Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

We propose a topology optimisation approach that can effectively account for the size effect of periodic composite plates to determine the optimal material distribution for achieving the largest bandgap width. The approach is based on the modified couple stress continuum and uses the relative bandgap width as the objective function, with volume constraints defined as the constraint function. The material properties are represented by the solid isotropic material with penalisation (SIMP) interpolation model, and the optimality criteria (OC) algorithm is employed to update the design variables. To address the significant size effect of the microplate structure, we use the modified couple stress continuum to model the dynamic behaviour of the unit cell. The Melosh-Zienkiewicz-Cheung (MZC) finite element is employed to ensure nodal C1 continuity and achieve high-order elasticity with respect to inter-element continuity. Our results demonstrate that the proposed topology optimisation methodology is capable of effectively designing optimal unit cell configurations that account for size effect and significantly improve the bandgap width. We also investigate the impact of thickness and volume limitations on the optimised unit cell configuration. The obtained results suggest that the proposed topology optimisation framework is a promising approach for designing unit cell geometries with the account for size effect.