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

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. 1. Introduction Perforated plates are widely used in nuclear power equipments, heat exchangers, and pressure vessels. The holes in the plate are arranged in various regular penetration patterns. Industrial applications include both square and triangular array perforation patterns. Cutouts are found in mechanical, civil, marine, and aerospace structures commonly to access ports for mechanical and electrical systems, or simply to reduce weight. Cutouts are also made to provide ventilation and modify the resonant frequency of the structures. Perforated plates are often utilized as head plates, end covers, or supports for tube bundles typically including tube sheets and support plates. Many studies have been done on perforated plates having rectangular/square and triangular array of holes, especially [1–3] dealing with equivalent properties of material for perforated plate. These equivalent material properties are used in vibration analysis to consider perforated plate as full solid plate. Burgemeister and Hansen [4] showed that, to predict accurately the resonance frequencies of simply supported perforated panel, effective material constants cannot be used in classical equations. They used cubic function fitted from ANSYS results to determine the effective resonance frequency ratio for large range of panel geometries with an error of less than 3%. Mali and Singru [5] introduced concept of concentrated negative masses for perforation holes and determined fundamental frequency of rectangular plate carrying four circular perforations in rectangular