Design of a metastructure for vibration isolation with quasi-zero-stiffness characteristics using bistable curved beam

This work designs and analyzes a metastructure-based vibration isolation model to improve small-scale equipment's isolation effectiveness under low-frequency excitations. The feature of the proposed model is the high static and low dynamic stiffness characteristics, also called quasi-zero-stiffness (QZS), possessed by the metastructure under vertical load. The metastructure consists of four parallelly arranged unit cells, and the QZS property is realized in each unit cell by the snap-through behavior of the cosine beam system and the bending-dominated behavior of semicircular arches. The static characteristics of the metastructure are studied analytically and numerically and validated with experimental results. Based on the static analysis results, the dynamic equation of the proposed metastructure is set up in the form of Duffing's equation. The harmonic balance method is used to calculate the frequency response and motion transmissibility of the metastructure at steady state for a harmonic load. The time and frequency responses under the sinusoidal base excitation are examined analytically and numerically, and their results are compared. The simulation results revealed that the proposed QZS metastructure obtains lower transmissibility and wider effective isolation range compared to the equivalent linear model. The parametric study shows that in the low-frequency excitation region, the motion transmissibility increases with decreasing damping ratio, whereas for the effective isolation range, the motion transmissibility increases with increasing damping ratio. Finally, stability analysis is performed to study the unstable region in the frequency response curve. The parametric study indicates that the unstable region reduces with the increase in damping ratio and remains unaffected with varying excitation amplitude.

Automated summary

This paper introduces a metastructure-based vibration isolation model with high static and low dynamic stiffness properties to enhance isolation effectiveness of small-scale equipment under low-frequency excitations. The quasi-zero-stiffness (QZS) effect is achieved through the snap-through behavior of cosine beam systems and bending-dominated behavior of semicircular arches within each unit cell. Analytical and numerical studies as well as experimental validation confirm the static and dynamic characteristics of the proposed metastructure, showing lower transmissibility and wider isolation range compared to a linear model. The parametric study reveals that motion transmissibility decreases with decreasing damping ratio in the low-frequency region, while increasing damping ratio leads to wider effective isolation range. Stability analysis shows the unstable region in the frequency response curve reduces with higher damping ratio and is independent of excitation amplitude.