Topology optimization of programable quasi-zero-stiffness metastructures for low-frequency vibration isolation

Quasi-zero-stiffness (QZS) isolators have been demonstrated to realize low-frequency vibration isolation without loss of static stiffness. However, most previous designs are based on spring-driven links, cam-roller structures, or two-phased network structures resorting to complex assembling components, other than compact and integrative single-phased solid structures. In this paper, we propose a topology optimization scheme to inversely design QZS metastructures with smooth boundaries for customized nonlinear force-displacement curves. The optimization model is established based on the distinguishing features of the QZS force-displacement curve. The boundary smoothing procedure is introduced in the genetic algorithm to improve the convergence and stability of topology optimization. The designed metastructures are verified to have robust QZS feature. A linear relationship between the platform force and the initial modulus of the base material is obtained. We numerically show the high-static-low-dynamic performance, the load bearing, and even full band vibration isolation capabilities of the designed QZS metastructures. In addition, experiments are performed to verify the QZS feature of the designed metastructure. The inverse design scheme developed in this paper can efficiently design QZS isolators suitable for different scenarios with great flexibility. The metastructures with smooth boundaries are obtained so that postprocessing is not required before manufacture. The proposed inverse-design methodology paves the way for low-frequency vibration isolation using compact solid structures without any positive or negative stiffness units.