Bandgap properties and multi-objective optimization of double-cone pentamode metamaterials with curved side

Abstract Pentamode metamaterials (PM) have a promising application in noise reduction fields. In this paper, in order to improve the acoustic modulation capability of PMs, several novel curve PMs are proposed by replacing the straight sides of conventional PMs with curves. At first, the elliptic PMs (EPMs) with various unit cell arrangements (i.e., triangular, square, and hexagonal) are designed, respectively, and their bandgap properties are studied numerically in detail. The EPM with hexagonal unit cell arrangement (EPMH) presents better comprehensive bandgap properties in the EPMs. Subsequently, sinusoidal and power curves are introduced into the EPMH respectively to explore the influences of curve types on bandgap properties. The results show that the bandgap properties improvement of EPMH is higher in comparison with introducing other curves, and the reasons behind these improvements are carefully disclosed in combination with the spring-mass system. Finally, to further improve the bandgap properties of EPMH, a high accuracy Kriging model is constructed according to both the Latin hypercube design and double-point infilling. The Pareto optimal solution sets are determined using a non-dominated sorting genetic algorithm (NSGA-II), and the final compromise solution is gained by employing a fitness function. The bandwidths of phononic bandgap and single mode bandgap, and the total bandwidth of optimized EPMH are increased respectively by about 114.5, 4.3, and 7.7 times than those of the conventional straight side PMs. This investigation provides a fresh strategy for designing PMs with excellent bandgap properties.