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Abstract
We consider the localized vibrational modes that can exist at the edge of a semi-infinite plate and at the end of a semi-infinite bar of small thickness. It is known that for certain special values of Poisson’s ratio σ these modes are perfectly localized, are uncoupled to bulk modes, and thus do not lose energy by acoustic radiation. We show that for other values of σ it is possible to modify the shape of the end of the plate or bar in a way such that a perfectly localized edge mode is formed. Finally, we discuss the effect of this localization phenomenon on the vibrational modes of plates and bars of finite length.
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