Abstract
In this study, we estimate an efficient layout of sound absorbing materials in three-dimensional spaces. For this purpose, we use damping contributions with eigenvectors as weight coefficients. Three-dimensional finite Elements of absorbing materials are modeled using a complex effective density and a complex bulk modulus of elasticity. By expanding the solution of complex eigenvalue problem with a small parameter related to damping, we derive the first order approximate equations of motion with respect to the small parameter. From these equations, the contribution of each element to modal damping is derived in consideration of multiple modes. The sound absorbing materials are arranged in three-dimensional spaces according to this contribution and by considering the components of eigenvectors at the evaluation points as the weight coefficients. The effectiveness of this method is verified using an expanded chamber.
