Analysis of eigenfrequencies of finite periodic structures in view of location of frequency pas- and stop-bands

Analysis of wave-guide properties of infinite periodic structures is a well establish research subject. The existence of frequency stop-bands, in which transmission of the vibro-acoustic energy is impossible, suggests that these structures may be used for vibro-isolation. In any technical application, however, only a finite segment of such a structure can be used. This paper is concerned with comparison of the eigenfrequency spectra of finite periodic structures with location of stop-bands for their infinite counterparts. Special attention is paid to eigenfrequencies of a single periodicity cell with various boundary conditions. Two classical models of periodic structures are considered, for which closed form solutions are obtained and analyzed. The regular and irregular eigenfrequencies of periodicity cells and finite periodic structures are identified, and the eigenmodes are compared.