Tunable phononic bandgap materials designed via topology optimization

Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet-Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion-deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.

Automated summary

Topology optimization is applied to design mechanically tunable phononic bandgap materials. A periodic media model is considered, and dispersion relations are obtained by analyzing a single unit cell subjected to Floquet-Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to modify its geometry and dispersion. The dispersion-deformation relation is tuned by solving a topology optimization problem using nonlinear programming.