The vibration of an inhomogeneous circular membrane was researched, the second-order center difference scheme was used and the difference discrete model for axial symmetric vibration of a circular membrane with arbitrary supports was estab-lished. This model belongs to a positive Jacobi system. Thus, some qualitative properties of the system were obtained.%本文研究非均匀圆环形薄膜的微振动，由二阶中心差分格式导出了内外边界均任意支承的圆环形薄膜轴对称振动的差分离散模型，说明了该模型属于雅可比正系统，进而引出了该系统的振动定性性质。
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