Analytical solution using the state-space method for free vibration analysis of rotating functionally graded nanotubes
AL Aouinat, A Boukhalfa, SA Belalia - Journal of Vibration Engineering & …, 2023 - Springer
AL Aouinat, A Boukhalfa, SA Belalia
Journal of Vibration Engineering & Technologies, 2023•SpringerPurpose The main aim of this work is to investigate the free vibration of functionally graded
rotating nanotubes using the Euler–Bernoulli beam theory under the assumptions of
Eringen's nonlocal elasticity theory, which gets close to the nanostructure's behaviors. The
material properties are assumed to be graded in the nanotube thickness direction according
to the power-law distribution. Methods Hamilton's principle is used to derive equations of
motion and boundary conditions, which are uncoupled and solved analytically using the …
rotating nanotubes using the Euler–Bernoulli beam theory under the assumptions of
Eringen's nonlocal elasticity theory, which gets close to the nanostructure's behaviors. The
material properties are assumed to be graded in the nanotube thickness direction according
to the power-law distribution. Methods Hamilton's principle is used to derive equations of
motion and boundary conditions, which are uncoupled and solved analytically using the …
Purpose
The main aim of this work is to investigate the free vibration of functionally graded rotating nanotubes using the Euler–Bernoulli beam theory under the assumptions of Eringen’s nonlocal elasticity theory, which gets close to the nanostructure’s behaviors. The material properties are assumed to be graded in the nanotube thickness direction according to the power-law distribution.
Methods
Hamilton’s principle is used to derive equations of motion and boundary conditions, which are uncoupled and solved analytically using the state-space method. The gyroscopic effect is considered in the equations of motion and, unprecedentedly, in the boundary conditions.
Results
The effects of rotating speed, mode number, material power-law index, and geometrical and nonlocal parameters on both critical speeds and natural frequencies under various boundary conditions for functionally graded rotating nanotubes are plotted and investigated for the first time.
Conclusion
The current formulation of the rotating FG-NT is expected to serve as a standard for assessing the accuracy of designing various nanomotors, whether experimental, numerical, or analytical.
Springer
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