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

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.

Frequency comb in a parametrically modulated micro-resonator

In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical modulation.When the electrostatically actuated rhombic micro-resonator is modulated axially by a low-frequency periodic excitation,a comb-like vibration response with few equidistant positioned fingers in the frequency domain is observed.The finger spacing of frequency comb response is exactly consistent with modulation frequency and the number and amplitude of the fingers can be tuned by modulation strength.A mixed frequency comb with extra comb fingers is further generated when the resonator is modulated simultaneously by two different low-frequency excitation signals.By adjusting the relation of the two modulation frequencies,unequal spacing frequency combs are achieved for the first time,which leads to a more flexible tunability of the comb spacing for different applications.Theoretical analysis based on the dynamic model well explains the corresponding observations.