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Scaled Boundary Finite Element Method for Mid-Frequency Acoustics of Cavities
Journal of Theoretical and Computational Acoustics ( IF 1.9 ) Pub Date : 2021-03-08 , DOI: 10.1142/s2591728521500018
Sundararajan Natarajan 1 , Chandramouli Padmanabhan 1
Affiliation  

In this paper, a semi-analytical framework, based on the scaled boundary finite element method (SBFEM), is proposed, to study interior acoustic problems in the mid-frequency range in two and three dimensions. The SBFEM shares the advantages of both the finite element method (FEM) and the boundary element method (BEM). Like the FEM, it does not require the fundamental solution (Green’s function) and similar to the BEM only the boundary is discretized, thus reducing the spatial dimensionality by one. The solution within the domain is represented analytically, while on the boundary, it is represented by finite elements. Although different boundary representations are possible, only the Lagrangian description is investigated in this paper. The proposed framework is validated using closed-form solutions, and direct comparisons are made with the conventional FEM based on Lagrangian description; this will be demonstrated using two 2D cavities from literature as well as one 3D cavity. The improved accuracy and reduced computational time can be attributed to the semi-analytical formulation combined with the boundary discretization.

中文翻译:

腔体中频声学的标度边界有限元法

本文提出了一种基于尺度边界有限元法(SBFEM)的半解析框架,用于研究二维和三维中频范围内的内部声学问题。SBFEM 具有有限元法 (FEM) 和边界元法 (BEM) 的优点。与 FEM 一样,它不需要基本解(格林函数),并且与 BEM 类似,只是边界被离散化,从而将空间维度减少一维。域内的解用解析表示,而在边界上,它用有限元表示。虽然不同的边界表示是可能的,但本文只研究了拉格朗日描述。建议的框架使用封闭式解决方案进行验证,并与基于拉格朗日描述的常规有限元法进行了直接比较;这将使用文献中的两个 2D 型腔和一个 3D 型腔来演示。提高的准确性和减少的计算时间可归因于结合边界离散化的半解析公式。
更新日期:2021-03-08
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