The free vibration analysis of a nano-plate is investigated based on the first order shear deformation theory considering the small scale effect. The governing equations of motion are obtained using Hamilton’s principle by considering the nonlocal constitutive equations of Eringen. These coupled partial differential equations are reformulated into two new equations called the edge-zone and interior equations. Analytical solutions are obtained for a nano-plate with Levy boundary conditions. In order to find the natural frequencies of the nano-plate, the various boundary conditions at one direction of the plate should be imposed. Applying these conditions and setting the determinant of the six order coefficient matrix equal to zero, the natural frequencies of the nano-plate are evaluated. Non-dimensional frequency parameters are presented for over a wide range of nonlocal parameters and different boundary conditions. In addition, the effects of nonlocal parameter on the natural frequency of a nano-plate are discussed in details.
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ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis
July 12–14, 2010
Istanbul, Turkey
Conference Sponsors:
- International
ISBN:
978-0-7918-4919-4
PROCEEDINGS PAPER
A Theoretical Approach for Free Vibration Analysis of the Nano-Plates Considering the Small Scale Effect
Emad Jomehzadeh,
Emad Jomehzadeh
Shahid Bahonar University of Kerman, Kerman, Iran
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Ali Reza Saidi
Ali Reza Saidi
Shahid Bahonar University of Kerman, Kerman, Iran
Search for other works by this author on:
Emad Jomehzadeh
Shahid Bahonar University of Kerman, Kerman, Iran
Ali Reza Saidi
Shahid Bahonar University of Kerman, Kerman, Iran
Paper No:
ESDA2010-24400, pp. 571-576; 6 pages
Published Online:
December 28, 2010
Citation
Jomehzadeh, E, & Saidi, AR. "A Theoretical Approach for Free Vibration Analysis of the Nano-Plates Considering the Small Scale Effect." Proceedings of the ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Volume 5. Istanbul, Turkey. July 12–14, 2010. pp. 571-576. ASME. https://doi.org/10.1115/ESDA2010-24400
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