An Experimental Investigation of Acoustic Band Gaps and Localization in Granular Elastic Chains

Abstract

We assembled a chain composed of a periodic arrangement of aluminum and steel spheres encased in a 4-rod polycarbonate holder with tunable static precompression applied by means of a lever actuated system. To excite periodic oscillations we perturbed the chain with a piezo-stack actuator driven by both continuous and finite bursts of a sinusoidally varying periodic signal. The amplitude of the periodic signal ranged from linear to strongly nonlinear regimes. We report the tunability of the frequency range for the band gap edges as a function of the material parameters, chain geometry and stress conditioning. We analyze the data by means of force-time plot and Fast Fourier Transforms (FFT). We observe a dramatic reduction of the transmitted wave amplitude for harmonic excitations with fundamental frequencies within the gap. The application of both continuous and short bursts of perturbation allows for observation of different dynamic phenomena at selected frequency ranges (in particular close to the lower optical branch edge). By varying the amplitude of the dynamic excitation (and therefore the level of the nonlinearity present in the system) we seek localized discrete breathing modes and surface instabilities. The comparison between continuum theory, discrete numerical modeling and experiments show a qualitative agreement and provide fundamental understanding for future investigation and numerous engineering applications. The challenges and considerations involved with the construction of an experimental system capable of capturing and leveraging on the described phenomena will be detailed.

Additional details