Circular Annular and Elliptic Annular Plates
This chapter provides the free vibration analysis of annular elliptic plates for all the nine boundary conditions at the inner and outer edges. The annular elliptic and circular plates are used quite often in aeronautical and ship structures, and in several other industrial applications. Therefore, the vibration analyses of these shapes are becoming more important. Annular circular plates are special cases of annular elliptic plates and are quite simple to analyze using polar coordinates. A survey of literature on the vibration of annular circular plates and the results of several cases are provided in a monograph by Leissa. The computations can be simplified by considering the shape functions to represent symmetric–symmetric, symmetric–antisymmetric, antisymmetric–ymmetric, and antisymmetric–antisymmetric groups. The use of 2D boundary characteristic orthogonal polynomials in the Rayleigh–Ritz method makes the said problem a computationally efficient and simple numerical technique for finding the vibration characteristics.