Assessment of the geometrically nonlinear forced vibration of the doubly-curved laminated composite shallow shell panels enriched by nanocomposites have been carried out in this paper. The proposed shells incorporate some layers composed of fibres and nanocomposite-reinforced resin, resting on the two types Winkler and Pasternak elastic foundations. Since the thin and moderately thick shells are investigated, the first-order transverse shear deformation theory (FSDT) is employed for extending the governing equations. The achieved system of differential equations incorporating the geometrical nonlinear terms is solved by applying the principles of the Galerkin method. This approach yields a closed-form semi-analytical solution for motion differential equation of the shell which is solved by fourth-order Runge-Kutta method. The consequence of the present approach is a strong and robust tool without any time-consuming computational process. The applicability of the proposed method is verified by considering some benchmark problems from the literature and comparing the relevant results with those are achieved in this study. Finally, by solving several examples, the effects of various factors on the forced-vibration of proposed shells are evaluated.

本文对纳米复合材料富集的双曲叠层复合浅壳板的几何非线性强迫振动进行了评估。提议的外壳包含一些由纤维和纳米复合增强树脂组成的层，位于两种类型的 Winkler 和 Pasternak 弹性基础上。由于研究了薄壳和中等厚壳，因此采用一阶横向剪切变形理论（FSDT）来扩展控制方程。所实现的微分方程系统包含几何非线性项通过应用 Galerkin 方法的原理来求解。该方法产生了壳运动​​微分方程的闭式半解析解，该解由四阶龙格-库塔法求解。本方法的结果是没有任何耗时的计算过程的强大而稳健的工具。通过考虑文献中的一些基准问题并将相关结果与本研究中获得的结果进行比较，验证了所提出方法的适用性。最后，通过求解几个例子，评估了各种因素对拟壳受迫振动的影响。