Bio-Inspired Nonlinear Locally Resonant Metamaterial Beam for Low-Frequency Vibration Reduction: Theoretical and Experimental Analysis

Abstract

Inspired by the intricate biomechanics of flea locomotion, a nonlinear locally resonant metamaterial beam has been designed and analyzed for the suppression of low-frequency vibrations. The bandgap structure of the metamaterial is derived using Hamilton's principle, and the theoretical predictions are validated through numerical simulations and finite element analysis. Utilizing COMSOL software alongside the Galerkin method, the dynamic behavior of the metamaterial beam is simulated, with a particular focus on the evolution of bandgaps and the emergence of complex nonlinear phenomena, such as chaos and bifurcation, under varying excitation amplitudes. Results demonstrate that increasing excitation amplitudes lead to significant shifts in the bandgap range, accompanied by increasingly complex nonlinear responses. Furthermore, the impact of geometric asymmetry and the quantity of unit cells on the beam's vibration control capabilities is investigated, revealing that while adding more unit cells enhances vibration suppression, it also introduces more intricate coupling effects. Experimental validation confirms the practicality of this design, offering novel insights into the suppression of low-frequency vibrations and noise.

Keywords: Bio-inspired structure, Metamaterial Beam, Nonlinear Bandgap, Low-Frequency Bandgap Control, Nonlinear Dynamic