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Advances in Nano Research Volume 15, Number 1, July 2023 , pages 75-89 DOI: https://doi.org/10.12989/anr.2023.15.1.075 |
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Bishop theory and longitudinal vibration of nano-beams by two-phase local/nonlocal elasticity |
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Reza Nazemnezhad, Roozbeh Ashrafian and Alireza Mirafzal
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| Abstract | ||
| In this paper, Bishop theory performs longitudinal vibration analysis of Nano-beams. Its governing equation, due to integrated displacement field and more considered primarily effects compared with other theories, enjoys fully completed status, and more reliable results as well. This article aims to find how Bishop theory and Two-phase elasticity work together. In other words, whether Bishop theory will be compatible with Two-phase local/nonlocal elasticity. Hamilton's principle is employed to derive governing equation of motion, and then the 6th order of Generalized Differential Quadrature Method (GDQM) as a constructive numerical method is utilized to attain the discretized two-phase formulation. To acquire a proper verification procedure, exact solution is prepared to be compared with current results. Furthermore, the effects of key parameters on the objective are investigated. | ||
| Key Words | ||
| axial vibration; bishop theory; generalised differential quadrature method (GDQM); nano-beams; two-phase local/nonlocal elasticity | ||
| Address | ||
| Reza Nazemnezhad and Roozbeh Ashrafian: School of Engineering, Damghan University, Damghan, Iran Alireza Mirafzal: Faculty of Mechanical Engineering, Semnan University, Semnan, Iran | ||