Modeling of programmable low-frequency isolator with quasi-zero stiffness metamaterials

Vibration isolation is crucial for scientific instruments that require precise measurements and are highly sensitive to disturbances, especially in microgravity environments, such as ultracold atom interferometry and electrostatic space accelerometers. To minimize micro-oscillations at low frequencies, attention has been drawn toward isolators with quasi-zero stiffness (QZS) and nonlinear properties. Specifically, structures such as curved beams or thin-walled domes that exhibit the potential for elastic buckling have emerged as promising candidates for creating QZS isolators, in contrast to conventional approaches that rely on combining springs with positive and negative stiffness in a larger occupied volume. The idea of mechanical metamaterials, featuring programmable properties, presents a novel approach to achieving QZS characteristics. This paper introduces a new mechanical metamaterial design that arranges QZS units in a Cartesian pattern using curved beams and establishes the dynamic model under base excitation. Initially, the QZS unit, based on a Euler beam with a cosine configuration, is modeled and the analytical force–displacement relationship is constructed by controlling buckling only at low-order modes. The dynamic response of a single QZS unit is analyzed using the harmonic balance method. Subsequently, periodic metastructures with both horizontal and vertical patterns are created and the geometric parameters and overall response of the QZS metamaterials are evaluated. The impact of structural damping, excitation amplitude, and prescribed displacement on the transmission characteristics is also examined. Validation of the analytical results is carried out using the finite element method. In conclusion, this work presents a novel approach to designing QZS vibration isolators that utilize elastic buckling structures for achieving low-frequency isolation.