Frequency- and Amplitude-Dependent Transmission of Stress Waves in Curved One-Dimensional Granular Crystals Composed of Diatomic Particles

Abstract

We study the stress wave propagation in curved chains of particles (granular crystals) confined by bent elastic guides. We report the frequency- and amplitude-dependent filtering of transmitted waves in relation to various impact conditions and geometrical configurations. The granular crystals studied consist of alternating cylindrical and spherical particles pre-compressed with variable static loads. First, we excite the granular crystals with small-amplitude, broadband perturbations using a piezoelectric actuator to generate oscillatory elastic waves. We find that the linear frequency spectrum of the transmitted waves creates pass- and stop-bands in agreement with the theoretical dispersion relation, demonstrating the frequency-dependent filtering of input excitations through the diatomic granular crystals. Next, we excite high-amplitude nonlinear pulses in the crystals using striker impacts. Experimental tests verify the formation and propagation of highly nonlinear solitary waves that exhibit amplitude-dependent attenuation. We show that the wave propagation can be easily tuned by manipulating the pre-compression imposed to the chain or by varying the initial curvature of the granular chains. We use a combined discrete element (DE) and finite element (FE) numerical model to simulate the propagation of both dispersive linear waves and compactly-supported highly nonlinear waves. We find that the tunable, frequency- and amplitude-dependent filtering of the incoming signals results from the close interplay between the granular particles and the soft elastic media. The findings in this study suggest that hybrid structures composed of granular particles and linear elastic media can be employed as new passive acoustic filtering materials that selectively transmit or mitigate excitations in a desired range of frequencies and amplitudes.

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