基於協合應力偶理論(Consistent Couple Stress Theory, CCST)，本文發展Hermitian C2有限層狀元素法(Finite Layer Method, FLM)，用於分析受到週期性軸向壓縮和外圍壓力組合作用下具簡支承邊界條件的功能性(Functionally Graded, FG)圓柱微米殼的動態不穩定行為。上述 FLM 是將圓柱微米殼劃分為多層，每層的彈性場主變數在中曲面上假設為雙傅立葉函數分布，在厚度方向上則用Hermitian C2多項式插值擬合。本文的Hermitian C2 FLM 準確性和收斂速度將以文獻中的FG宏觀圓柱殼和單層納米碳管的精確二維解進行驗證。本文探討對簡支FG微米圓柱殼參數共振的第一主要不穩定區間和第一次要不穩定區間有影響的重要因素，其中包含材料尺度參數、材料特性梯度指數、半徑-厚度比、長度-半徑比、荷載大小，與靜態和動態荷載因子。本文提出的三維解決方案可以作為評估使用基於CCST和MCST的精細殼理論獲得的二維近似結果的參考。

This work develops a three-dimensional (3D) weak formulation, based on the consistent couple stress theory (CCST), for analyzing the size-dependent dynamic instability behavior of simply-supported, functionally graded (FG) cylindrical microshells which are subjected to combinations of periodic axial compression and external pressure. In our formulation, the microshells are artificially divided into nl layers. The displacement components of each individual layer are selected as the primary variables, which are expanded as a double Fourier series in the in-plane domain and are interpolated with Hermitian C2 polynomials in the thickness direction. Incorporating the layer-wise displacement models into our weak formulation, we subsequently develop a Hermitian C2 finite layer method (FLM) for addressing the current issue. The accuracy and the convergence rate of our Hermitian C2 FLM are validated by comparing the solutions it produces with the accurate two-dimensional solutions of critical loads and critical pressure of FG cylindrical macroshells and single-walled carbon nanotubes, which were reported in the literature. The impacts of some essential factors on the first principal and first secondary instability regions of parametric resonance of simply-supported FG cylindrical microshells are examined and revealed to be significant. These factors, in particular, include the material length-scale parameter, the in-homogeneity index, the radius-to-thickness and length-to-radius ratios, the load magnitude ratio, and the static and dynamic load factors.

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