Modeling and analysis of a metamaterial beam with electromechanical resonators

Abstract

Structural and acoustic metamaterials explore the generation of bandgaps, which are frequency regions with high levels of wave attenuation, to control vibration and noise on a structure. Metamaterials are usually obtained by periodicity, where the main structure is composed of many repeated sub-elements, called cells. In this context, this paper investigates the design of local resonances by coupling a mechanical structure to an electrical circuit comprised of a combination of capacitance, inductance, and electrical resistance. The system considering is a beam in free-free configuration, and the electromechanical coupling is obtained using an electromagnetic transducer made of a permanent magnet that moves through a coil wire. The Euler Bernoulli beam is modeled using the dynamic stiffness method, and local impedances attached at the periodic arrangements along the beam are added at the dynamic stiffness matrix. Tunable bandgaps are obtained by adding electromechanical resonators to the modeled beam and are analyzed.