Low-frequency tunable locally resonant band gaps in acoustic metamaterials through large deformation

Acoustic metamaterials have subwavelength characteristics and hence they can be used for the low-frequency noise and vibration control. Usually, acoustic metamaterials have constant material properties and their dynamic responses are difficult to tune once manufactured, resulting in a fixed and narrow working band and limiting the number of possible applications. In this paper, by mean of elastomeric matrix with a square array of circular holes and resonating elements (including elastomeric coating and resonating mass), we design a new kind of tunable acoustic metamaterials with resonating elements embedded into the elastomeric matrix. Under equibiaxial compression, the deformation induced geometry and material nonlinearities of the elastomeric matrix and coating are intentionally exploited to tune the dynamic responses of acoustic metamaterials. We numerically investigate the stress–strain curves of the elastomeric matrix and coating, and the evolution of band gaps during deformation. Furthermore, the transmissions of the finite-sized acoustic metamaterial structures in the undeformed and deformed configurations are calculated to verify the tunability of the band structures. The numerical results indicate the locally resonant and Bragg scattering band gaps can be simultaneously controlled by deformation. The primitive low-frequency locally resonant band gap at 0.197∼0.226 is shifted and widened to 0.168∼0.364 in the deformed configuration and the width of band gap is increased 7.76 times, which provide a useful guideline for the low-frequency noise and vibration control.