Maximizing attenuation of sound waves preserving air permeability in sonic crystals via topology optimization

The evanescent waves within a bandgap can describe the sound wave attenuation degree. A topology optimization method of designing sonic crystals (SnCs) with maximum sound wave attenuation properties is presented in this paper. The optimization procedure maximized the minimum positive imaginary component of the wave vector at the designated frequency. To ensure that an SnC would maintain adequate air permeability and an acceptable air channel width even when the solid material configuration is highly complex, the virtual temperature method was used in the optimization model along with filtering and threshold projection techniques. The material-field series expansion scheme was adopted to refine the SnC configurations, and the Kriging-based optimization algorithm was utilized to solve the complex problem. Optimization results were obtained for different air channel widths and frequencies, and each optimization process culminated in the establishment of an omnidirectional bandgap of sound waves at the target frequency. For most of the optimization results, the minimum decay contours were approximately circular, which indicates that the optimized SnC structures possessed comparable spatial attenuation properties for sound waves in all directions. Finite element simulations and physical experiments validated the effectiveness of the proposed optimization method of designing air–solid SnCs that exhibit enhanced spatial decay of evanescent waves. These optimized SnCs displayed excellent sound attenuation performance, thereby demonstrating their significant potential for noise-reduction applications.