Nonlinear Dynamics of Quasi-Zero Stiffness Metamaterials for Advanced Vibration Isolation: A Computational and Experimental Investigation of Novel QZS Design

Abstract

This research addresses the inherent limitations of linear isolators in achieving effective low-frequency vibration isolation by focusing on engineered nonlinearity. The primary objective is to design, computationally analyze, and experimentally validate novel 3D metamaterial unit cells exhibiting Quasi-Zero Stiffness (QZS) behavior, a hallmark of advanced nonlinear systems. The novelty resides in developing distinct QZS designs: a monolithic structure and a composite system integrating negative stiffness mechanisms with a positive stiffness component, strategically leveraging nonlinearity to overcome conventional linear constraints. The methodology employs comprehensive computational mechanics, utilizing SolidWorks for modeling and ANSYS Workbench for rigorous numerical simulations to characterize the highly nonlinear static force-displacement responses. These analyses were crucial in confirming the vital QZS region, which is characterized by High Static Low Dynamic (HSLD) stiffness. The metamaterial's nonlinear restoring force equation was empirically derived through the least squares method, providing a robust analytical tool for dynamic analysis. To ensure geometric stability and enhanced payload capacity in a practical system, unit cells were integrated into a metastructure, which subsequently underwent compression testing to validate its nonlinear QZS characteristics. Dynamic performance was meticulously assessed via the Harmonic Balance Method for frequency response and the Perturbation Method for stability analysis. Key observations, including characteristic jump phenomena in the amplitude-frequency response, emphatically demonstrate the system's inherent and beneficial nonlinearity. This work underscores the efficacy of computational modeling coupled with experimental validation in advancing nonlinear vibration control.