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A Theoretical Approach for Free Vibration Analysis of the Nano-Plates Considering the Small Scale Effect

[+] Author Affiliations
Emad Jomehzadeh, Ali Reza Saidi

Shahid Bahonar University of Kerman, Kerman, Iran

Paper No. ESDA2010-24400, pp. 571-576; 6 pages
doi:10.1115/ESDA2010-24400
From:
  • 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
  • Conference Sponsors: International
  • ISBN: 978-0-7918-4919-4 | eISBN: 978-0-7918-3877-8
  • Copyright © 2010 by ASME

abstract

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.

Copyright © 2010 by ASME

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