Topology Optimization of Magnetorheological Smart Materials Included PnCs for Tunable Wide Bandgap Design

Design and application of tunable phononic crystals (PnCs) are attracting increasing interest due to their promising capabilities to manipulate acoustic and elastic waves effectively. This paper investigates topology optimization of the magnetorheological (MR) materials including PnCs for opening the tunable and wide bandgaps. Therein, the bandgap tunability of the PnCs is achieved by shear modulus variation of MR materials under a continuously changing applied magnetic field. The pseudo elemental densities representing the bi-material distribution inside the PnC unit cell are taken as design variables and interpolated with an artificial MR penalization model. An aggregated bandgap index for enveloping the extreme values of bandgap width and tunable range of the MR included smart PnCs is proposed as the objective function. In this context, the sensitivity analysis scheme is derived, and the optimization problem is solved with the gradient-based mathematical programming method. The effectiveness of the proposed optimization method is demonstrated by numerical examples, where the optimized solutions present tunable and stably wide bandgap characteristics under different magnetic fields. The tunable optimized PnCs based device that can provide a wider tunable bandgap range is also explored.