Periodicity-induced effects and methods in vibro-acoustics

The paper is concerned with the modelling of wave propagation in and vibration of periodic elastic structures. Although analysis of waveguide properties of infinite periodic structures is a well establish research subject, some issues have not yet been fully addressed in the literature. The aim of the paper is to illustrate these issues in simple examples and to discuss possible applications and generalisations. First, the eigenfrequency spectra of finite periodic structures are compared with the location of stop-bands for their infinite counterparts. 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 spectrum is analyzed. Several features are found and discussed in the context of the existing knowledge on the subject. Another issue addressed in the paper is an influence of the corrugation shape and amplitude on the broadness and location of the stop- and pass-bands in an infinite periodic structure. Explicit asymptotic formulae for the stop band borders are given and the topology of the stop band pattern is explained. Transient dynamics of a periodic rod is analysed numerically and the difference in structural response when excitation is done in either stop- or pass bands is demonstrated. The results of experimental studies recently conducted at Aalborg University are reported.