Isogeometric Shape Optimization of Metamaterials for Noise Reduction

Low-frequency noise reduction remains a challenge especially in medical, aerospace, communication, and military fields. High-frequency sound is usually reduced by using soft, porous materials that absorb the sound wave energy. Adopting this approach for low-frequency noise reduction may result in the thickness of absorbing material well beyond 1 meter. Hence, it is quite impractical and costly to use conventional noise absorption methods due to the long wavelength of low-frequency sound. In order to reduce the size of absorbing materials, it is necessary to enable subwavelength properties such that the sound-absorbing material is much smaller than the wavelength of sound.  Recent studies have shown that metamaterials can be utilized for noise reduction more effectively than conventional materials while considerably reducing the thickness of the noise reduction medium. It is also possible to design sparse metamaterials that allow the passage of fluids and yet absorb the sound energy. It is the structural design of the metamaterial that provides the desired properties not found in naturally occurring material such as negative refractive index, negative permeability, etc. and offers the possibility of operation in sub-wavelength frequencies. However, the metamaterial designs are often specific to one frequency and not tunable for practical applications. In this work, we designed and optimized a novel metamaterial by combining Isogeometric analysis with parameter and shape optimization. The numerical analysis captured the behavior of the acoustic wave inside and around the metamaterial surrounded by ducts. Differential Evolution algorithm was used to perform optimization by moving the control points defining the shape of the metamaterials. Differential Evolution was selected due to its speed and rate of success in finding the global optimum. First, the objective of the optimizations, which was defined as the acoustic pressure at the end of the duct, was decreased by modifying the size parameters of the Wunderlich curves employed. Next, shape optimization was performed to achieve maximum noise reduction by deviating from the Wunderlich curve. Only three control points were used to perform shape optimization. As a result, we were able to reduce the acoustic pressure inside the duct by over 99% for targeted frequencies of 400 Hz, 500 Hz, and 600 Hz. By designing and optimizing metamaterial cells for each frequency, we also demonstrate the tunability of our design. The sparsity and tunability of our design allow numerous applications for biomedical, aerospace, military, and communication applications. We are currently working to design sparse and tunable metamaterials for energy harvesting applications.