Enhanced low-frequency band gap of nonlinear quasi-zero-stiffness metamaterial by lowering stiffness coupling

For existing multi-dimensional quasi-zero-stiffness (QZS) metamaterials, the stiffness coupling is always ignored in the design procedure, which restricts them from achieving the desired QZS property and thus opening quite low-frequency band gaps. To deal with this issue, this paper proposes a new type of two-dimensional (2D) nonlinear QZS metamaterial, whose elastic elements are optimized to lower the stiffness coupling. Main optimization steps include: Firstly, a crank-slider mechanism is optimized based on the pseudo-rigid body (PRB) method. Secondly, by equivalent small-length flexural pivots (SLFPs), the optimized crank-slider mechanism is converted to a lumped compliance configuration. Thirdly, to reduce stress concentration, the lumped compliance configuration is improved into a distributed compliance one, and by optimizing the distributed compliance configuration, the final multi-segment variable thickness beam can be obtained. Dynamic analyses of the 2D QZS metamaterial constructed by these optimized beams are conducted by theoretical derivations and finite element (FE) simulations. Results show that the stiffness of the proposed 2D resonator is as low as 0.45 N/mm. Based on such an ideal QZS property, a low-frequency locally resonant (LR) band gap can be opened. Meanwhile, the low-frequency vibration attenuation is verified by experiments. Therefore, this paper provides a guideline for the design of low-frequency band gaps by lowering the stiffness coupling.