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Smart Structures and Systems Volume 18, Number 5, November 2016 , pages 1029-1062 DOI: https://doi.org/10.12989/sss.2016.18.5.1029 |
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Nonlinear vibration analysis of MSGT boron-nitride micro ribbon based mass sensor using DQEM |
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M. Mohammadimehr and Ahmad A. Monajemi
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| Abstract | ||
| In this research, the nonlinear free vibration analysis of boron-nitride micro ribbon (BNMR) on the Pasternak elastic foundation under electrical, mechanical and thermal loadings using modified strain gradient theory (MSGT) is studied. Employing the von Kármán nonlinear geometry theory, the nonlinear equations of motion for the graphene micro ribbon (GMR) using Euler-Bernoulli beam model with considering attached mass and size effects based on Hamilton\'s principle is obtained. These equations are converted into the nonlinear ordinary differential equations by elimination of the time variable using Kantorovich time-averaging method. To determine nonlinear frequency of GMR under various boundary conditions, and considering mass effect, differential quadrature element method (DQEM) is used. Based on modified strain MSGT, the results of the current model are compared with the obtained results by classical and modified couple stress theories (CT and MCST). Furthermore, the effect of various parameters such as material length scale parameter, attached mass, temperature change, piezoelectric coefficient, two parameters of elastic foundations on the natural frequencies of BNMR is investigated. The results show that for all boundary conditions, by increasing the mass intensity in a fixed position, the linear and nonlinear natural frequency of the GMR reduces. In addition, with increasing of material length scale parameter, the frequency ratio decreases. This results can be used to design and control nano/micro devices and nano electronics to avoid resonance phenomenon. | ||
| Key Words | ||
| nonlinear vibration analysis; boron-nitride micro ribbon; mass sensor; MSGT; DQEM | ||
| Address | ||
| M. Mohammadimehr and Ahmad A. Monajemi: Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Iran | ||