Abstract
The torsional vibration analysis of small-scaled rods is studied in the framework of Eringen's nonlocal theory. The equations of motion and related boundary conditions are deduced by employing the Hamilton principle. The nonlocal elasticity theory based on Eringen's model is used to cover the size-dependent behavior of the nanorods. Galerkin's analytical method is used to solve the equation of motion. In the present work, time-dependent torsional vibration in an elliptical nanorod under the linear and harmonic distributed external torques along with determined amplitude is considered with clamped-clamped end supports. When discussing free vibration analysis, the small-scale effect shows the sufficiency of natural frequencies in different modes. These results are best verified by comparison with results available in the literature. The influences of effective parameters such as nonlocal parameters, the value of aspect ratio, and excitation frequency variations in time-dependent angular displacement and non-dimensional angular displacement are discussed in detail. It is found that an increase in the nonlocal parameter leads to a rise in the value of non-dimensional angular displacement. Also, it is concluded that the aspect ratio and frequency of excitation are inversely related to angular displacement.
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