Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Free vibration analysis of rotating functionally graded microbeams

Authors
Seyyed Mohammad Hossein Hosseini 1
Hadi Arvin Boroujeni 2
Mohsen Botshekanan 2
1 MSc., Faculty of engineering, Shahrekord University, Shahrekord
2 Associate Professor, Faculty of engineering, Shahrekord University, Shahrekord
10.30506/ijmep.2021.120790.1675
Abstract
The free vibration features of rotating functionally graded microbeams in thermal environment
are presented in this paper. The governing equations are extracted on the basis of the Euler-
Bernoulli beam assumptions beside the modified couple stress theory. The finite element
method is applied on the weak form of the strain and the kinetic energies to extract the natural
frequencies and the associated modeshapes. The nonlinear static equations of motion due to the
rotation and the thermal environment are treated employing the Newton-Raphson technique.
Moreover, the natural frequencies are estimated from the linearized equations of motion about
the static configuration. After the validation of the present results, the rotation speed, the
material length scale parameter, the temperature change, the power law exponent and the
slenderness ratio impacts on the fundamental natural frequency and the first and the second
modeshapes are examined. The outcomes indicate the increment of the natural frequency after
a threshold value of the power law exponent depends on a given rotation speed for the rotating
microbeams in comparison with the stationary microbeams. Furthermore, the modeshapes of
rotating functionally graded microbeams vary by the power law exponent while for stationary
functionally graded microbeams the modeshapes are invariant with respect to the power law
exponent even in the presence of the thermal environment.
Keywords
Rotating microbeams
functionally graded materials
finite element method
Newton-Raphson method
modeshape

Subjects

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  • Receive Date 27 January 2020
  • Revise Date 01 March 2020
  • Accept Date 12 October 2021