Finite Difference and Finite Element Methods
Finite Difference and Finite Element Methods
复制标题
有限差分和有限元方法
DOI：
10.1007/978-3-7091-2482-6_5
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
T. Johansen
中科院分区：
文献类型：
--
作者：
U. Kristiansen;M. Dhainaut;T. Johansen
介绍了有限差分和有限元技术在振动声学问题中的应用。概述了这两种方法的基本思想和数学描述，并举例说明了这种数值技术的潜力。通过研究弹性板封闭腔体的谐振频率和强迫响应，说明了有限差分法的有效性。亥姆霍兹和基尔霍夫板方程是离散化的起始点。还演示了如何使用理查德森外推法来最小化数值计算中的误差。对于有限元法，首先通过解决一个简单的声道问题来说明这一思想。它进一步展示了如何建立基于厚板理论的振动板模型，以及弹性固体中的波传播模型。通过计算不同板腔几何形状的共振频率，再次说明了板腔与声场的耦合。考虑的另一个例子是海底圆柱体的激励。由于多孔材料的声阻尼在噪声控制中具有重要意义，本文给出了多孔弹性材料的有限元模型（Biot理论）。通过对多孔材料构成的墙壁的声音传播的研究，说明了该模型的使用！夹在两块弹性板之间的。
Applications of the finite difference and finite element techniques to vibroacoustic problems are presented. The basic ideas and the mathematical descriptions are outlined for both of the methods and examples are given to demonstrate the potential of such numerical techniques. The finite difference method is illustrated by studying the resonant frequencies and forced response of a cavity closed by an elastic plate. The Helmholtz and Kirchhoff plate equations are the starting points for the discretization. It is also demonstrated how the Richardson extrapolation method can be used to minimize the errors in the numerical calculations. For the finite element method, the idea is first illustrated by solving a simple acoustic duct problem. It is further shown how models can be made for vibrating plates based on a thick plate theory, and for wave propagation in elastic solids. The coupling of plates and acoustic fields is again illustrated by calculations of resonant frequencies for different plate cavity geometries. Another example considered is the excitation of a cylinder on the ocean floor. As the acoustic damping by porous materials is of importance in noise control, it is shown how a finite element model can be made for a porous elastic material (Biot theory). Use of the model is illustrated by a study of sound transmission through a wall made up by a porous materia! sandwiched between two elastic plates.