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Vibrations of nonuniform bidirectional functionally graded nanotubes based on the refined beam theory in a thermal environment

Nikola Despenić, Goran Janevski and Ivan Pavlović

Vol. 18 (2023), No. 1, 59–74

We investigate a model of a nonuniform bidirectional functionally graded (BDFG) nanotube, based on refined beam theory in the framework of nonlocal strain gradient theory. Material properties change smoothly in the radial and axial direction of the nanotube, based on the power-law distribution. We obtain equations of motion by using Hamilton’s principle, and eigenvalues through Galerkin’s method. We also investigate the impact of temperature. The dynamic response of the nonuniform BDFG nanotube, not considered in the past, will be a topic of consideration. The main consideration is how the geometrical coefficient has an effect on the natural frequency, i.e., how increasing the slope of the nanotube has impact on the natural frequency. We also consider the critical temperature load, as well as the influence of the nonlocal and strain gradient parameter on the natural frequency. Finally, we observe the effect of the power-law indices on the natural frequency.

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nanotube, vibration, nonuniform, bidirectional functionally graded materials, temperature effect
Received: 18 May 2022
Revised: 7 September 2022
Accepted: 17 October 2022
Published: 24 March 2023
Nikola Despenić
Faculty of Mechanical Engineering
University of Niš
Goran Janevski
Faculty of Mechanical Engineering
University of Niš
Ivan Pavlović
Faculty of Mechanical Engineering
University of Niš