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Coiled carbon nanotubes (CCNTs) belong to one of the prominent classes of carbon nanostructures with unique mechanical properties and vibrational behavior due to their helical geometries. In this paper, the free transverse vibration behavior of single-walled CCNTs is investigated by molecular dynamics (MD) simulations and the adaptive intermolecular reactive empirical bond-order (AIREBO) potential under different boundary conditions (B.Cs.). The beating phenomenon is observed in CCNTs due to the presence of longitudinal, transverse, and torsional coupled vibrations and the proximity of their corresponding frequency. Generally, the frequency of the CCNTs decreases by increasing the length ( L ) or the number of pitches ( n p). Moreover, the pitch angle ( α ¯ ) plays a more decisive role compared to other geometric parameters. At constant length ( L ) of CCNTs, the frequency increases by enhancing the pitch angle ( α ¯ ). Furthermore, the fundamental frequency range of the studied CCNTs is obtained less than 331.9 GHz for lengths greater than 2 nm under different boundary conditions. This indicates that CCNTs have a higher vibration sensitivity than straight CNTs. Therefore, CCNTs can be a proper alternative to straight CNTs in sensors. The results of this study can be used in the design and analysis of nanoelectromechanical systems (NEMs) with CCNTs elements as well as to calibrate continuum mechanics methods. [ABSTRACT FROM AUTHOR]

In this study, dynamic response of functionally graded (FG) nanobeam under a moving load in a thermal environment has been investigated. By considering the size effect, nonlocal Euler–Bernoulli beam theory has been used to model a FG nanobeam. By applying Hamilton's principle, governing equations of motion and boundary conditions, have been derived. Analytical solution by using Laplace transform method has been achieved. Presented results have been verified by comparing with the results found in the literature, which this comparison shows good agreement between them. Influences of the nonlocal parameter, material distribution index, velocity of the moving load, and temperature changes on the response of the FG nanobeam have been investigated. The results show that increasing the nonlocal parameter and temperature changes leads to raising the dynamic deflection of the FG nanobeam. [ABSTRACT FROM AUTHOR]

This paper studied the free vibration behavior of coiled carbon nanotubes (CCNTs) using continuum mechanics methods and molecular dynamics (MD) simulations. Based on the continuum mechanics method, a new elasticity model called the nonlocal generalized Washizu beam (NGWB) was innovated by considering the effects of the curvature and cross-section thickness of nanotubes, as well as size-dependent effect. Then, the governing equations for the vibrational behavior of CCNTs were derived and solved using the numerical generalized differential quadrature method (GDQM). The free vibration behavior of CCNTs was also examined by performing the MD simulations to determine the calibrated values of the nonlocal parameter ( μ) that are applied in the NGWB elasticity model and to validate and evaluate the obtained results. Since the NGWB elasticity model considers the size-dependent effect on the vibrational behavior, obtained results from it well agrees with the MD simulation results in the present study. For CCNTs, there was a coupling between transverse, longitudinal, and torsional vibrations, which led to the beating phenomenon. The natural frequencies decreases by increasing the number of pitches ( n p) , aspect ratio (p / D) , and pitch angle (α ¯). The nonlocal parameter has a more significant effect on the frequencies of CCNTs with smaller geometrical parameters. In addition, the type of boundary conditions affects the calibrated values of the nonlocal parameter, frequency values, and arrangement of vibrating mode shapes of CCNTs. Results of the present study can be applied in the design and analysis of nano-electro-mechanical systems (NEMS), sensors, and nano-composite structures containing CCNTs. Also, the NGWB elasticity model might be useful in the statics and wave propagation studies of CCNTs, and other coiled and curved nano-structures. [ABSTRACT FROM AUTHOR]