Vibration analysis of perforated plates

Abstract

Plates are used as structural elements in major engineering applications. It is common to see openings in these plated structures for various reasons. For example, openings are needed for electric wiring, water pipes, plumbing etc. In case of the perforated plates, openings are often introduced in the regular array. Industrial applications use both the rectangular and triangular array of the perforations. The existence of large open area can change the mass distribution and stiffness around the opening regions, thus changing the vibration characteristics of the plates. The extent to which the perforations can change the vibration behavior of the plated structures depends on the size, shape, locations, numbers and type of the perforation pattern. Existing literature on free vibration of the perforated plate lacks formulation of the analytical models. Existing studies are more related to the determination of the equivalent material properties and their use in calculation of the fundamental frequency. In this thesis, analytical models are formulated to determine the fundamental frequency of the thin perforated plates. Approximate analytical methods such as the Rayleigh s method, Rayleigh s Ritz method and the Galerkin method are used to formulate the analytical models. For analytical models different aspects are considered for plates with clamped all edges. Analytical models are formulated for the rectangular plates with circular/rectangular/square openings arranged in the regular array. Proposed analytical models are based on the special functions to express the variation of the material properties due to the perforations, negative mass concept for perforation and replacing circular perforation with the equivalent square perforation. Expression for modal constant for fundamental frequency of perforated plate is also determined. To establish this modal constant, experimental vibration data is used. The parameters of interest are the size of the opening, the ratio of the area of full solid plate to that of perforat.