Nonlinear vibration and dynamic response of functionally graded moderately thick toroidal shell segments resting on Pasternak type elastic foundation are investigated in this paper. Functionally graded materials are made from ceramic and metal, and the volume fraction of constituents are assumed to vary through the thickness direction according to a power law function. Reddy’s third order shear deformation, von Karman nonlinearity, Airy stress function method and analytical solutions are used to derive the governing equations. Galerkin method is used to convert the governing equation into nonlinear differential equation, then the explicit expressions of natural frequencies and nonlinear frequency–amplitude relations are obtained. Using Runge–Kutta method, the nonlinear differential equation of motion is solved, and then nonlinear vibration and dynamic response of shells are analyzed. The effects of temperature, material and geometrical properties, and foundation parameters on nonlinear vibration and dynamic characteristics are investigated and discussed in detail.

本文研究了基于Pasternak型弹性地基的功能梯度中等厚度的环形壳段的非线性振动和动力响应。功能分级的材料由陶瓷和金属制成，并且假定成分的体积分数根据幂律函数在厚度方向上发生变化。雷迪的三阶剪切变形，冯·卡曼非线性，艾里应力函数法和解析解被用于导出控制方程。用Galerkin方法将控制方程转化为非线性微分方程，得到固有频率和非线性频率-振幅关系的显式。使用Runge–Kutta方法，解决了运动的非线性微分方程，然后分析了壳体的非线性振动和动力响应。研究和讨论了温度，材料和几何特性以及基础参数对非线性振动和动态特性的影响。