This paper introduces the first attempt to employ a localized meshless method to analyze time-harmonic acoustic wave propagation on curved surfaces with periodic holes/inclusions. In particular, the generalized finite difference method is used as a localized meshless technique to discretize the surface gradient and Laplace-Beltrami operators defined extrinsically in the governing equations. An absorbing boundary condition is introduced to reduce reflections from boundaries and accurately simulate wave propagation on unclosed surfaces with periodic inclusions. Several benchmark examples demonstrate the efficiency and accuracy of the proposed method in simulating acoustic wave propagation on surfaces with diverse geometries, including complex shapes and periodic holes or inclusions.

翻译：本文首次尝试采用局部无网格方法分析带有周期性孔洞/夹杂物的弯曲表面上的时谐声波传播问题。具体而言，采用广义有限差分法作为局部无网格技术，离散求解控制方程中基于外在定义的曲面梯度算子和拉普拉斯-贝尔特拉米算子。引入吸收边界条件以减少边界反射，并准确模拟带有周期性夹杂物的非封闭表面上的波传播。多个基准算例验证了所提方法在模拟不同几何形状（包括复杂形状及周期性孔洞/夹杂物）的表面上声波传播时的有效性和准确性。