In this article, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency, and chaotic responses of the graphene nanoplatelet (GPL) reinforced composite (GPLRC) doubly-curved panel subject to an external harmonic load. Using Hamilton's principle and the Von-Karman nonlinear theory, the nonlinear governing equations are derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. The results show that GPL's pattern, radius to length ratio, harmonic load, and thickness to length ratio have important role in the chaotic motion of the doubly-curved panel. The fundamental and golden results of this paper is that the chaotic motion and nonlinear frequency of the panel is hardly dependent on the value of the smaller radius to length ratio ($R_1/a$ parameter) and viscoelastic foundation. It means that by increasing the value of $R_1/a$ parameter, and taking into account the viscoelastic foundation, the motion of the system tends to show the chaotic motion. Moreover, for GPL-A, GPL-V, and GPL-UD patterns, when the value of the $R_1/a$ parameter or the curvature shape of the doubly-curved panel increases, the chaoticity in motion response improves while for the GPL-O pattern, this matter reverses.

本文通过数学推导为非线性频率建立了非线性动力学模型，并研究了石墨烯纳米片材（GPL）增强复合材料（GPLRC）双曲面板在外部谐波载荷作用下的混沌响应。利用汉密尔顿原理和冯-卡尔曼非线性理论，推导了非线性控制方程。为了开发精确的求解方法，最终采用了广义差分正交方法（GDQM）和微扰方法（PA）。结果表明，GPL的图案，半径与长度之比，谐波载荷以及厚度与长度之比在双曲面板的混沌运动中具有重要作用。${\mathrm{[R}}_{\mathrm{1个}}/\mathrm{一种}$参数）和粘弹性基础。这意味着通过增加${\mathrm{[R}}_{\mathrm{1个}}/\mathrm{一种}$参数，并考虑到粘弹性基础，系统的运动往往表现出混沌运动。此外，对于GPL-A，GPL-V和GPL-UD模式，当${\mathrm{[R}}_{\mathrm{1个}}/\mathrm{一种}$ 参数或双曲面板的曲率形状增加，运动响应的混沌性提高，而对于GPL-O模式，则相反。