Distribution Optimization for Acoustic Design of Porous Layer by the Boundary Element Method
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ORIGINAL PAPER
Distribution Optimization for Acoustic Design of Porous Layer by the Boundary Element Method Yanming Xu1 · Wenchang Zhao1 · Leilei Chen2 · Haibo Chen1 Received: 27 November 2019 / Accepted: 29 February 2020 © Australian Acoustical Society 2020
Abstract In this work, we develop an optimization approach to optimize the distribution of porous material layer inside cavity. The optimization seeks to improve the absorbing effects of the porous material, decreasing the noise level at regions of interest or increasing the sound energy dissipated by the porous material. To achieve the preset optimization aim, two different objective functions are accordingly defined. The acoustic absorption characteristics of porous materials are numerically described using the Delany–Bazley–Miki empirical model and modeled by the admittance boundary conditions in the boundary element analysis. Based on the solid isotropic material with penalization method, an admittance interpolation scheme is established between the element admittance and artificial element density. This transforms the discrete optimization into a continuous optimization problem, which can be solved by a gradient solver with the sensitivity information. As a key treatment in this study, we develop a fast sensitivity analysis approach based on an adjoint variable method and the fast multipole method to calculate the sensitivities of the objective function with respect to a large number of design variables. Finally, we validate the proposed optimization approach through a cabin example. Keywords Topology optimization · Porous material · Boundary element method · Adjoint variable method · Fast multipole method
1 Introduction Porous material has been proven to be an efficient tool to absorb sound energy and decrease the noise level inside vehicles [1] and buildings [2]. Even in outside environment, it also helps to decrease the sound reflection and yield a lower noise level, e.g., the sound barrier [3,4]. Considering various industrial limits including expenses, laying porous material over some specific regions is typically preferred. Thus, it is highly desired to generate a distribution of porous layer under given constraints which absorbs noise the best. This demand finally consists in the distribution optimization problem, which can be achieved by the topology optimization
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Leilei Chen [email protected]
1
CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, Anhui, People’s Republic of China
2
College of Architecture and Civil Engineering, Xinyang Normal University, Xinyang 464000, Henan, People’s Republic of China
techniques. Topology optimization was first introduced by Bendsøe and Kikuchi [5] for structural optimization. It can generate holes in structures flexibly to decrease the weights, maximize the first natural frequency, etc. Many researchers also introduce these techniques into the acoustic design, such as reducing the sound
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