The current investigation deals with the nonlinear oscillation response of conical microshells made of a composite material with functional graded (FG) in-plane heterogeneity is studied in the presence of the size dependency. To accomplish this purpose, various types of homogenization schemes including Voigt model, Reuss model, Mori-Tanaka model, and Hashin-Shtrikman bounds model are employed. The size-dependent characteristics are taken into consideration on the basis of the modified couple stress theory of elasticity within the framework of the higher-order shear deformation shell theory. The couple stress-based differential equations of motion are constructed via the Hamilton's principle. An efficient numerical solution methodology adopting generalized differential quadrature (GDQ) method together with the pseudo-arc technique is put to use to obtain the modified couple stress-based nonlinear frequency of homogenized FG composite conical microshells. It is demonstrated that by increasing the value of the maximum shell deflection, the couple stress type of size effect plays more important role in the nonlinear vibration response of FG composite conical microshells. Additionally, it is indicated by changing the boundary conditions from simply supported one to clamped one, the influence of couple stress size dependency decreases.

当前的研究涉及在具有尺寸依赖性的情况下研究了具有功能梯度（FG）平面内异质性的复合材料制成的圆锥形微壳的非线性振动响应。为了实现该目的，采用了各种类型的均化方案，包括Voigt模型，Reuss模型，Mori-Tanaka模型和Hashin-Shtrikman边界模型。在高阶剪切变形壳理论的框架内，基于修改后的弹性耦合应力理论，考虑了尺寸相关的特性。基于汉密尔顿原理构造了基于应力的耦合运动微分方程。提出了一种有效的数值求解方法，该方法采用了广义微分正交（GDQ）方法和拟弧技术，来获得均质的FG复合圆锥微壳基于变应力的非线性频率。结果表明，通过增加最大壳挠度值，尺寸效应的耦合应力类型在FG复合锥形微壳的非线性振动响应中起着更为重要的作用。另外，通过将边界条件从简单支撑的一种变为夹紧的一种，表明耦合应力大小依赖性的影响减小了。尺寸效应的偶应力类型在FG复合锥形微壳的非线性振动响应中起着重要作用。另外，通过将边界条件从简单支撑的一种变为夹紧的一种，表明耦合应力大小依赖性的影响减小了。尺寸效应的偶应力类型在FG复合锥形微壳的非线性振动响应中起着重要作用。另外，通过将边界条件从简单支撑的一种变为夹紧的一种，表明耦合应力大小依赖性的影响减小了。