Investigation of dissipative effects in periodic structures

Abstract

Periodic structures are composed of identical substructures or cells that are connected end to end in a similar manner, with their periodicity characterized by geometrical or material discontinuity. Due to their periodicity, these structures present special dynamic characteristics, acting as a mechanical filter for elasticwaves propagating in specific frequency intervals, known as stop bands or band gaps. Most of previous investigations disregard energy dissipation effects. However, engineering structures dissipate energy by various mechanisms when they vibrate, for instance, due to friction at connections, opening and closing of material microcracks or internal material friction when deformed. Energy dissipation, also known as vibration damping, can alter frequency band structures, thus modifying the behavior of wave propagation. The purpose of this dissertation is to analyze the effects of damping on the attenuation of elastic waves in periodic structures when subjected to forced harmonic excitation. The viscous and hysteretic damping models are investigated when applied to four different configurations of periodic structures, with and without internal resonators, modeled as lumpedmass-spring-damper subsystems. Also, these damping models will also be applied for periodic continuous structures, the composite rod and the sandwich beam. For each configuration, the equations of motion of the unit cell are derived, and the transfer matrix method is implemented to model the elastic wave propagation along the periodic structure and to obtain the propagation constant that allows the construction of dispersion curves. Different levels of damping are considered, and their effects in pass bands, stop bands and frequency response functions are analyzed. It is shown that the dispersion curves are altered when adding damping in periodic structures, increasing the attenuation level in the pass band regions. It is also shown that in the case of viscoelastic damping, the band gaps are shifted in the frequency axis.