A compact 3-DoF nonlinearity-tuning motif for multi-direction vibration isolation

This paper introduces a compact 3-DoF structural motif equipped with multiple nonlinear stiffness-tuning mechanisms, developed to address the need for broadband, high-performance vibration isolation in multi-degree-of-freedom (multi-DoF) mechanical systems for multi-direction vibration isolation or suppression. Two quantitative indicators for capturing the quality of nonlinear stiffness and quasi-zero-stiffness (QZS) behavior are proposed to rigorously evaluate both static and dynamic characteristics. The proposed motif achieves precise global and local stiffness shaping in Z-translation, X-translation, and Y-rotation, and can therefore enable the construction of highly tailorable nonlinear restoring-force profiles. Dynamic analyses show that the integrated tuning mechanisms can effectively suppress complex nonlinear responses, including stiffness softening and internal resonances, and result in stable, broadband low-frequency isolation across all three DoFs. The high degree of tunability substantially enhances the feasibility of configuring multi-direction vibration-isolation platforms while maintaining predictable and identifiable dynamic behavior. Three prototyped platforms incorporating two, three, and four motifs are developed, experimentally validated, and benchmarked against established designs. The results consistently demonstrate exceptional adaptability, strong robustness to payload variation, and effective low-frequency isolation across all six DoFs. With these results, this work establishes a new tunable, nonlinear building block for multi-DoF vibration-isolation systems. The proposed 3-DoF motif is demonstrated to be a versatile and experimentally validated foundation with strong relevance to applications in vibration and noise control, structural dynamics, energy harvesting, and advanced robotic and mechatronic design, where multi-directional stiffness tuning is essentially demanded. © 2026 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC license. http://creativecommons.org/licenses/by-nc/4.0/