Modeling and analysis of gradient metamaterials for broad fusion bandgaps

A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial.The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically.The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps.Finally,the effects of the design parameters on multiple bandgaps are discussed.The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.

Multi-layer quasi-zero-stiffness meta-structure for high-efficiency vibration isolation at low frequency

An easily stackable multi-layer quasi-zero-stiffness(ML-QZS)meta-structure is proposed to achieve highly efficient vibration isolation performance at low frequency.First,the distributed shape optimization method is used to design the unit cel,i.e.,the single-layer QZS(SL-QZS)meta-structure.Second,the stiffness feature of the unit cell is investigated and verified through static experiments.Third,the unit cells are stacked one by one along the direction of vibration isolation,and thus the ML-QZS meta-structure is constructed.Fourth,the dynamic modeling of the ML-QZS vibration isolation metastructure is conducted,and the dynamic responses are obtained from the equations of motion,and verified by finite element(FE)simulations.Finally,a prototype of the ML-QZS vibration isolation meta-structure is fabricated by additive manufacturing,and the vibration isolation performance is evaluated experimentally.The results show that the vibration isolation performance substantially enhances when the number of unit cells increases.More importantly,the ML-QZS meta-structure can be easily extended in the direction of vibration isolation when the unit cells are properly stacked.Hence,the ML-FQZS vibration isolation meta-structure should be a fascinating solution for highly efficient vibration isolation performance at low frequency.

Modeling and analysis of the friction in a non-linear sliding-mode triboelectric energy harvester

Friction plays a pivotal role in the sliding-mode triboelectric energy harvester(TEH),which not only enables the charge transfer between two dielectrics,but also influences the energy harvesting performance by affecting the dynamic response of the TEH.How to evaluate the effects of the friction on TEHs is important for optimizing TEHs in engineering practices.In order to analyze the effects of the friction on the dynamic response and evaluate the energy harvesting performance ofTEHs,the paper models the friction of a devised non-linear TEH based on the Coulomb friction model and the Macro-slip friction theory.The TEH equips a pair of magnets,rendering a switching between the bistability and the monostability by tuning the distance between two magnets.The dynamic model of the non-linear TEH is established by the extended Hamilton principle.The effects of friction in slidingmode TEH are dissected in detail.The influences of parameters on both the mechanical and electrical responses are also systemically studied to explore an optimal energy harvesting performance in the low-frequency range.This work provides a guideline for designing and accurately analyzing a sliding-mode TEH.