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.

使用导波 (GW) 测试技术进行材料和结构无损评估依赖于波色散特性的知识。在研究具有复杂几何形状的流体-固体耦合波导时使用半解析有限元 (SAFE) 方法，可能需要过多的计算工作，尤其是在高频范围内。在本文中，我们展示了一种称为半解析等几何分析 (SAIGA) 的高效计算方法的稳健性，该方法用于计算与声流体耦合的 3D 各向异性弹性波导中的波色散。这种方法基于使用非均匀有理 B 样条 (NURBS) 作为几何表示以及压力/位移场近似的基础函数。将所得结果与使用传统 SAFE 方法得出的结果进行比较，该方法使用拉格朗日多项式。结果表明，对于计算 GW 的离散度，使用 SAIGA 比使用具有相同形状函数阶数的传统 SAFE 导致更快的收敛速度。对于浸入流体中的空心棱柱结构，使用高阶 NURBS（例如，$磷=8$) 特别有效，因为它只需要几个元素即可实现与 SAFE 获得的解具有相同精度的解，后者需要多达五倍的自由度数。此外，由于 NURBS 的平滑特性，可以显着改善流固界面法向位移的连续性，这表明 SAIGA 在评估流固耦合系统中的 GW 形状模式方面优于 SAFE。