Due to its lightweight design and high load-bearing capacity, the nanocomposite plate structure is extensively applied in flight wings, ship hulls and aerospace structures. In particular, there is a lack of research on the nonlinear dynamic response of the shear deformable plates with initial geometric imperfection and damping ratio. Inspired by this, this article investigates the nonlinear stability behavior of an imperfect nanocomposite plate under axial compression loading. Material properties are presumed to vary in thickness directions according to three different CNT distributions patterns, in which the material properties are calculated with the help of the mixing rule. Subsequently, considering the effect of shear stresses, initial geometrical imperfections and damping ratio, the dynamic model is constructed according to the shear deformation theory (SDT) and Von Karman-form of the nonlinearity. Then, the nonlinear equations of motion are of the plate is derived based on the Hamilton principle. Then, the procedure of the superposition and Galerkin-based method are applied in order to convert the non-linear partial differential expressions of CNTs plate for the non-linear ordinary differential form. The resulted non-linear differential expressions are numerically solved via fourth-order Runge-Kutta-based scheme. Simultaneously, the analytical results of the presented expression are compared with other published literatures to verify the accuracy of this article, and the comparisons show that there is no notable variation between the present data and existing literature. In addition, a parametric investigation is presented to reveal the impacts of axial velocities, initial imperfections, damping, CNTs distribution and volume fraction, geometry parameters and buckling modes on the non-linear dynamic buckling responses of the CNTs plate. It can be found that the presence of initial imperfection will significantly affect the nonlinear dynamic behavior of the nanocomposite plates.

中文翻译：

---

面内速度作用下简支不完美纳米复合材料剪切变形板的非线性动态屈曲


纳米复合板结构由于其轻量化设计和高承载能力，广泛应用于飞行机翼、船体和航空航天结构。尤其缺乏对具有初始几何缺陷和阻尼比的剪切变形板的非线性动力响应的研究。受此启发，本文研究了不完美纳米复合材料板在轴向压缩载荷下的非线性稳定性行为。根据三种不同的碳纳米管分布模式，假定材料特性在厚度方向上变化，其中材料特性是借助混合规则计算的。随后，考虑剪应力、初始几何缺陷和阻尼比的影响，根据剪切变形理论（SDT）和非线性冯卡门形式构建动态模型。然后，根据哈密顿原理推导了板的非线性运动方程。然后，应用叠加过程和基于伽辽金的方法将碳纳米管板的非线性偏微分表达式转换为非线性常微分形式。所得到的非线性微分表达式通过基于四阶龙格-库塔的方案进行数值求解。同时，将所提出的表达式的分析结果与其他已发表的文献进行了比较，以验证本文的准确性，比较结果表明，本数据与现有文献之间没有显着差异。 此外，还进行了参数研究，揭示了轴向速度、初始缺陷、阻尼、碳纳米管分布和体积分数、几何参数和屈曲模式对碳纳米管板非线性动态屈曲响应的影响。可以发现，初始缺陷的存在会显着影响纳米复合材料板的非线性动力学行为。