Inertial amplified resonators for tunable metasurfaces

In this work, we propose an inertial amplified resonator (IAR) as a building block of a tunable locally resonant metasurface. The IAR consists in a mass–spring resonator coupled with two inerters, realized by two inclined rigid links connected to an additional mass. The IAR has a static behaviour equivalent to that of a standard mass–spring oscillator whereas its dynamic response can be controlled by means of the geometrical configuration and mass of the inerters. We derive the dynamic amplification factor and the base force of the IAR for an imposed harmonic motion and perform a parametric study to unveil its peculiar dynamics. Next, we use an effective medium approach to derive the closed-form dispersion law of a metasurface consisting of IARs coupled to a semi-infinite elastic substrate. We show that the IAR enriches the dynamics of the metasurface providing the ability (1) to shift its bandgap frequency spectrum without changing the mass and stiffness of the resonators, (2) to design single frequency or multi-frequency (metawedges) metasurfaces, (3) to obtain a high-frequency behavior typical of an added dead mass layer (i.e., non-resonant), which confers to the metasurface additional filtering properties.