This paper investigated the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells on elastic foundations in thermal environment. The material properties of the nanocomposite elliptical cylindrical shells are assumed to depend on temperature and graded in the thickness direction according to various linear functions. The shell is subjected to the combination of the uniformly distributed transverse load in harmonic form and the uniform temperature rise. The motion and geometrical compatibility equations are derived based on the Reddy’s higher order shear deformation shell theory. The natural frequencies and the deflection amplitude–time curves of the shell are determined by using the Galerkin method and fourth-order Runge–Kutta method. The numerical results show not only the positive influences of carbon nanotube volume fraction and elastic foundations but also the negative influences of initial imperfection and temperature increment on the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells. The reliability of the present results is verified by comparing with other publications.

本文研究了热环境下碳纳米管聚合物复合椭圆圆柱壳在弹性基础上的非线性振动和动力响应。假定纳米复合椭圆圆柱壳的材料性能取决于温度，并根据各种线性函数在厚度方向上进行分级。壳体承受谐波形式的均匀分布的横向载荷和均匀的温度升高的共同作用。运动和几何相容性方程是根据Reddy的高阶剪切变形壳理论导出的。壳体的固有频率和挠度振幅-时间曲线通过Galerkin方法和四阶Runge-Kutta方法确定。数值结果表明，不仅碳纳米管的体积分数和弹性基础的正影响，而且初始缺陷和温度升高对碳纳米管聚合物复合椭圆圆柱壳的非线性振动和动力响应的负面影响。通过与其他出版物进行比较，验证了本结果的可靠性。