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In the present paper, a two-dimensional periodic curved panel which rests on an orthogonal array of equispaced simple line supports has been analyzed by a FEM. A periodic unit of the system is represented by an accurate high-precision curved triangular shallow shell finite-element model to find out frequencies of plane wave motion in terms of propagation constants for the two-dimensional periodic shell. The natural frequencies of vibration of a full cylindrical shell have been obtained for different propagation constants in the axial and circumferential directions. The propagation surface is found using the optimum periodic curved panel in the analysis. It is observed that the lowest frequency can be found out at the lower bound of first propagation surface, by choosing an optimum periodic angle of curved panel. All the natural frequencies of orthogonally multisupported open curved panel of (Nx×Ny) elements have been found out from the propagation surface and compared with NASTRAN results. It is shown that by this approach the order of the resulting matrices in the FEM is considerably reduced leading to a significant decrease in computational effort.
Pany et al. (Tue,) studied this question.