The main target of this paper is to evaluate the geometrically nonlinear and size-dependent response of shallow sandwich curved micro-panels (SCMPs). In this regard, the governing equations are developed by using modified couple stress theory (MCST) based on the first-order shear deformation theory (FSDT). The proposed sandwich micro panels are assumed to be made of three layers so that the middle layer is a porous core and the other ones are the nanocomposite enriched face-sheets. The extended nonlinear differential equations are analytically solved by using the main concepts of the Galerkin method which results a closed-form formulation for the nonlinear equation of motion of the proposed micro-panels. Then, the obtained equation of motion is solved numerically using the forth-order Runge-Kutta method. Accuracy of the present method is validated by comparing the results of some examples with those are available in the other studies. Using an extensive parametric study, the effects of various mechanical and geometrical properties on the size-dependent forced vibration of proposed micro-panels are evaluated.

本文的主要目标是评估浅夹层曲面微面板 (SCMP) 的几何非线性和尺寸相关响应。在这方面，控制方程是使用基于一阶剪切变形理论（FSDT）的修正耦合应力理论（MCST）开发的。假设所提出的夹层微面板由三层制成，因此中间层是多孔芯，其他层是富含纳米复合材料的面板。扩展的非线性微分方程通过使用 Galerkin 方法的主要概念进行解析求解，从而为所提出的微面板的非线性运动方程提供了一个封闭形式的公式。然后，使用四阶龙格-库塔方法对获得的运动方程进行数值求解。通过将一些示例的结果与其他研究中可用的结果进行比较，验证了本方法的准确性。使用广泛的参数研究，评估了各种机械和几何特性对所提议的微型面板的尺寸相关强制振动的影响。