本文基於協合應力偶理論(Consistent couple stress theory, CCST)推演一套歸一的理論體系，用於功能性(Functionally graded, FG)複合材料微米梁(Microscale beams , MBs)的靜態撓曲和自然振動分析，透過在理論推演中沿FGMB厚度方向假設剪切變形之特定形狀函數，即可獲得基於CCST之Euler-Bernoulli, Timoshenko, 和Reddy梁理論，以及基於CCST之正弦、指數和雙曲線剪切變形梁理論對應之強形式數學方程式，因此上述理論皆可視為本歸一協合應力偶梁理論之特例。本文將對於上述各微米梁理論求得之結果作綜合比較，藉由材料長度比例參數、縱橫比和材料屬性梯度指數，檢測其造成FGMB的變形、應力和自然頻率參數之影響。

Based on the consistent couple stress theory (CCST), the authors develop a unified formulation for static bending and free vibration analyses of functionally graded (FG) microscale beams (MBs). The strong forms of the CCST-based Euler-Bernoulli, Timoshenko, and Reddy beam theories as well as the CCST-based sinusoidal, exponential, and hyperbolic shear deformation beam theories can be obtained by assigning some specific shape functions of the shear deformations through the thickness direction of the FGMB in the unified formulation. The above theories are thus included as special cases of the unified consistent couple stress beam theory. A comparative study between the results obtained using a variety of CCST-based beam theories and those obtained using their modified couple stress theory-based counterparts is carried out. Some key effects on the deformation, stress, and natural frequency parameters of the FGMB are examined, including the material length scale parameter, the aspect ratio, and the material-property gradient index.
Keywords: consistent couple stress theory; deformation; microscale beams; modified couple stress theory; unified shear deformation theory; vibration.

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