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

Kiran D Mali,Pravin M Singru

doi:10.1155/2013/972409

Kiran D Mali, Pravin M Singru

Open Access

https://doi.org/10.1155/2013/972409

Copy DOI

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.

Highlights

Perforated plates are widely used in nuclear power equipments, heat exchangers, and pressure vessels
Perforated plates are often utilized as head plates, end covers, or supports for tube bundles typically including tube sheets and support plates
From the literature on vibration of perforated plates, authors found that, there is no evidence on the analytical formulation by considering negative mass approach for holes except for reference [5] where authors have studied only four specimens of rectangular plates with four circular perforations

Summary

Introduction

Perforated plates are widely used in nuclear power equipments, heat exchangers, and pressure vessels. Low et al [10, 11] obtained natural frequencies of rectangular plates carrying a single and multiple concentrated masses by using Rayleigh-Ritz method for different boundary conditions From the literature on vibration of perforated plates, authors found that, there is no evidence on the analytical formulation by considering negative mass approach for holes except for reference [5] where authors have studied only four specimens of rectangular plates with four circular perforations They have not discussed the limiting condition of the approach for obtaining the accuracy in predicted value of fundamental frequency. Present analytical model is more useful for predicting accurately the fundamental frequencies of wide range of small size perforation geometries, for rectangular plates with rectangular penetration pattern for all edges clamped support condition

Analytical Formulations

Numerical Simulation

Results and Discussions

Conclusions