flexible shaft-disk rotor
  • Force transmissibility
  • Frequency response
  • Harmonic balance method
  • Unbalance force
  • Viscoelastic element

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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