The role of material and geometric nonlinearities and damping effects in designing mechanically tunable acoustic metamaterials

Elastomeric material (as rubber) can be used to design the mechanically tunable acoustic metamaterial (AM) with reversible and repeatable deformation utilizing its geometric and material nonlinearities introduced by the large deformation. Meanwhile, an elastomeric material usually possesses the inherent damping effect, which will complicate the dynamic responses of AMs. In this paper, taking the AMs comprising different resonating elements (include soft elastomeric coating and hard core) embedded into an elastomeric matrix with a square array of circular holes of varying size as examples, we try to reveal the roles of material and geometric nonlinearities and damping effects (Rayleigh damping and linear viscoelastic damping) in the process of elastic wave manipulation by calculating the band structures and the transmittances of the finite-sized AM structures with and without damping. The numerical results indicate that the geometrical nonlinearity of the AM (mainly from matrix and coating) and the nonlinearity of coating material can simultaneously manipulate the locally resonant and Bragg scattering band gaps. Still, the nonlinearity of the matrix material mainly affects the Bragg scattering band gaps. The analysis of geometrical parameters indicates that the AM with holes of large size, thin coating, and a hard core of large radius benefits enhance its bandgap?s tunability. The transmittances of the finite-sized AMs without damping drastically reduce in the frequency ranges of band gaps, which agree well with the numerical predictions of band gaps. The damping effect in the elastomeric matrix and coating materials can lead to the appearance of a new band region and the changes in the position and width of the band region. However, excessive damping in the coating and matrix materials suppresses the elastic wave propagation in the AM structures so that it is difficult to identify the band regions from the transmittance spectrums. The above researches demonstrate the roles of these influencing factors above in the process of elastic wave manipulation. They can help us design new AMs to meet the unique needs of noise and vibration control.

Automated summary

This study investigates the roles of material and geometric nonlinearities and damping effects in the process of elastic wave manipulation in mechanically tunable acoustic metamaterials (AMs). It was found that geometrical nonlinearity and coating material nonlinearity can manipulate locally resonant and Bragg scattering band gaps, while the matrix material nonlinearity mainly affects the Bragg scattering band gaps. Large holes, thin coating, and large core radius in AM structures enhance their bandgap?s tunability. Furthermore, damping effects alter the position and width of band regions, making it challenging to identify band regions from transmittance spectra.