Design of Periodic Acoustic Barriers Using an Evolutionary Topological Optimization Procedure
Résumé
This work proposes a methodology to design periodic acoustic barriers using a topology optimization method. The acoustic problem is modeled using the Helmholtz equation where the barrier is considered rigid and defined as perfectly hard using equivalent material models. The design domain is divided into N periodic cells and the acoustic problem is solved using the finite element method in order to find the acoustic pressure field for closed systems. The optimization problem is defined as the minimization of the average squared pressure in a specific region of the acoustic domain while the volume of the rigid material is reduced. The Bi-directional Evolutionary Structural Optimization (BESO) method is used to solve the optimization problem. Since the BESO is a density-based binary method, it is necessary to calculate the derivative of the average squared pressure with respect to the design variables, whose indicate if a finite element is filled with air (x=0) or rigid material (x=1), where x is the pseudo-density variviable. Then, the periodicity condition is imposed and the implemented algorithm finds the best rigid material distribution in the barrier that minimizes the objective function based on the sensitivity numbers. This study is performed in different sets of frequency ranges and boundary conditions. The obtained results using an periodicity constraint are compared with the case where no periodicity is imposed in order to show the capabilities of the implemented methodology and to allow the investigation of possible band gaps.
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