Mobilities of periodic structures in terms of asymptotic modal properties

The natural frequencies of periodic structures lie in distinct frequency bands and become densely spaced when the number of periodic segments is large. This paper shows that within such frequency bands the structure has modal properties with asymptotic characteristics. This feature of periodic structures is used to develop an asymptotic integral expression for the mobility function. The asymptotic theory provides an alternate view of periodic structures that complements existing wave and transfer matrix based methods.