Acta Mechanica Sinica

, Volume 34, Issue 5, pp 970–982 | Cite as

Forced oscillations and stability analysis of a nonlinear micro-rotating shaft incorporating a non-classical theory

  • S. Ali Ghasabi
  • Mohammadreza ArbabtaftiEmail author
  • Majid Shahgholi
Research Paper


In this paper, the stability and bifurcation analysis of symmetrical and asymmetrical micro-rotating shafts are investigated when the rotational speed is in the vicinity of the critical speed. With the help of Hamilton’s principle, nonlinear equations of motion are derived based on non-classical theories such as the strain gradient theory. In the dynamic modeling, the geometric nonlinearities due to strains, and strain gradients are considered. The bifurcations and steady state solution are compared between the classical theory and the non-classical theories. It is observed that using a non-classical theory has considerable effect in the steady-state response and bifurcations of the system. As a result, under the classical theory, the symmetrical shaft becomes completely stable in the least damping coefficient, while the asymmetrical shaft becomes completely stable in the highest damping coefficient. Under the modified strain gradient theory, the symmetrical shaft becomes completely stable in the least total eccentricity, and under the classical theory the asymmetrical shaft becomes completely stable in the highest total eccentricity. Also, it is shown that by increasing the ratio of the radius of gyration per length scale parameter, the results of the non-classical theory approach those of the classical theory.


Strain gradient theory Micro-rotating shaft Stability Nonlinear oscillation Bifurcation Multiple scales method 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • S. Ali Ghasabi
    • 1
  • Mohammadreza Arbabtafti
    • 1
    Email author
  • Majid Shahgholi
    • 1
  1. 1.Mechanical Engineering FacultyShahid Rajaee Teacher Training UniversityTehranIran

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