Abstract
In this paper we present a comprehensive study on the multi-objective optimization of two-dimensional porous phononic crystals (PnCs) in both square and triangular lattices with the reduced topology symmetry of the unit-cell. The fast non-dominated sorting-based genetic algorithm II is used to perform the optimization, and the Pareto-optimal solutions are obtained. The results demonstrate that the symmetry reduction significantly influences the optimized structures. The physical mechanism of the optimized structures is analyzed. Topology optimization combined with the symmetry reduction can discover new structures and offer new degrees of freedom to design PnC-based devices. Especially, the rotationally symmetrical structures presented here can be utilized to explore and design new chiral metamaterials.
Highlights
Understanding, modulating and controlling the wave propagation in periodic composite structures, known as phononic crystals (PnCs),[1] are important to design the novel acoustic-based devices.It is essential to determine the wave dispersion through Bragg’s scattering or local resonances to achieve a range of spectra (ω-space), wave vector (k-space), and phase properties (ø-space).[2]
In this paper we present a comprehensive study on the multi-objective optimization of two-dimensional porous phononic crystals (PnCs) in both square and triangular lattices with the reduced topology symmetry of the unit-cell
In this paper, based on the multi-objective topology optimization, we present a comprehensive study about the effect of the symmetry reduction of the unit-cell on the optimized porous PnCs
Summary
Understanding, modulating and controlling the wave propagation in periodic composite structures, known as phononic crystals (PnCs),[1] are important to design the novel acoustic-based devices.It is essential to determine the wave dispersion through Bragg’s scattering or local resonances to achieve a range of spectra (ω-space), wave vector (k-space), and phase properties (ø-space).[2]. Some researchers have been conducted and focused on topology optimization of photonic crystals (PtCs),[26,27] PnCs28–33 and phoxonic crystals (PxCs).[34] Recent studies have shown that the topology optimization can greatly enhance the performance of PnCs, for bulk waves,[28,29,30,31,32,33,34] and for surface waves[35] and plate waves.[36] because of the high computational effort and the complex optimization procedure, most topology optimizations of bandgap maximization assumed that the unit-cell has a primary high-symmetry.[26,27,28,30,31,33,34,36] Sigmund and Hougaard[26] discovered some surprisingly simple geometric properties of optimal PtCs based on the optimization of highly symmetrical square and triangular latticed structures. They showed how topology optimization can be used to effectively design
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