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Advances in Acoustics and Vibration
Volume 2013, Article ID 972409, 6 pages
http://dx.doi.org/10.1155/2013/972409
Research Article

Determination of the Fundamental Frequency of Perforated Rectangular Plates: Concentrated Negative Mass Approach for the Perforation

Department of Mechanical Engineering, Birla Institute of Technology and Science, Pilani, K.K. Birla Goa Campus, Zuarinagar, Goa 403726, India

Received 28 February 2013; Revised 1 May 2013; Accepted 12 May 2013

Academic Editor: Joseph CS Lai

Copyright © 2013 Kiran D. Mali and Pravin M. Singru. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with a vibration analysis of perforated rectangular plates with rectangular perforation pattern of circular holes. The study is particularly useful in the understanding of the vibration of sound absorbing screens, head plates, end covers, or supports for tube bundles typically including tube sheets and support plates used in the mechanical devices. An energy method is developed to obtain analytical frequencies of the perforated plates with clamped edge, support conditions. Perforated plate is considered as plate with uniformly distributed mass. Holes are considered as concentrated negative masses. The analytical procedure using the Galerkin method is adopted. The deflected surface of the plate is approximated by the cosine series which satisfies the boundary conditions. Finite element method (FEM) results have been used to illustrate the validity of the analytical model. The comparisons show that the analytical model predicts natural frequencies reasonably well for holes of small size.