Re-Entrant Auxetic Structures for Vibration Isolation: A Comprehensive Review of the Associated Design Principles, Dynamic Behaviors, and Industrial Application Potential

Structural vibration is a significant problem created by industrial machinery (i.e., compressors, motors, and generators) that can negatively affect the performance of equipment as well as the overall integrity of buildings or structures. Although various vibration isolation technologies are available for reducing the structural vibrations produced by machinery, most of these methods have inherent limitations because of a lack of sufficient damping at lower frequencies relative to that observed higher frequency ranges. The purpose of this paper is to evaluate the use of advanced vibration isolation technologies using re-entrant auxetic structures that are characterized by their negative Poisson ratios. Through a comprehensive evaluation of 92 published articles within the areas of auxetic unit cell design and topology optimization, the mechanics of materials related to negative Poisson ratios, energy absorption mechanisms, vibration reduction in sandwich structures, and dynamic analyses of frame and plate systems, this review presents the current state-of-the-art re-entrant auxetic structures that can be employed as vibration isolation technologies for machine foundations. The analysis reveals that compared with standard structures, re-entrant geometry-based structures exhibit high levels of energy absorption (up to a 767% increase over the standard designs), along with superior vibration isolation characteristics. A hybrid approach utilizing combinations of geometric modification, multimaterial fabrication, and foam filling is identified as the most promising method for optimizing the relationship between stiffness and damping capacity. Additionally, advancements in additive manufacturing have made it possible to fabricate complex auxetic geometries that were previously unfeasible via traditional processes. In addition to identifying significant research gaps, such as scaling up to large macroscale steel implementations, this paper presents general design guidelines for future vibration isolation systems for industrial machinery.