Volume 17, Issue 4 (2017)                   Modares Mechanical Engineering 2017, 17(4): 134-142 | Back to browse issues page

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Ghasabi S A, Shahgholi M, Arbab Tafti M R. Nonlinear vibrations and stability analysis of a micro rotating shaft by considering the modified couple stress theory and micro inertia effect. Modares Mechanical Engineering. 2017; 17 (4) :134-142
URL: http://journals.modares.ac.ir/article-15-10161-en.html
Abstract:   (1846 Views)
In this paper stability analysis of a nonlinear micro rotating shaft near the primary resonances by considering the modified couple stress theory and micro inertia effect is investigated. The geometric nonlinearities due to classical and non-classical theory (the modified couple stress theory) are considered. Using Hamilton principle, the nonlinear equations of motion are obtained. In order to solve the equations of motion the multiple scales method are used and an analytical expression is presented for forward and backward frequencies which can be seen the effects of modified couple stress theory and micro inertia effect. The frequency response curves, amplitude versus damping coefficient, amplitude versus total eccentricities, etc. are reported. It is seen that due to the modified couple stress theory and micro inertia effect the amplitude of the system is decreased and the loci of bifurcation points is changed. Symmetrical micro-shaft in the presence of classical theory and without micro inertia effects becomes completely stable in the least damping coefficient and asymmetrical micro-shaft in the presence of classical theory and without micro inertia effects becomes completely stable in the most damping coefficient. Symmetrical micro-shaft in the presence of modified couple stress theory and with micro inertia effects becomes completely stable in the least total eccentricity and asymmetrical micro-shaft in the presence of classical theory and without micro inertia effects becomes completely stable in the most total eccentricity. So, considering the small-scale effects due to strain and velocity gradients for analysis of the system is mandatory.
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Article Type: Research Article | Subject: Vibration
Received: 2016/12/26 | Accepted: 2017/02/12 | Published: 2017/04/8

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