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In-plane bending vibration of L-shaped cantilever nanobeams carrying a tip nanoparticle by nonlocal elasticity

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Abstract

Some arms of nanorobots display L-shaped structures. The transverse free bending vibration of an L-shaped cantilever nanobeam carrying a tip nanoparticle is investigated. Based on the nonlocal elasticity, the nonlocal parameter is introduced to capture the size effect of the mechanical behavior of the cantilever–mass system. The frequency equation is deduced analytically. Exact resonance frequencies of the L-shaped nanocantilever–mass system are numerically evaluated and compared with their corresponding values of the macro-scale L-shaped cantilever–mass system. The numerical results show that the nonlocal parameter declines the resonance frequencies. If removing the nonlocal parameter, our results reduce to the resonance frequencies of transverse bending vibration of L-shaped cantilevers with an attached tip mass. The effects of the nonlocal parameter, the ratio of the attached mass to the structure mass, the length ratio of two members of the L-shaped cantilever–mass system on the resonance frequencies are analyzed.

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Acknowledgements

This work was supported by the Natural Science Foundation of Hunan Province of China (Grant No. 2022JJ30583) and Scientific Research Fund of Hunan Provincial Education Department (Grant No. 21B0315).

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  1. School of Civil Engineering, Central South University, Changsha, 410075, People’s Republic of China

    Y. Q. Han

  2. School of Civil Engineering, Changsha University of Science and Technology, Changsha, 410114, People’s Republic of China

    X. L. Peng

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Han, Y.Q., Peng, X.L. In-plane bending vibration of L-shaped cantilever nanobeams carrying a tip nanoparticle by nonlocal elasticity. Acta Mech (2024). https://doi.org/10.1007/s00707-024-03905-2

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