Parametric Analysis and Multi-Objective Optimization of Pentamode Metamaterial

Abstract

Pentamode metamaterial (PM) has enormous application potential in the design of lightweight bodies with superior vibration and noise-reduction performance. To offer systematic insights into the investigation of PMs, this paper studies the various effects (i.e., unit cell arrangement, material, and geometry) on bandgap properties through the finite element method (FEM). With regards to the influences of unit cell arrangements on bandgap properties, the results show that the PM with triangular cell arrangement (PMT) possesses better bandgap properties than the others. The effects of material and geometry on bandgap properties are then explored thoroughly. In light of the spring-mass system theory, the regulation mechanism of bandgap properties is discussed. Multi-objective optimization is conducted to further enhance the bandgap properties of PMT. Based on the Latin hypercube design and double-points infilling, a high-accuracy Kriging model, which represents the relationship between the phononic bandgap (PBG), single mode phononic bandgap (SPBG), double-cone width, and node radius, is established to seek the Pareto optimal solution sets, using the non-dominated sorting genetic algorithm (NSGA-II). A fitness function is then employed to obtain the final compromise solution. The PBG and total bandgap of PMT are widened approximately 2.2 and 0.27 times, respectively, while the SPBG is narrowed by about 0.51 times. The research offers important understanding for the investigation of PM with superior acoustic regulation capacity.