Design of metadevices based on isotropic materials for eigenfrequency recovery in lightened structures

This work presents a novel approach for the design of metadevices conceived to recover a prescribed set of the natural eigenfrequencies of a structure lightened by machining arbitrary shape holes, using classical topology optimization (TO) techniques. This TO metadevice design (TOMD) is performed by minimizing the error of an eigenfrequency recovery task, using the finite element method (FEM) as an analysis tool, ensuring manufacturability via the solid isotropic material with penalization (SIMP) approach with Heaviside filtering to reduce intermediate-density areas. The spatial variation of mechanical properties derives from the macroscopically distinguishable dual material distribution obtained from the TOMD problem. The methodology was first tested on lightened thin steel plates and then extended to a real-world 3D mechanical component with additional mechanical performance testing. In all cases, the optimized metadevice yielded lower error in recovering eigenfrequencies compared to the lightened component without the metadevice. Furthermore, the metadevice generally achieved further mass reduction, demonstrating its potential for lightweight design while restoring its original eigenfrequencies.