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Published online by Cambridge University Press: 05 July 2011
SeeTheory of Sound, § 226.
[1899. In general the bending of a square plate with free edges takes place in both planes; but when the material is such that Poisson's ratio vanishes, i.e. when longitudinal extension entails no lateral contraction, the bending may be in one plane only, so that the surface remains cylindrical. In this case the bending follows the law of a simple bar, and the nodal system consists of two straight lines parallel to one pair of edges.
By superposing, after Wheatstone, two such modes of vibration, the phases being the same and the amplitudes equal or opposite, we obtain other nodal systems easily constructed from the known functions expressing the free vibrations of a bar. In the latter case symmetry suffices to shew that the nodal lines are the diagonals of the plate.]
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