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Differences between stress-driven nonlocal integral model and Eringen differential model in the vibrations analysis of carbon nanotubes conveying magnetic nanoflow

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Abstract

The present paper investigated nonlinear free and forced vibration of carbon nanotubes conveying magnetic nanoflow and subjected to a longitudinal magnetic field resting on a viscoelastic foundation. The nonlinear equations of motion were established using Hamilton's principle and solved by employing the Galerkin method. Stress-driven nonlocal integral model has been used to model small-scale effects, its results are compared with Eringen differential model. The instability of divergence and flutter are investigated for different boundary conditions. The primary and secondary resonance of carbon nanotubes is addressed for four boundary conditions. In addition, the effects of length small scale parameters, longitudinal magnetic field, magnetic nanofluid, and boundary conditions on nonlinear free and forced vibration of carbon nanotubes are discussed in detail. As the most important result, it can be seen that Eringen differential model shows an increasing trend by increasing the nonlocal parameter for a cantilever carbon nanotube and in other boundary conditions shows a decreasing trend in free and forced vibrations. While stress-driven nonlocal integral model, by increasing the length scale parameter, always shows increasing behavior, both in free and forced vibrations for all boundary conditions.

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  1. Department of Mechanical Engineering, Borujerd Branch, Islamic Azad University, Borujerd, Iran

    E. Mahmoudpour

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Mahmoudpour, E. Differences between stress-driven nonlocal integral model and Eringen differential model in the vibrations analysis of carbon nanotubes conveying magnetic nanoflow. J Braz. Soc. Mech. Sci. Eng. 43, 555 (2021). https://doi.org/10.1007/s40430-021-03273-1

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