Abstract
Waves in periodic structures are highly dispersive, experiencing either small or large spatial decays depending on whether the frequency lies in a pass or stop band. For ribbed plates, these dispersion relations have been analytically derived by Rumerman [M. L. Rumerman, J. Acoust. Soc. Am. 57, 370–373 (1975)]. This presentation concerns the dispersion of waves in doubly periodic structures, which have received considerably less attention in the literature. The problem analyzed here consists of an infinitely long beam or plate which is attached to two types of substructures. Each type of substructure is characterized in the frequency domain by a complex impedance and is attached to the beam at evenly spaced positions. The presentation will describe the extent to which singly periodic physics prevail and the possibility of creating very wide stop or pass bands by adjusting the parameters of the doubly periodic structure. Ultimately, this work is intended to aid in the design of structures which either confine or release energy near drive-points over very wide frequency bands. [Work supported by NSF.]
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