An analytical solution PML technique for the guided waves in surrounding rockbolts based on the Legendre orthogonal polynomials

When studying the propagation characteristics of guided waves in surrounding rock structures, the mathematical model employs artificial boundary truncation of a specific region rather than representing the actually infinite surrounding rock structures. Consequently, wave reflections at the artificial boundaries will inevitably introduce errors. An ideal solution is to construct a Perfectly Matched Layer (PML) to absorb the boundary waves. The existing PML techniques are predominantly developed based on the finite difference method and the finite element method, which have shortcomings such as poor convergence, inadequate boundary absorption performance, and limited adaptability. In this paper, an analytical solution PML technique for guided wave propagation in surrounding rockbolts is proposed. By utilising Legendre orthogonal polynomials, this technique enables the analytical calculation of the complete solution, encompassing wave speeds and attenuations, thereby significantly enhancing computational efficiency. The construction form and the optimal layer thickness of the PML are thoroughly analysed. Moreover, guided wave experiments on the surrounding rockbolt structure are conducted to validate the theoretical results. Finally, a brief introduction is given on the scalability of the proposed method for other infinite structures.