Periodicity-induced effects and method in vibro-acoustics

The lecture is concerned with the modelling of wave propagation in and vibration of periodic elastic structures. Although analysis of wave-guide 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 lecture 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. This is done with the special attention being paid to eigenfrequencies of a single periodicity cell with various boundary conditions. Another issue addressed in the lecture 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. The concluding part of the lecture is concerned with the numerical implementation of the Floquet theory and the experimental demonstration of periodicity effects. A brief exposition of the Wave Finite Element method and an assessment of its validity range in canonical benchmark problems are presented. The results of experimental studies recently conducted at Aalborg University are reported.