In present work, a nonlinear functionally graded curved beam model including the von Kármán geometric nonlinearity is developed on the basis of the third-order shear deformation theory. Due to incorporating the trapezoidal shape factor in the proposed model, the errors caused by geometric curvatures are eliminated. The governing equations of motions related to the dynamics of curved beams are derived by Lagrange method and solved using a standard Newmark time iteration procedure in conjunction with Newton–Raphson technique. Some comparisons are performed and indicate that the results from our model coincide favorably with semi-analytical solutions. Afterwards, utilizing the proposed model, the present investigation focuses on the nonlinear transient response of functionally graded multilayer curved beams reinforced by graphene oxide nano-fillers subjected to moving loads. A modified Halpin–Tsai micromechanical model is implemented to determine the effective modulus of graphene oxide/polymer nanocomposite, and the rule of mixture is used to calculate the mass density and Poisson’s ratio. The curved beams are assumed to rest on a visco-Pasternak foundation. The effects GO nano-fillers, including their weight fractions, distribution patterns and size on the nonlinear dynamic responses of the nanocomposite curved beams subjected to moving loads are studied. Moreover, the effects of radius-to-span ratios and visco-Pasternak foundation on the nonlinear dynamic response of curved beams are also discussed as subtopics.

在目前的工作中，基于三阶剪切变形理论，建立了包括冯·卡曼几何非线性的非线性功能梯度弯曲梁模型。由于在所提出的模型中加入了梯形形状因数，因此消除了由几何曲率引起的误差。与弯曲梁动力学有关的运动控制方程是通过拉格朗日方法推导的，并使用标准的纽马克时间迭代程序结合牛顿-拉夫森技术进行求解。进行了一些比较，并表明我们模型的结果与半解析解相吻合。然后，利用提议的模型，目前的研究集中在功能梯度多层弯曲梁的非线性瞬态响应上，该多层弯曲梁由氧化石墨烯纳米填料增强，承受移动载荷。修改后的Halpin-Tsai微力学模型用于确定氧化石墨烯/聚合物纳米复合材料的有效模量，并使用混合规则计算质量密度和泊松比。假定弯曲梁搁置在粘性Pasternak基础上。研究了GO纳米填料的重量分数，分布模式和尺寸对移动载荷作用下纳米复合弯曲梁非线性动力响应的影响。此外，还讨论了半径-跨度比和粘滞Pasternak基础对弯曲梁非线性动力响应的影响。