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Received Oct 1, 2017; Revised Nov 8, 2017; Accepted Nov 13, 2017
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.
1. Introduction
For decades, thin plates have been used to model the vibration behaviour of low curvature two-dimensional structures having very small thicknesses compared to the other dimensions. Their versatility has led to them being used especially in the aerospace industry, where they have found extensive applications. At the onset of airframe design, engineers are required to simulate the vibration behaviour of the airframe component to determine the operational range of frequencies and the mode shapes that arise under real-life conditions. When such a modal analysis is carried out, the effects of loading and boundary conditions and the contributions from any nearby vibrating entities are also incorporated as these factors could modify the vibration characteristics of the entire system. Thus, in order to avoid the dangers of resonance that could occur if the operational and resonant frequencies overlap, it is imperative that the results obtained from the preliminary modal analysis are highly accurate.
Among the many methods available for vibration analysis, the analytical methods yield the highest accuracy but one major hurdle in using these methods is that they require the closed form solution to the governing partial differential equation. This can be a very tedious process, if at all a tractable one. To circumvent this problem, many simplifying assumptions have been incorporated in to the existing exact methods and, as a result, they exhibit many limitations. Having lost their generality, these exact methods are then only applicable to specific plate shapes and plates subjected to certain boundary conditions, as briefly discussed below.
For example, the Navier method [1], which is one of the most popular analytical methods, transforms the governing partial differential equation into an algebraic expression by using a double Fourier trigonometric series; however, it is only applicable to plates having at least two edges simply supported. Levy [2, 3] made a noteworthy contribution to plate vibration analysis by utilizing a single Fourier trigonometric series to solve the governing equation. Nevertheless, the Levy method is also only applicable to plates that...
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