A lightweight helical plate elastic metamaterial for low-frequency vibration suppression

Abstract

In this paper, we propose a lightweight helical plate elastic metamaterial with gradient springs for low-frequency vibration suppression, leveraging the local resonance effect of helical gradient springs to achieve both an ultra-wide complete bandgap and a bending wave bandgap in the low-frequency range. Theoretical analysis and finite element simulations reveal the critical role of helical gradient springs in stiffness tuning and the local resonance mechanism. By integrating multiple pitches and radii, the design offers greater flexibility in stiffness adjustment compared with conventional single-pitch and single-radius springs. This enables the realization of negative stiffness characteristics and allows more flexible optimization of the bandgap range and performance. Moreover, adjusting the number of helical gradient spring arrays further enhances the bandgap width, system stability, and lightweight properties. After determining suitable geometric parameters through parametric analysis, the proposed structure achieves bending wave bandgaps from 29 Hz to 454 Hz and a complete bandgap from 72 Hz to 436 Hz, both representing ultra-wide low-frequency ranges. Additionally, intrinsic modal analysis and transmission spectrum characterization elucidate the physical mechanisms of bandgap formation and validate the design. This helical gradient spring-based local resonance structure addresses the challenges posed by the high mass and volume of traditional phononic crystals, offering a promising approach for engineering applications in low-frequency acoustic isolation metamaterials.