In this work, nonlinear forced vibrations of truncated conical shells are presented using a semi-analytical method. The material properties are varied along the thickness direction as a power law distribution. The functionally graded truncated conical shells are exposed to external harmonic load and placed in the thermal environment and have an initial imperfection. Furthermore, the functionally graded truncated conical shells rests on generalized nonlinear viscoelastic foundations which consisted of a Winkler and Pasternak foundation parameters augmented by a Kelvin–Voigt viscoelastic model and a nonlinear cubic stiffness. The fundamental equations are extracted using first-order shear deformation theory in conjunction with nonlinear von Kármán relationships. The partial differential equations of truncated conical shells are reduced through Galerkin’s method, and the result is extracted using the multiple scales method. To analyze the resonance analyses, a two-term external excitation is considered. In this regard, various secondary resonances are investigated, and finally, the analyses about combination resonances are represented. To investigate the presented approach, a comparison study is performed with those addressed by other researchers. To analyze the nonlinear combination resonance behavior of truncated conical shells, the effect of geometrical characteristics, material properties, power law index, thermal effects, external load amplitude, and initial imperfection are examined. Finally, the steady-state responses of the nonlinear system are analyzed. As one of the most interesting results, the softening behavior of truncated conical shells with inverse quadratic distribution is the most, and for the quadratic distribution is the least.

在这项工作中，使用半解析方法提出了截锥形壳体的非线性强迫振动。材料特性沿幂方向分布沿厚度方向变化。功能分级的截头圆锥形壳体承受外部谐波载荷，并放置在热环境中，并具有初始缺陷。此外，功能渐变的圆锥台壳基于广义的非线性粘弹性基础，该基础由Winkler和Pasternak基础参数组成，并通过Kelvin-Voigt粘弹性模型和非线性三次刚度进行了扩充。基本方程是使用一阶剪切变形理论结合非线性vonKármán关系提取的。截短的圆锥壳的偏微分方程通过Galerkin方法简化，并使用多尺度方法提取结果。为了分析共振分析，考虑了两个外部激励。在这方面，研究了各种次级共振，最后表示了关于组合共振的分析。为了研究提出的方法，与其他研究人员进行的比较研究进行了比较。为了分析截头圆锥壳的非线性组合共振行为，研究了几何特性，材料特性，幂律指数，热效应，外部载荷振幅和初始缺陷的影响。最后，分析了非线性系统的稳态响应。作为最有趣的结果之一，