Design and Analysis of Nonlinear-Stiffness-Based Metastructures for Vibration Isolation Applications

Abstract

The increasing demand of small-scale precision instruments for application in microscopes, balancing and scaling instruments, robot grippers, etc., requires a robust vibration isolation device to effectively isolate unwanted low-frequency excitations which can affect the functionality and accuracy of the system. The vibration isolation is generally achieved using active and passive control system; however, the cost limitation of active isolator leads to the wide application of passive isolators. The effective frequency range of a linear passive vibration isolator is often limited by the static stiffness required to support a load. This limitation is improved in this study by incorporating nonlinearity in the form of stiffness to obtain quasi-zero-stiffness (QZS) characteristics for enhancing vibration isolation in lowfrequency ranges. The QZS characteristics works on the high static and low dynamic stiffness (HSLDS) mechanism, where the low dynamic stiffness leads to low-natural frequency of system with high static stiffness for supporting the mass. This requirement of obtaining QZS behavior using a deformable material that can effectively dissipate undesired vibrations in low-frequency ranges paved the way for the application of mechanical metamaterials in the vibration isolation field. Mechanical metamaterials are artificially engineered composites designed by varying the geometrical configuration to obtain the required properties. In this research work, the unit cell of metamaterials exhibiting QZS characteristic is achieved using two techniques- (i) designing negative and positive stiffness elements separately and combining them to form a single unit cell exhibiting QZS, and (ii) designing single element metamaterial exhibiting QZS. Four different designs are proposed in this study. The first design is a combination of bistable inclined beams and semicircular arches. The second design is the combination of a bistable cosine beam system and semicircular arches. The third design is the tunable single-beam element for fixed-guided boundary conditions. The fourth design is the tunable bottom reinforced cosine beam element for fixed-fixed boundary conditions. All the developed designs are modeled in SOLIDWORKS and fabricated using a 3D Printing technique. The deformable elements are printed using Thermoplastic polyurethane (TPU) material, and stiffer walls are printed using Polylactic acid (PLA). The static study is performed analytically, numerically using finite element simulation software (ANSYS) and validated using experimental results. The designed unit cells are then arranged in a parallel direction to form a cubic-like structure, which acts as a platform to mount the QZS payload on top and mitigate the incoming vibration due to base excitation. Based on the static results, the nonlinear force-displacement relation is obtained by curve-fitting the experimentally obtained results using seventh-order nonlinear regression analysis. Further, the dynamic behavior of the proposed designs is studied by deriving the approximate nonlinear dynamic equation and solved using the Harmonic Balance Method (HBM) technique. The obtained frequency response and transmissibility curve for all the designs show bending to the right depicting the jump phenomenon and validating the nonlinear behavior. A parametric study is also performed by varying excitation amplitude and damping ratio; the results suggest that the structure should be designed for low excitation amplitude with optimum damping. The stability of the steadystate response is also studied to explore the unstable region of the proposed designs. Further, a dynamic experiment is performed on all four designs using an electrodynamic shaker setup to validate the proof-of concept. The results suggest a low transmissibility peak, low resonance frequency, and wide isolation range for the QZS payload compared to the linear payload. A comparative study is performed to study the isolation effectiveness by designing all the proposed metamaterials for a common QZS payload. Finally, this research presented a proof of concept where the mass can be customized based on the frequency requirement. It is also observed that the QZS characteristic gets influenced by the geometrical parameters, which can be used to tune the design as per the mass requirement for the practical application.