Wave dispersion analysis of three-dimensional vibroacoustic waveguides with semi-analytical isogeometric method

Abstract

Material and structural non-destructive evaluations using guided-wave (GW) testing techniques rely on the knowledge of wave dispersion characteristics. When studying coupled fluid–solid waveguides having complex geometries using the semi-analytical finite element (SAFE) method, an excessive computational effort may be required, especially at high-frequency ranges. In this paper, we show the robustness of an efficient computational approach so-called the semi-analytical isogeometric analysis (SAIGA) for computing the wave dispersion in 3D anisotropic elastic waveguides coupled with acoustic fluids. This approach is based on the use of Non-Uniform Rational B-splines (NURBS) as the basis functions for the geometry representation as well as for the approximation of pressure/displacement fields. The obtained results are compared with the ones derived from using the conventional SAFE method which uses Lagrange polynomials. It is shown that for computing the dispersion of GWs, using SAIGA leads to a much faster convergence rate than using the conventional SAFE with the same shape function’s order. For hollow prismatic structures immersed in fluids, using high-order NURBS (e.g, p=8) is particularly efficient as it only requires a few elements to achieve solutions having the same precision as the ones obtained by SAFE which requires up to five times of number of DOFs. Moreover, the continuity of normal displacement at fluid–solid interfaces could be significantly improved thanks to the smoothness feature of NURBS, showing the advantage of SAIGA over SAFE in the evaluation of the shape modes of GWs in coupled fluid–solid systems.