Abstract
In this work, we applied the spectral element method (SEM) to analyze the dynamic characteristics of fluid conveying single-walled carbon nanotubes (SWCNTs). First, the dynamic equations for fluid conveying SWCNTs were deduced based on the nonlocal Timoshenko beam theory. Then, the spectral element formulation was established for a free/forced vibration analysis of fluid conveying SWCNTs by introducing discrete Fourier transform. Furthermore, the proposed method was validated using several comparison examples. Finally, the natural frequencies and dynamic responses of a simply-supported fluid conveying SWCNTs were calculated by the SEM, considering different internal fluid velocities and small-scale parameters (SSPs). The effects of fluid velocity and SSPs on the dynamic characteristics of SWCNTs conveying fluid were revealed by the numerical results. Compared with other methods, the SEM shows high accuracy and efficiency.
Highlights
Carbon nanotubes (CNTs) have been extensively used in numerous areas due to their excellent mechanical properties [1,2]
Cai et al [12,13] discussed the dynamic responses of a CNT-based nanobeam, which was considered a model of nanobalance
In this paper, based on the spectral element method (SEM), which was originally proposed by Doyle [45] for the analysis of macrostructure dynamics, we developed a method for the free/forced vibration analysis of a CNT conveying fluid
Summary
Carbon nanotubes (CNTs) have been extensively used in numerous areas due to their excellent mechanical properties [1,2]. The modified couple stress theory and nonlocal Euler–Bernoulli beam theory were successively employed by Wang [36,37,38] to study the vibration and instability of tubular micro- and nano- beams conveying fluid He discussed the effect of nonlocal parameters on natural frequencies and the critical velocity of fluid conveying CNTs, and demonstrated that the effect on critical velocity can be neglected. Considering the small-size effects and Knudsen number, the vertical nanotube conveying fluid was studied by Bahaadini et al [40] based on the nonlocal strain gradient Timoshenko beam theory. Zhen and Fang [42] deduced the nonlinear equation of CNTs conveying fluid in terms of nonlocal Euler–Bernoulli beam theory and discussed the relationship between internal resonance and the axial external excitation force in detail. Numerical examples were given to show the validity of the proposed SEM
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