Design of tunable pneumatic metamaterials for low-frequency vibration control

For addressing the limitations of traditional elastic metamaterials in opening wide bandgaps below 100 Hz, a tunable pneumatic metamaterial plate with airbag local resonators is proposed. Utilizing the characteristics of airbags, such as small volume, large load-bearing capacity, easy stiffness adjustment, and the ability to provide multi-directional restoring forces, a structured low-stiffness local resonator with a certain load-bearing capacity is designed. By varying the gauge pressure of the airbag, the bandgap can be moved toward lower frequencies, thereby achieving a broad low-frequency vibration suppression capability for various wave propagations. The low-frequency vibration bandgap characteristics of the tunable pneumatic metamaterial are analyzed and verified by applying the finite element method. The results illustrate that this tunable pneumatic metamaterial can attenuate bending waves in the range of 22-121 Hz by adjusting the air pressure. Moreover, increasing the gauge pressure will not only shift the complete bandgap toward lower frequencies but also significantly expand the bandwidth of the complete bandgap. For instance, increasing the gauge pressure from 0 to 50 kPa reduces the opening frequency of the complete bandgap from 36 to 22 Hz while enhancing the relative bandwidth from 0.52 to 0.85. Extending from this, a parametric study was conducted to examine the impact of the structural parameters of airbag-type resonant units on bandgap evolution, summarizing the general principles for achieving wide low-frequency bandgaps. Finally, the bandgap characteristics of the tunable pneumatic metamaterial are confirmed through the frequency response function of a finite periodic structure.