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Nonlocal effects on the longitudinal vibration of a complex multi-nanorod system subjected to the transverse magnetic field

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Abstract

In this communication we examine the free longitudinal vibration of a complex multi-nanorod system (CMNRS) using the nonlocal elasticity theory. Discussion is limited to the cases of two types of boundary conditions, namely, clamped–clamped (C–C) and clamped–free (C–F), where nanorods are coupled in the “Free-Chain” system by an elastic medium. Each nanorod in CMNRS is subjected to the influence of transversal magnetic field. The longitudinal vibration of the system are described by a set of m partial differential equations, derived by using D’Alembert’s principle and classical Maxwell’s relation, which includes Lorentz magnetic force. Analytical expressions for the nonlocal natural frequencies are obtained in closed-form by using the method of separations of variables and trigonometric method. Results for the nonlocal natural frequencies are compared for the special cases of a single and double-nanorod system with the existing results in the literature. Numerical examples are given in order to examine the effects of nonlocal parameter, stiffness coefficient and transversal magnetic field on nonlocal natural frequencies of axially vibrating CMNRS.

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Acknowledgments

This research was supported by the research grants of the Serbian Ministry of Education, Science and Technological Development under the numbers ON 174001 and ON 174011.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Niš, A. Medvedeva 14, 18000, Nis, Serbia

    Danilo Karličić & Predrag Kozić

  2. Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001, Belgrade, Serbia

    Milan Cajić

  3. School of Engineering, University of the West of Scotland, Paisley, PA1 2BE, UK

    Tony Murmu

  4. College of Engineering, Swansea University, Singleton Park, Swansea, SA2 8PP, UK

    Sondipon Adhikari

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  1. Danilo Karličić
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  2. Milan Cajić
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  3. Tony Murmu
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  4. Predrag Kozić
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  5. Sondipon Adhikari
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Correspondence to Danilo Karličić.

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Karličić, D., Cajić, M., Murmu, T. et al. Nonlocal effects on the longitudinal vibration of a complex multi-nanorod system subjected to the transverse magnetic field. Meccanica 50, 1605–1621 (2015). https://doi.org/10.1007/s11012-015-0111-6

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  • DOI: https://doi.org/10.1007/s11012-015-0111-6

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