"E. Mathieu adapted to the problem [of curved plates or shells ] the method which Poisson had used for plates. He observed that the modes of vibration possible to a shell do not fall into classes characterized respectively by normal and tangential displacements, and he adopted equations of motion that could be deduced from Aron's formula for the by retaining the terms that depend on the stretching of the middle-surface only."
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A Treatise on the Mathematical Theory of Elasticity
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