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

The existence of frequency stop-bands, in which transmission of the vibro-acoustic energy is impossible, suggests that the periodic 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. A hierarchy of four mathematical models is considered. In each case, special attention is paid to eigenfrequencies and eigenmodes of a single periodicity cell with appropriate boundary conditions. The influence of the amount of periodicity cells in a finite compound structure on its eigenfrequency spectn.im is analyzed. Several features common for the considered models are found and discussed in the context of the existing knowledge on the subject. (C) 2015 Published by Elsevier Ltd.