Harnessing inclusions to tune post-buckling deformation and bandgaps of soft porous periodic structures

The emergence of phononic crystals paves a new way for manipulating elastic waves in structures for their particular bandgap properties. In this paper, the two-dimensional soft porous periodic structures that can be filled with hard inclusions are considered. Both numerical simulations and experiments are conducted to study the effects of inclusions on the buckling modes, post-buckling deformations, and band structures in soft porous periodic structures. It is found that either the number or the arrangement (i.e. filling pattern) of the inclusions has a great influence on the bandgap characteristics. Meanwhile, the material damping affects the wave propagation in soft phononic crystals significantly in the high frequency range. Compared with the unfilled soft porous structure, the sensitivity of the post-buckling deformation to the initial geometrical imperfections can be significantly reduced for the structure filled with inclusions. This means the post-buckling deformation could develop robustly. Further numerical study indicates that the bandgaps can be tuned in a versatile and reversible way when the structure undergoes a large deformation. A more fruitful manner to tune the bandgaps therefore can be achieved by changing the filling pattern of inclusions along with dramatically deforming the structure. The work provides a useful reference for the design of tunable phononic switches and acoustic filters.