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Smart Structures and Systems Volume 25, Number 4, April 2020 , pages 501-514 DOI: https://doi.org/10.12989/sss.2020.25.4.501 |
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Vibration of nonlocal perforated nanobeams with general boundary conditions |
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Mohamed A. Eltaher and Norhan A. Mohamed
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| Abstract | ||
| This article presents a comprehensive model to investigate a free vibration and resonance frequencies of nanostructure perforated beam element as nano-resonator. Nano-scale size dependency of regular square perforated beam is considered by using nonlocal differential form of Eringen constitutive equation. Equivalent mass, inertia, bending and shear rigidities of perforated beam structure are developed. Kinematic displacement assumptions of both Timoshenko and Euler-Bernoulli are assumed to consider thick and thin beams, respectively. So, this model considers the effect of shear on natural frequencies of perforated nanobeams. Equations of motion for local and nonlocal elastic beam are derived. After that, analytical solutions of frequency equations are deduced as function of nonlocal and perforation parameters. The proposed model is validated and verified with previous works. Parametric studies are performed to illustrate the influence of a long-range atomic interaction, hole perforation size, number of rows of holes and boundary conditions on fundamental frequencies of perforated nanobeams. The proposed model is supportive in designing and production of nanobeam resonator used in nanoelectromechanical systems NEMS. | ||
| Key Words | ||
| resonance frequencies; free vibration; perforated nonlocal nanobeam; analytical solution; frequency equations | ||
| Address | ||
| (1) Mohamed A. Eltaher: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia; (2) Mohamed A. Eltaher: Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt; (3) Norhan A. Mohamed: Engineering Mathematics and Physics Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt. | ||