In this paper, we present an approach to model the propagation of high-frequency elastic guided waves in solid or hollow cylinders. This formulation requires only discretization of the radial direction, whereas the circumferential direction is approximated via a truncated Fourier series, and the axial direction is described analytically. The model is extended to allow applying arbitrary non-symmetric loads $f(r,\theta )$ on the flat cylinder surface. Efficiency is increased by a proposed methodology to limit the number of Fourier coefficients and by the implementation of hierarchical shape functions to dynamically adjust discretization with respect to frequency. Results are validated against conventional finite element applications, demonstrating the accuracy of the model and a reduction of the computing time by three orders of magnitude. Additionally, we apply a matrix function solution for the scaled boundary finite element method leading to a linear solution in the static case.

在本文中，我们提出了一种对固体或空心圆柱体中高频弹性导波传播进行建模的方法。该公式仅要求径向离散化，而圆周方向则通过截短的傅里叶级数来近似，而轴向则通过分析来描述。扩展了模型以允许施加任意非对称载荷$F（\mathrm{[R}，\theta ）$在平坦的圆柱表面上。通过提出的方法来限制傅立叶系数的数量，以及通过实现分层形状函数来动态调整关于频率的离散化，可以提高效率。通过常规的有限元应用对结果进行了验证，证明了模型的准确性并将计算时间减少了三个数量级。此外，我们将矩阵函数解应用于比例边界有限元方法，从而在静态情况下得出线性解。