Abstract
Doubly curved plates and regions of general shells may be easily investigated for both vibratory behavior and instability using a form of Donnell's equation. The new eighth-order equation provides more precision than Donnell's and also offers simple closed form relations that provide insight to the physical behavior of the shell. Examples are presented to depict the increased accuracy and the range of applicability of the equation. One result is a particularly simple relation between instability loading and natural frequency. In another demonstration the cylinder form of the general shell equation is shown to yield Levy's result for ring mode buckling of a cylinder under external pressure, which Donnell's equation does not do.
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