Unraveling interactions of resonances for tunable low frequency bandgap in multiphase metamaterials under applied deformation

Abstract Metamaterial with various degrees of bandgap tunability is an emerging area in manipulating elastic wave transmission characteristics for next generation phononic devices. Although several attempts are made employing multi-fields such as magnetic, electric and thermal etc., mechanical deformation based tunable bandgap is a major interest. However, achieving tunability in terms of broadening or terminating the bandgap in locally resonant acoustic metamaterial (LRAM) remains as challenging tasks. In this work, we propose LRAM by integrating a two-dimensionally periodically arranged square unit cells consisting of soft coated hard inclusion embedded in a polymer scaffold. We develop computational framework to simulate the low frequency bandgap of unit cell under external deformation. At first quasi-static analysis of unit cell has been performed to find static displacement field under prescribed deformation. Further, utilizing Bloch-Floquet wave analysis for the periodic unit cell and finite element based numerical scheme, an eigenvalue problem is formulated to predict dispersion response within irreducible Brillouin zone (IBZ). Analyzing the symmetry group of the unit cell under deformed state for a series of loading, we extract the bandgap responses. Moreover, we illustrate tunable bandgap at low frequency regimes for different inclusion shapes and sizes. To correlate extension and suppression of bandgap under the applied deformation, evolution of local resonances are described with vibration mode shapes.