The semi-analytical finite element (SAFE) method is widely used for studying properties of guided waves along composite waveguides. However, evaluating the modes associated to high wave numbers requires important mesh refinements and may significantly increase the computational cost. This paper presents a semi-analytical isogeometric analysis (SAIGA) to calculate the dispersion relation of functionally graded or multilayer plates coupling with fluids. High-order elements based on non-uniform B-splines (NURBS) basis functions are used. Several numerical examples are then studied for different problems in order to assess the efficiency of proposed method: (i) homogeneous plates; (ii) functionally graded plates; (iii) composite plates (with strong contrast of rigidity between layers); (iv) fluid-immersed plates. The results obtained are compared with the ones derived from analytical approaches and by the conventional SAFE method using Lagrange polynomials. For all cases, the dispersion curves evaluated by using enriched-NURBS basis functions achieve a significant better precision than using conventional Lagrangian functions (for the same number of degrees of freedom or the same order of shape functions), especially for the higher modes. The continuity of the stress shape modes at the interfaces is also shown to be much improved by using SAIGA.

中文翻译：

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浸入流体中的功能梯度板中波色散的半解析等几何分析

半解析有限元 (SAFE) 方法广泛用于研究沿复合波导的导波特性。然而，评估与高波数相关的模式需要重要的网格细化，并且可能会显着增加计算成本。本文提出了一种半解析等几何分析（SAIGA）来计算与流体耦合的功能梯度或多层板的色散关系。使用基于非均匀 B 样条 (NURBS) 基函数的高阶元素。然后针对不同问题研究了几个数值示例，以评估所提出方法的效率：(i) 均质板；(ii) 功能分级板；(iii) 复合板（层间刚性对比强烈）；(iv) 浸液板。将获得的结果与从分析方法和使用拉格朗日多项式的传统 SAFE 方法得出的结果进行比较。对于所有情况，使用富集 NURBS 基函数评估的色散曲线比使用传统拉格朗日函数（对于相同数量的自由度或相同阶数的形状函数）获得了显着更好的精度，尤其是对于更高的模式。通过使用 SAIGA，界面处应力形状模式的连续性也得到了很大改善。使用富集 NURBS 基函数评估的色散曲线比使用传统拉格朗日函数（对于相同数量的自由度或相同阶数的形状函数）获得了明显更好的精度，尤其是对于更高的模式。通过使用 SAIGA，界面处应力形状模式的连续性也得到了很大改善。使用富集 NURBS 基函数评估的色散曲线比使用传统拉格朗日函数（对于相同数量的自由度或相同阶数的形状函数）获得了明显更好的精度，尤其是对于更高的模式。通过使用 SAIGA，界面处应力形状模式的连续性也得到了很大改善。