Water-wave propagation through an infinite array of floating structures

The frequency-domain problem of water-wave propagation through a periodically arranged infinite array of structures is solved using the method of matched asymptotic expansions for both shallow and deep water; the structures are assumed to be small relative to the wavelength and the array periodicity, and may be fixed or float freely. Explicit approximations to the frequencies of propagating modes are obtained, and used to illustrate how the frequencies are affected by geometrical and other parameters.