本文主旨在研究彈性圓柱形薄殼管件的變形問題，當圓柱薄殼受側向與軸向壓力時，不同的長度、厚度與半徑比均會影響管件本身的變形量，因此藉由改變圓柱尺寸與外加負載的情形下觀察其半徑變化與圓柱尺寸的關係，並根據改變不同方向負載所造成的管件變形來反求材料的楊氏模數與普松比。但在有限外力下，管件的變形量在微米等級，不易以常規機械方式量測；由於中空管件本身為一共振腔結構，故可利用共振腔在不同環境溫度及施予不同外加負載時，其電磁場共振頻率會隨腔體變形而飄移的現象反推材料的機械特性；並可利用內部氣體含量變化所造成的共振頻率飄移反推其氣體介電常數的變異。模擬方面使用有限元素分析軟體ANSYS建立模型，結合結構變形與電磁場場域分析，利用共振腔之 模態的電磁場，由腔體變形前後共振頻率的飄移量與腔體變形量進行討論，並用古典板殼理論模型與Maxwell 方程式的解析解以驗證其準確性。但古典板殼理論只能探討無限長管件的變形量，而分析軟體則可進行有限長度管件的模擬，與實驗結果相互驗證，結果誤差值皆在可容許範圍內，並證明可由此研究方法建立金屬材料的楊氏模數、普松比及熱膨脹係數的新式量測方法。並可進一步應用到低溫下金屬材料之機械性質量測與氣體介電常數量測。

The circular cylindrical shell is a popular structure in engineering applications. As being evacuated, the external pressure deforms this structure with limited displacements. For a metallic cylindrical circular cylindrical shell, the high strength leads to a tiny deformation and thus difficult to measure with the traditional methods. But a metallic circular cylindrical shell is a perfect cavity in which the discrete resonant electromagnetic fields can be excited with the proper input microwaves. When the cavity deformed, some of its specified resonance frequencies of the electromagnetic fields also shifted. Thanks to the high resolution of the modern network analyzers, the frequency shift due to a small deformation can be measured. Thereafter the deformation can be deduced from the resonance frequency shift. Since the structure deformation are dominated by three material properties: the Young’s modulus, the Poison’s ratio and the coefficient of the thermal expansion, it is thus practical to calculate these properties by measuring the frequency shifts of the cavity structure under various loading conditions. The variation of the permittivity of the gas inside the cavity, which dominates the resonant frequencies, must be taken into consideration when it is not in vacuum condition. A measurement process to determine the permittivity of the gas under different pressure condition was also established in this study. Theoretical formulas to link the structure deformation and the resonance frequency of a specified mode were established, while the finite element code ANSYS was adopted for 3-D numerical calculations. Together with the tests and measurements, a new method to measure the mechanical properties of metals is proposed and proved.

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