Abstract
A method is developed to determine the natural frequencies and mode shapes of circular and noncircular cylindrical panels. The panels are assumed to be freely supported along their curved edges and to have arbitrary straight-edge boundary conditions. The Donnell equations of equilibrium for noncircular cylindrical shells are used. The displacement functions, assumed to be mixed power and trigonometric series, reduce the Donnell equations to a set of coupled, algebraic recurrence formulas. It is shown that this method yields the exact solution. A study was also made to investigate the effects of neglecting in-surface inertias. For each noncircular segment an equivalent circular panel, which vibrates at the same natural frequency as the corresponding noncircular panel, was found. A significant advantage of the power series method is that the natural frequencies of circular and noncircular panels can be obtained for all combinations of straight-edge boundary conditions without having to reformulate the problem for each set of boundary conditions.
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