本文主旨在於對薄殼狀結構的超導共振腔體在受到不同的負載條件下，腔體結構變形與共振基頻的電磁場特性進行分析與討論。當模擬共振腔體受到結構變形與其共振基頻變化的相關性時，使用有限單元分析軟體ANSYS建立模型，並且對於共振腔體進行結構變形與電磁場特性的跨領域分析。於分析的過程中，設定邊界條件和給予結構單元必要的機械性質與電磁場的常數，接著對於不同厚度的腔體施加軸向位移與壓力及溫度變化等，討論在各種參數條件下，結構變形與電磁場特性的相關性。
首先以不同單元密度的劃分方式，在沒有外加負載的情況下，分析腔體共振基頻的收斂情形及微波之腔體的電場與磁場特性。之後固定腔體模型中薄殼單元的厚度與楊氏係數，分析內部虛擬實體單元不同的楊氏係數，在給予固定軸向壓縮位移與內外壓力差時，腔體的反作用力、最大等效應力與變形後共振基頻飄移的收斂性。接著對於相同厚度殼單元結構，給予不同的壓縮位移與內外壓力差，以及改變薄殼單元之楊氏係數、普松比，探討不同機械性質對於腔體變形後共振基頻飄移量之影響，並且分析腔體由室溫冷卻至液態氦的溫度時，不同熱膨脹係數對共振基頻飄移量的影響。
由於共振腔體在加工的過程中厚度難免會有變化，因此分析在承受內外壓力差及端面位移負載的情況下，探討厚度對腔體結構變形及共振頻率變化的影響，以便在進行實驗時，於量測將腔體抽真空後內部的共振頻率後，能推算出腔體在經過加工之後的等效厚度；最後以此等效厚度對數值計算與實驗量測的結果進行相互的驗證。

This thesis examines the structure deformation and electromagnetic resonance characteristic of a superconducting radio frequency (SRF) cavity. This SRF cavity is a shell-liked structure; it not only deforms but also shifts the electromagnetic resonance frequencies while being externally loaded. The finite element software ANSYS is used for numerical simulation; a single-model process links the structural deformation and its relative high-frequency electromagnetic computations and thus improves both the efficiency and accuracy. Proper boundary conditions and material properties are assigned to the model, while external loading such as surface pressure, longitudinal displacement and temperature difference were applied on the model for structural deformation computing only. Characteristics of the electromagnetic field, especially the fundamental resonance mode, of the deformed cavity with various thickness, external loading conditions, and mechanical properties, are discussed.
Convergence test on the resonance frequency of the unloaded SRF cavity was firstly performed to determine the suitable element density, then various virtual Young’s modulus which are assigned to the interior vacuum space of the cavity with particular thickness and Young’s modulus but under either surface pressure or longitudinal compression to determine the upper bound of the virtual Young’s modulus by examine its convergence on both the maximum von Mises stress and the resonance frequency. With fixed mesh and virtual Young’s modulus, the effects of mechanical properties including Young’s modulus, Poisson ratio, and coefficient of thermal expansion, on the drift of electromagnetic resonance frequency under various external loading were systematically studied.
In practical, the SRF cavity is formed from a uniform plate but turn out its final thickness varies along the cavity wall due to uneven stretching during machining. Therefore, it is essential to establish a complete matrix on the effects of uniform thickness on the structure deformation and consequent frequency drift of the SRF cavity, so that an equivalent thickness of a real cavity could be estimated after measuring its resonance frequency shift for the cavity under various external loads. And then the equivalent thickness could be used to predict further physical behavior of the real cavity by numerical simulations.

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