Abstract
A study has been made of free wave propagation in doubly-periodic structures consisting of the repetition of a basic unit which is a periodic structure in itself. It has been found that the propagation zones in these structures are distributed in a pattern which is to some extent doubly-periodic in nature. The bounding frequencies of the pattern zones can be identified with the natural frequencies of the multi-span structure constituting the basic unit with various end conditions. The analysis has been simplified by introducing a direct and a cross-chain-receptance for the multi-span structure and by utilizing the concept of the equivalent internal restraint. The natural frequencies of a finite, doubly-periodic structure are then easily obtained from the propagation constant-frequency parameter diagram.
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