The X-structure/mechanism approach to beneficial nonlinear design in engineering

• Published in: Applied mathematics and mechanics Vol. 43; no. 7; pp. 979 - 1000
• Main Author: Jing, Xingjian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022; Springer Nature B.V; Department of Mechanical Engineering,City University of Hong Kong,Kowloon Tong,Hong Kong,China
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Design analysis; Diamond machining; Diamonds; Dynamic response; Energy harvesting; Fluid- and Aerodynamics; Geometric nonlinearity; Inertia; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Mechanical components; Partial Differential Equations; Quadrilaterals; Resonant frequencies; Stiffness; Structural design; Vibration control; Vibration damping; O322; 70K50; nonlinear inertia; nonlinear stiffness; 70K30; nonlinear damping; vibration
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-022-2862-6

Nonlinearity can take an important and critical role in engineering systems, and thus cannot be simply ignored in structural design, dynamic response analysis, and parameter selection. A key issue is how to analyze and design potential nonlinearities introduced to or inherent in a system under study. This is a must-do task in many practical applications involving vibration control, energy harvesting, sensor systems, robotic technology, etc. This paper presents an up-to-date review on a cutting-edge method for nonlinearity manipulation and employment developed in recent several years, named as the X-structure/mechanism approach. The method is inspired from animal leg/limb skeletons, and can provide passive low-cost high-efficiency adjustable and beneficial nonlinear stiffness (high static & ultra-low dynamic), nonlinear damping (dependent on resonant frequency and/or relative vibration displacement), and nonlinear inertia (low static & high dynamic) individually or simultaneously. The X-structure/mechanism is a generic and basic structure/mechanism, representing a class of structures/mechanisms which can achieve beneficial geometric nonlinearity during structural deflection or mechanism motion, can be flexibly realized through commonly-used mechanical components, and have many different forms (with a basic unit taking a shape like X/K/Z/S/V, quadrilateral, diamond, polygon, etc.). Importantly, all variant structures/mechanisms may share similar geometric nonlinearities and thus exhibit similar nonlinear stiffness/damping properties in vibration. Moreover, they are generally flexible in design and easy to implement. This paper systematically reviews the research background, motivation, essential bio-inspired ideas, advantages of this novel method, the beneficial nonlinear properties in stiffness, damping, and inertia, and the potential applications, and ends with some remarks and conclusions.