Single-phase continuum soft elastic metamaterial design based on variable boundary conditions through topology optimization

Abstract

Wide bandgaps are challenging to achieve in the low-frequency regime. Herein, we develop a mode conversion-based method that considers variable boundary conditions. Based on this method, a soft single-phase continuum elastic metamaterial is designed. Unlike the previous method, which needs to balance design trade-offs such as bending and shearing stiffness, mass, and moment of inertia, this method provides a pure bending stiffness-based design with frequency-dependent boundary conditions. Furthermore, for weight reduction, we perform topology optimization for the unit cell components (i.e., the plate and mass block). The boundary conditions of the plate can be regarded as either being clamped on one end at a low frequency or clamped on both ends at a high frequency. The fundamental eigenfrequency and bandgap are thus maximized. Finally, we experimentally validate the proposed design and successfully achieve a lightweight metamaterial with wide bandgaps at low frequencies.