Abstract In this work, porosity-dependent nonlinear large-amplitude oscillation responses of rectangular microplates with and without a central square cutout made of a porous functionally graded material (PFGM) is explored using modified couple stress theory of elasticity (MCSTE). The associated nonlinear size-dependent modified couple stress-based differential motion equations are obtained based on third-order shear deformation plate model (TSDPM). A new power-law function incorporating simultaneously the material gradient and porosity dependency is employed for the extraction of the effective mechanical characteristics of PFGM microplates. Afterwards, the non-uniform rational B-spline (NURBS)-based isogeometric technique is put to use as an efficient discretization method taking the C−1 continuity satisfaction into account. It is observed that among various patterns of porosity distribution, the lowest and greatest effects of couple stress size dependency are observed on the nonlinear frequencies of microplates in which the porosity from top and down surfaces to center is increased and decreased, respectively. Also, it was observed that increase of the material property gradient index as well as plate deflection reduces couple stress size effect on the nonlinear oscillations of PFGM microplates. It was shown that there is a specific length to thickness ratio, corresponding to which the modified couple stress-based frequency ratio becomes minimum. This minimum value enhances with the increase of the porosity index of PFGM microplates.

中文翻译：

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使用基于 NURBS 的等几何方法对多孔功能梯度微板进行基于修正偶应力的几何非线性振荡

摘要 在这项工作中，使用修正的弹性耦合应力理论 (MCSTE) 探索了带有和不带有由多孔功能梯度材料 (PFGM) 制成的中心方形切口的矩形微板的孔隙度相关非线性大振幅振荡响应。基于三阶剪切变形板模型（TSDPM）获得相关的非线性尺寸相关修正偶应力微分运动方程。同时结合材料梯度和孔隙率依赖性的新幂律函数用于提取 PFGM 微板的有效机械特性。之后，基于非均匀有理 B 样条 (NURBS) 的等几何技术被用作考虑 C-1 连续性满足的有效离散化方法。据观察，在孔隙率分布的各种模式中，耦合应力大小依赖性对微板的非线性频率的影响最小和最大，其中从顶面和下表面到中心的孔隙率分别增加和减少。此外，还观察到材料特性梯度指数的增加以及板偏转减少了对 PFGM 微板非线性振荡的耦合应力大小影响。结果表明，存在特定的长厚比，对应于修正的基于应力的耦合频率比变得最小。该最小值随着 PFGM 微孔板孔隙率指数的增加而增强。在微板的非线性频率上观察到耦合应力大小依赖性的最低和最大影响，其中从顶面和底面到中心的孔隙率分别增加和减少。此外，还观察到材料特性梯度指数的增加以及板偏转减少了对 PFGM 微板非线性振荡的耦合应力大小影响。结果表明，存在特定的长厚比，对应于修正的基于应力的耦合频率比变得最小。该最小值随着 PFGM 微孔板孔隙率指数的增加而增强。在微板的非线性频率上观察到耦合应力大小依赖性的最低和最大影响，其中从顶面和底面到中心的孔隙率分别增加和减少。此外，还观察到材料特性梯度指数的增加以及板偏转减少了对 PFGM 微板非线性振荡的耦合应力大小影响。结果表明，存在特定的长厚比，对应于修正的基于应力的耦合频率比变得最小。该最小值随着 PFGM 微孔板孔隙率指数的增加而增强。据观察，材料特性梯度指数的增加以及板偏转减少了对 PFGM 微板非线性振荡的耦合应力大小影响。结果表明，存在特定的长厚比，对应于修正的基于应力的耦合频率比变得最小。该最小值随着 PFGM 微孔板孔隙率指数的增加而增强。据观察，材料特性梯度指数的增加以及板偏转减少了对 PFGM 微板非线性振荡的耦合应力大小影响。结果表明，存在特定的长厚比，对应于修正的基于应力的耦合频率比变得最小。该最小值随着 PFGM 微孔板孔隙率指数的增加而增强。