Topology optimization of array of split-ring resonators in two-dimensional acoustic waveguide for low-frequency transmission problems

Abstract

This work focuses on the topology optimization of an array of split-ring resonators to achieve nearly zero transmission in the low-frequency regime ranging from 500 Hz to 1000 Hz in 2D waveguide, under the condition of normal-incident plane wave and based on a homogenization scheme known as the Effective Medium Approach (EMA). The EMA transforms each individual resonator defined by its outer radius (rout), neck thickness (h), and the slit width (d), into a homogenous medium characterized by frequency-dependent physical parameters. The transmission coefficient (Tcoeff) of the array can thus be easily evaluated without relying on computationally expensive Finite Element (FE) software. Two optimization algorithms, namely “Sequential Quadratic Programming (SQP)” and “Genetic Algorithm (GA),” have been implemented to the abovementioned topological parameters with sum of Tcoeff being the objective function to minimize. Accuracy of the results has also been validated using software COMSOL Multiphysics® and the satisfactory level of accuracy has proven this approach to be a more efficient and time-saving method to conduct topology optimization of split-ring resonators in low-frequency regime. Moreover, it is noteworthy that the optimized dimensions of resonators are over 20 times smaller than the wavelength in the low frequency range where almost-zero transmission is achieved.