This article investigates nonlinear free vibrations of porous functionally graded (FG) annular spherical shell segments surrounded by elastic medium and reinforced by circumferential stiffeners. Porous FG material contains distributed even and un-even porosities and is modeled based on refined power–law function. The governing equations of stiffened porous annular spherical shell segments have been derived according to thin shell theory with the geometrical nonlinear in von Karman–Donnell sense and the smeared stiffeners method. An analytical trend has been provided for solving the nonlinear governing equations. Obtained results demonstrate the significance of porosity distribution, geometric nonlinearity, foundation factors, stiffeners and curvature radius on vibration characteristics of porous FG annular spherical shell segments.

本文研究了多孔功能梯度（FG）环形球形壳段的非线性自由振动，该环形壳段被弹性介质包围并由周向加强筋加强。多孔FG材料包含分布均匀且不均匀的孔隙，并基于精确的幂律函数进行建模。根据薄壳理论，采用von Karman–Donnell意义上的几何非线性和涂抹加劲肋方法，推导了加劲多孔环形球壳段的控制方程。为解决非线性控制方程提供了一种分析趋势。所得结果表明，孔隙度分布，几何非线性，基础因素，加劲肋和曲率半径对多孔FG环形球壳段的振动特性具有重要意义。