Free-Wave Propagation Relationships of Second-Order and Fourth-Order Periodic Systems

摘要

This report develops an analytical expression for the determinant of two diagonally-indexed, full matrices when they are zero. These matrices originate from second- and fourth-order periodic system theory. The partial differential equations of these systems are solved using a series solution and are converted into closed-form analytical expressions The denominators of these expressions are zero when free-wave propagation is present, and these denominators are equated to the determinants of the system matrices derived from a second analytical method. This process develops a relationship between frequency and wavenumber that is explicit for free-wave propagation in these systems. Two examples are included to illustrate this new method.