Coupled Analysis of Acoustic Space and Thin-Plate Vibrations by a Lumped-Mass Model Using Raviart?Thomas Elements
Coupled Analysis of Acoustic Space and Thin-Plate Vibrations by a Lumped-Mass Model Using Raviart?Thomas Elements
复制标题
使用 Raviart?Thomas 元件的集总质量模型对声学空间和薄板振动进行耦合分析
DOI：
10.1142/s259172852250013x
复制
发表时间：
2022
影响因子：
1.9
通讯作者：
Iwamoto Hiroyuki
中科院分区：
文献类型：
--
作者：
Hisano Shotaro;Ishikawa Satoshi;Iwamoto Hiroyuki
机械产品的噪声和振动抑制是一个重要的问题，人们研究了许多方法。特别是，由于机器重量减轻而引起的结构-声学耦合效应不容忽视。在结构-声耦合分析中，常用的是用声压描述声空间，用位移描述结构的有限元法。然而，该方法中的特征值分析需要大量的计算时间，因为质量和刚度矩阵是不对称的。相反，在本文中，我们提出了一个有效的三维声学空间和二维薄板的集中质量模型的耦合分析方法。所提出的建模方法是系统地使用Raviart-Thomas元素。此外，我们提出了一种坐标变换方法，通过减少自由度（DOF）的数量来加速计算。这样，一个对称的特征值问题，没有额外的自由度。数值计算结果证实了该方法的有效性。这种分析方法是特别有效的系统中的声学空间贡献的自由度的大部分，因为声学空间是稀疏的，由于采用边缘元素。
Suppression of noise and vibration in machine products is an important problem, and many methods have been studied. In particular, structural–acoustic coupled effects due to the weight reduction of machines cannot be ignored. In structural–acoustic coupled analysis, the finite-element method in which the acoustic space is described by sound pressure and the structure is described by displacement is often used. However, the eigenvalue analysis in that method takes a great deal of computational time because the mass and stiffness matrices are asymmetric. Instead, in this paper, we propose an efficient coupled analysis method for a three-dimensional acoustic space and a two-dimensional thin plate using a lumped-mass model. The proposed modeling method is derived systematically using Raviart–Thomas elements. In addition, we propose a coordinate transformation method that accelerates the calculations by reducing the number of degrees of freedom (DOF). In this way, a symmetric eigenvalue problem with no extra DOF is derived. The effectiveness of the proposed method is confirmed by numerical calculations. This analysis method is particularly effective for systems in which the acoustic space contributes to the majority of the DOF, since the acoustic space is sparse owing to the adoption of edge elements.