Mechanically Tunable Solid/Solid Phononic Crystals Through the Rearrangement of Hard Scatterers Controlled by the Deformation of Periodic Elastomeric Matrixes

Abstract

The fixed band gap characteristic of passive phononic crystals (PCs) is possible to limit their applications in engineering. To overcome this shortcoming, inspired by the tunable mechanism of the spider silks, a new class of tunable PCs comprising periodic scatterers and periodic elastomeric matrix are proposed to effectively tune the band gaps and directionality of propagating waves. The orientation and arrangement of hard scatterers are controlled by the deformation of the periodic elastomeric matrix to enhance the tunability of their dynamic responses. According to this idea, PCs with differently shaped and arranged cylindroid scatterers are designed. Through introducing the multiple scatterers into the periodic elastomeric matrix, the scattering coupling effect between them is enhanced. The simulation results indicate that the orientation and arrangement of the scatterers could be altered continuously during deformation. During deformation, the number, position, and width of band gaps can be effectively tuned due to the geometric nonlinearity of the matrix and the rearrangement of multiple scatterers. The transmissibility of finite-sized structures without damping decreases significantly in the frequency ranges of band gaps. However, introducing the damping into the matrix material significantly enhances the ability to suppress elastic wave propagation but makes it difficult to identify the band gaps from the transmittance spectrum. The directionality of wave propagation can be also effectively tuned. In the low-frequency range, such as the first two phase constant surfaces, the phase and group velocity profiles and the anisotropy indexes are calculated and the results indicate that the deformation makes the wave propagation more isotropic. The schemes presented in this paper provide an effective approach to tune the band gaps of the solid/solid PCs and open avenues for the design of tunable PCs.