Individual And Interactive Mechanisms For Localization And Dissipation In A Mono-Coupled Nearly-Periodic Structure

Abstract

The effect of structural damping on the dynamics of periodic and disordered nearly periodic systems is investigated. A chain of single-degree-of-freedom oscillators coupled by springs is used as a basic model of a mono-coupled periodic system. The dynamic response of the system to a harmonic excitation at the leftmost oscillator is considered. For a system with damping but no disorder (i.e., identical oscillators), an exact expression for the rate of exponential spatial amplitude decay is retrieved. It is found that the decay rate due to damping in a periodic system has a frequency dependence similar to that of the decay rate due to disorder in an undamped nearly periodic system. The magnitudes of the decay rates due to only damping or disorder are compared, and the concept of equivalent damping due to disorder is introduced. For systems with both disorder and damping, perturbation methods are used to find approximate expressions for the decay rate in the cases of strong and weak coupling between oscillators. It is shown that if the coupling is strong, the decay rates due to damping and disorder simply add up to produce the overall decay rate, and the effect of damping dominates. If the coupling is weak, however, the effects of damping and disorder on the overall decay are comparable in magnitude, and they interact in a more complicated manner.