Abstract：Anisotropic materials find widespread applications across various engineering domains, and the investigation of their vibrational properties holds significant significance for structural vibration mitigation and safety design. This paper introduces a novel approach, peridynamic operator method (PDOM), to construct a non-local anisotropic model and applies it to the analysis of free vibrations in anisotropic plates. This model incorporates the unique feature of PDOM, which transforms local differentials and their products into non-local integrals, thereby reformulating the strain energy density from its local form to a non-local form within classical anisotropic theory. Additionally, by employing a variational principle and introducing the free vibration equation, a PDOM solution is developed for addressing anisotropic free vibration problems. Through three numerical examples: anisotropic rectangular thin plate, anisotropic rectangular plate with cracks, and anisotropic rectangular plate with holes in free vibration, the results are compared with finite element results, demonstrating the convergence, stability, and high computational accuracy of the model when dealing with the free vibration of anisotropic plates with defects and discontinuities.
2024, Vol. 45 
