The Location of Pass and Stop Bands of an Infinite Periodic Structure Versus the Eigenfrequencies of Its Finite Segment Consisting of Several “Periodicity Cells”

Abstract

Abstract. On the classical example of a rod (membrane, string)

Free vibrations of finite periodic structures in pass- and stop-bands of the counterpart infinite waveguides

“…Any additional (to the set for a single cell) eigenfrequency is located in the pass-band, and its magnitude is the same for the fixed-fixed and free-free boundary conditions. This result agrees with the findings reported in [13] for a monocoupled system and in [16] for a string bearing point masses of two types.…”