Modular modeling approach for FDM printed structures and piezo disks for metamaterial design

Abstract Research in metamaterials has recently gained interest in the field of noise and vibration control. The ability of creating band gap zones with minimum added mass is the main feature behind its success. In addition, the use of 3D printed parts, particularly the Fused Deposition Modeling (FDM), offers a practical solution for manufacturing parts with intricate shapes that are challenging for standard manufacturing processes, which is the case of many structural metamaterials. The combination of this concept with smart materials can further improve performance, providing the means to overcome typical issues. From a design perspective, the problem with coupling rises, as both the mechanical and electrical responses relies on the load circuit and on the mechanical properties of the smart elements. Therefore, the modeling of such structures is a rather complex task, for it involves multiphysical simulations of systems with complex geometries and typically a high number of degrees of freedom. Hence, this paper presents a direct approach for modeling and simulating smart metamaterials using a state-space formulation, which allows the modular coupling of electromechanical resonators manufactured by FDM. The numerical results are compared to experimental data obtained with unit cells prototypes embedded with piezoelectric elements and connected with a tunable shunt electric circuit. The good agreement between test and simulated data validates the design procedure.