本文基於協合應力偶理論(Consistent couple stress theory , CCST)，發展各種剪切變形尺度相關板之歸一理論，對簡支撐多孔隙功能性(Functionally graded , FG) 壓電材料微米板進行自由振動分析，其中這些微米板的上下表面受電壓作用並放置在Winkler或Pasternak基礎上。透過此歸一理論，可將基於CCST的各種剪切變形理論所對應的形狀函數代入來重現基於CCST之古典板理論、一階剪力變形板理論、Reddy的優化剪力變形板理論、正弦剪力變形板理論、指數剪力變形板理論以及雙曲線剪力變形板理論，其中這些形狀函數表徵剪力變形的厚度分布。隨後使用此歸一理論來確定簡支撐多孔隙功能性壓電材料微米板的固有頻率及其相應的振動模態。研究後發現材料尺度參數、長厚比、材料性質梯度因子、不同的電壓值、孔隙率參數、孔隙分布模式、Winkler彈簧係數和彈性介質周圍的剪力模數對多孔隙功能性壓電材料微米板固有頻率的影響，這些影響似乎是顯著的。

Based on the consistent couple stress theory (CCST), we develop a unified size-dependent shear deformation theory to analyze the free vibration characteristics of simply supported, porous functionally graded (FG) piezoelectric microplates which are resting on a Winkler-Pasternak foundation and subjected to electric voltages. Various CCST-based shear deformation theories can be reproduced by incorporating their corresponding shape functions, which characterize the through-thickness distributions of the shear deformations, into the unified size-dependent theory. The reproduced CCST-based plate theories include the classical plate theory (CPT), the first-order shear deformation plate theory (SDPT), the Reddy’s refined SDPT, the sinusoidal SDPT, the exponential SDPT, and the hyperbolic SDPT. The unified size-dependent theory is subsequently used to determine the natural frequencies of simply supported, porous FG piezoelectric microplates and their corresponding vibration mode shapes. The effects of the material length scale parameter, the length-to-thickness ratio, the material-property gradient index, different values of the applied voltages, the porosity parameter, different porosity distribution patterns, the Winkler’s spring coefficient, and the shear modulus of the surrounding medium on the natural frequencies of the porous FG piezoelectric microplates are examined and appear to be significant.

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