Extraction of dispersion curves for waves propagating in free complex waveguides by standard finite element codes

• Published in: Ultrasonics Vol. 51; no. 4; pp. 503 - 515
• Main Authors: Sorohan, Ştefan, Constantin, Nicolae, Găvan, Mircea, Anghel, Viorel
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2011; Elsevier
• Subjects: Acoustics; Dispersion curves; Dispersions; Eigenvalues; Exact sciences and technology; Extraction; Finite element method; Fundamental areas of phenomenology (including applications); Guided wave propagation; Mathematical analysis; Mathematical models; Physics; Propagation; Transduction; acoustical devices for the generation and reproduction of sound; Wave propagation; Waveguide finite element methods; Waveguide finite element methods; Guided wave propagation; Dispersion curves; Modal analysis; Guided wave; Travelling wave; Waveguide; Modeling; Standards; Wave dispersion; Natural frequency; Finite element method; Aliasing; Eigenvalue problem; Propagation mode
• ISSN: 0041-624X; 1874-9968
• DOI: 10.1016/j.ultras.2010.12.003

► A method for dispersion curves extraction via common finite element codes is presented. ► It is based on modal analysis for a representative part of the waveguide structure. ► The main idea consists of changing the length of the structure representative part. ► Complete graphical representations of guided waves are possible. This paper presents a fast and reliable method, for obtaining all the range of dispersion curves for wave propagation usually used in practice, by numerical simulation only, via common commercial finite element codes. Essentially, the method is based on a simple and robust approach, consisting in a few series of modal analyses for a representative part of the inspected structure. In this way, for different wave lengths, one can find the mode shapes and corresponding natural frequencies by solving some real, symmetric and well numerically conditioned eigenvalue problems. The method allows the extraction of propagating modes only and, in spite of not producing continuous dispersion curves, it is not susceptible to aliasing effects, as some similar methods are. Additionally, complete graphical representations of guided waves are possible with some minor calculus effort.