Authors: Karličić, Danilo 
Ayed, Sadoon
Flaieh, Enass
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Nonlocal axial vibration of the multiple Bishop nanorod system
Journal: Mathematics and Mechanics of Solids
Volume: 24
Issue: 6
First page: 1668
Last page: 1691
Issue Date: 1-Jun-2019
Rank: M21
ISSN: 1081-2865
DOI: 10.1177/1081286518766577
Abstract: 
Construction of reliable dynamic models of nanostructures is an important task for design procedures of different nanoresonator devices. Such theoretical models allow as to perform different numerical experiments, which is the key point in the development of advanced nanodevices. This paper presents a new nanoresonator model based on the axial vibration of the elastic multi-nanorod system. It is assumed that the system of multiple nanorods is embedded in an elastic medium. The governing equations of motion of a coupled multi-nanorod system are derived using the Hamilton’s principle, the nonlocal elastic constitutive relation, and Bishop’s rod theory, where effects of inertia of the lateral motion and the shear stiffness are considered. Exact closed form solutions for natural frequencies are obtained for one and multiple nanorod systems with different boundary conditions. Then, results for natural frequencies obtained by the finite difference method are compared with the results obtained analytically. Effects of nonlocal parameter, different rod theories, number of nanorods and stiffness coefficient of an elastic medium on natural frequencies are examined through several numerical examples.
Keywords: Bishop nanorod | finite difference | multiple system | natural frequency | Nonlocal elasticity
Publisher: SAGE Journals
Project: Dynamics of hybrid systems with complex structures. Mechanics of materials. 

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