Nonlinear Dynamics of Bio-Inspired X-Structures: Progress Review

Yulong Gao; Zhijing Wu; Tao Yang; Grzegorz Litak; Marian Wiercigroch; Xingjian Jing

Abstract

Nonlinearities are critical in engineering systems, making their intentional utilization vital for structural design and dynamic analysis. Inspired by animal limb skeletons, X-structures offer a passive, low-cost, and highly adjustable approach to achieving beneficial and controllable nonlinearity in terms of stiffness, damping and inertia, also featured by elegant static and dynamic models for nonlinear analysis, design and prediction with less burden in a trial and error cycle. Since the establishment of foundational principles, relevant studies have been expanded dramatically. This review synthesizes recent advances, tracing the evolution of X-structures from vibration isolation to versatile platforms with complex designs and interdisciplinary integration. In nonlinear stiffness, QZS ranges exceed 85% of total stroke with resonant frequencies below 1 Hz, enabled by contact mechanisms, magnetic compensation, and active modulation. Nonlinear damping has advanced via integration with viscoelastic materials, friction elements, and passive magnetorheological dampers, achieving motion-dependent dissipation that suppresses resonance without deteriorating high-frequency isolation. Nonlinear inertia including several benchmark nonlinear forms is revealed as a third dimension for achieving desired system dynamic response. Architecturally, X-structures have evolved from single-axis isolators to 3-DOF units, 6-DOF Stewart platforms, and hierarchical designs. Interdisciplinary integration has yielded active control with 85% energy savings, metamaterials with 98% energy absorption, and self-powered sensing interfaces. Applications now venture into robotics, spacecraft on-orbit capture, and energy harvesting. This review concludes by identifying persistent challenges including high-dimensional nonlinear modeling, manufacturing precision, and extreme-condition reliability. Future directions focus on digital/intelligent X-structures, cross-scale, and sustainable X-structures. This scalable approach to beneficial nonlinearity will advance safer, greener and more efficient engineering systems.

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