Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach

Q1 Mathematics

Journal of Computational Acoustics Pub Date : 2017-03-31 DOI:10.1142/S0218396X17500308

V. Hernández, J. Estrada, E. Moreno, S. Rodriguez, A. Mansur

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引用次数: 7

Abstract

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenval...

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基于等几何方法的波浪沿板结构传播问题的数值求解

沿大型结构传播的超声导波作为一种无损评估方法具有很大的潜力。在这种情况下，获得取决于结构横截面的色散曲线是非常重要的。在本文中，我们使用半解析方法（SAFEM）和基于B样条函数的等几何方法计算了无限各向同性板状结构的色散曲线。SAFEM方法导致了一系列取决于波数的广义特征值问题。对于一个规定的波数，这个问题的解包括节点位移矢量和导波的频率。在这项工作中，将B样条形状函数获得的结果与二次拉格朗日形状函数的数值SAFEM解进行了比较。强调了等几何方法的优点，包括位移场分量的光滑性和求解相应广义特征值的计算成本。。。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Acoustics 物理-声学

CiteScore

3.90

自引率

0.00%

发文量

审稿时长

4.5 months

期刊介绍： Currently known as Journal of Theoretical and Computational Acoustics (JTCA).The aim of this journal is to provide an international forum for the dissemination of the state-of-the-art information in the field of Computational Acoustics. Topics covered by this journal include research and tutorial contributions in OCEAN ACOUSTICS (a subject of active research in relation with sonar detection and the design of noiseless ships), SEISMO-ACOUSTICS (of concern to earthquake science and engineering, and also to those doing underground prospection like searching for petroleum), AEROACOUSTICS (which includes the analysis of noise created by aircraft), COMPUTATIONAL METHODS, and SUPERCOMPUTING. In addition to the traditional issues and problems in computational methods, the journal also considers theoretical research acoustics papers which lead to large-scale scientific computations. The journal strives to be flexible in the type of high quality papers it publishes and their format. Equally desirable are Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational acoustics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research in which other than strictly computational arguments may be important in establishing a basis for further developments. Tutorial review papers, covering some of the important issues in Computational Mathematical Methods, Scientific Computing, and their applications. Short notes, which present specific new results and techniques in a brief communication. The journal will occasionally publish significant contributions which are larger than the usual format for regular papers. Special issues which report results of high quality workshops in related areas and monographs of significant contributions in the Series of Computational Acoustics will also be published.