This paper addresses the investigation of axisymmetric thermally induced vibrations in Functionally Graded Material (FGM) cylindrical shells. It considers temperature-dependent (TD) properties and geometric non-linearity (the von Karman effect). The study systematically solves a transient heat conduction equation using finite differences method and the Crank–Nicolson method. During the heating stages, the evaluation of thermal forces and moments takes place. Equations of motion are derived through the application of Hamilton’s principle. Spatial dependencies are discretized using the generalized Ritz method, while temporal dependencies are approximated using the $\beta$-Newmark method with Newton–Raphson linearization. A comparative analysis validates the procedure’s efficiency and precision. Parametric studies explore the influence of parameters, including the temperature-dependency material properties, geometric nonlinearity, and shell’s power-law index, providing valuable insights into FGM shell behavior under thermal shock.

本文研究了功能梯度材料 (FGM) 圆柱壳中的轴对称热致振动。它考虑了温度相关 (TD) 特性和几何非线性（冯卡门效应）。该研究使用有限差分法和 Crank-Nicolson 法系统地求解瞬态热传导方程。在加热阶段，会评估热力和力矩。运动方程是通过应用汉密尔顿原理推导出来的。空间依赖性使用广义 Ritz 方法进行离散化，而时间依赖性则使用$\beta$-具有牛顿-拉夫逊线性化的纽马克方法。比较分析验证了该过程的效率和精度。参数研究探索了参数的影响，包括温度依赖性材料特性、几何非线性和壳的幂律指数，为了解热冲击下 FGM 壳的行为提供了宝贵的见解。