Phononic crystal design: maximizing and customizing bandgaps using parameterized level set method-based topology optimization

Abstract

Phononic crystals are metamaterials capable of controlling the propagation of elastic waves through the periodic arrangement of unit cells. This study introduces a two-step method for the precise customization of bandgaps in phononic crystals, allowing for the attainment of specified bandwidths within a defined frequency range, in contrast to previous research primarily focused on maximizing bandwidth. The approach involves constructing two objective functions to maximize and tailor bandgaps effectively using a parameterized level set method with the level set band. Furthermore, an alternative scheme is innovatively proposed to achieve a smooth transition from the first stage to the second stage. This innovative strategy stabilizes the optimization process while maintaining the merits of the level set method in generating clear and smooth structures. Additionally, a multiple eigenvalue problem is addressed to obtain sensitivity information. Numerical simulations conducted in COMSOL demonstrate that wave propagation in the optimized structures is successfully confined within targeted maximum and designated bandgaps for both waveguide and energy harvesting models. A notable feature of this method is the independence from initial designs, as similar optimized structures can be achieved from uniformly or randomly distributed initial configurations in the bandgap maximization process. This research provides new insights into the design of phononic crystal bandgaps.

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