Physics-informed discrete element modeling for the bandgap engineering of cylinder chains

Abstract

We propose an efficient method to build a simple discrete element model (DEM) that accurately simulates the oscillation of a continuum beam. The DEM is based on the Timoshenko beam theory of slender cylindrical members and their corresponding wave dynamics in assembly. This physics-informed DEM accounts for multiple vibration modes of the constituting beam elements in wide frequency ranges. We construct various DEMs mimicking cylinder chains and compare their wave dynamics with those measured in experiments to validate the proposed method. Furthermore, we construct a graded woodpile chain of slender cylinders. We experimentally and numerically investigate the frequency bandgaps of the system and demonstrate the possibility of constructing a wide bandgap by consecutively superposing multiple stop bands generated from cylinders of various lengths. This system is highly efficient in blocking propagating waves by leveraging the vibration isolation effect stemming from the local resonance of the cylinders. The proposed DEM method can be useful for investigating and designing complex vibration systems in an efficient and accurate manner. Moreover, the design approach of manipulating the frequency bandgap can be exploited for developing vibration filters and impact mitigation devices.