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Free Torsional Vibration Analysis of Nanorods with Non-circular Cross-Sections Based on the Second-Order Strain Gradient Theory

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Abstract

Purpose

In this paper, the free torsional vibration characteristics of nanorods with non-circular (elliptical, rectangular, triangular) cross-sections are investigated.

Methods

The size-dependent behavior of the nanorod is modeled based on the second-order strain gradient theory and the governing equations and boundary conditions are derived utilizing Hamilton’s principle. The governing equations and boundary conditions are presented in a dimensionless form and are solved numerically via the differential quadrature method (DQM). First, the convergence of the presented solution is confirmed. Then, the accuracy of the results is approved through a comparison between the results and those provided in other works.

Results

Finally, the influences of different parameters on the natural frequencies of the nanorods are investigated for clamped–clamped (CC) and clamped-free (CF) nanorods such as cross-sectional dimensions-to-length ratio, small radius-to-large radius in the elliptical nanorods, the width-to-height ratio in the rectangular nanorods, boundary conditions, length scale parameters, and type of cross-section. It is shown that for all studied cross-sections and boundary conditions, the natural frequencies increase by increasing length scale parameters and the percentage of growth in the natural frequencies is weakly dependent on the type of the cross-section.

Conclusion

It is concluded that a small reduction can be observed in the natural frequencies by increasing cross-sectional dimensions. It is revealed that for the nanorods with elliptical and rectangular cross-sections, the maximum natural frequencies belong to the nanorods with circular and square cross-sections, respectively.

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Authors and Affiliations

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

    Roozbeh Shameli, Farshid Aghadavoudi & Mohammad Hashemian

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  1. Roozbeh Shameli
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  2. Farshid Aghadavoudi
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  3. Mohammad Hashemian
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Correspondence to Farshid Aghadavoudi.

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Shameli, R., Aghadavoudi, F. & Hashemian, M. Free Torsional Vibration Analysis of Nanorods with Non-circular Cross-Sections Based on the Second-Order Strain Gradient Theory. J. Vib. Eng. Technol. 11, 3039–3055 (2023). https://doi.org/10.1007/s42417-022-00729-z

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