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Longitudinal Vibration Analysis of Elastically Coupled Nanorods System with General Boundary Supports

Deshui Xu, Jingtao Du*, Yuhao Zhao

College of Power and Energy Engineering, Harbin Engineering University, Harbin, China.
* Corresponding Author: Jingtao Du. Email:

Sound & Vibration 2019, 53(2), 16-28.


In this paper, an accurate series solution for the longitudinal vibration analysis of elastically coupled nanorods system is established, in which artificial springs are introduced to simulate such general coupling and boundary conditions. Energy formulation is derived for the description of axial dynamics of multiple coupled nanorods based on Eringen nonlocal elasticity. For each nanorod component, its longitudinal vibration displacement function is invariantly assumed as the superposition of Fourier series and boundary smoothed supplementary polynomials, with the aim to make all the spatial differential sufficiently continuous across each rod. All the unknown coefficients are determined in conjunction with Rayleigh-Ritz procedure to solve a standard eigenvalue matrix. Numerical results are presented for the particular cases of two-nanorod and three-nanorod systems to demonstrate the correctness and effectiveness of the proposed model. Excellent agreements can be repeatedly observed in comparison with those from other approaches available in literature. Based on the model established, influence of elastic boundary and coupling conditions on the longitudinal modal characteristics of multiple nanorods system is investigated and addressed. This work can provide an efficient energy-based modeling framework for longitudinal vibration analysis of elastically connected nanorod system with complicated boundary conditions.


Cite This Article

Xu, D., Du, J., Zhao, Y. (2019). Longitudinal Vibration Analysis of Elastically Coupled Nanorods System with General Boundary Supports. Sound & Vibration, 53(2), 16–28.


cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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