本文將探討具有外加強環與內加強環之雙跨距複合材料層圓柱薄殼結構的自由振動特性，並考慮複合材料層圓柱薄殼中心面與加強環中心線之位移與轉角和橫斷面之剪切效應及轉動慣量。首先建立第i個跨距複合材料層圓柱薄殼之應力場、應變場與位移場之關係，進而推導複合材料層圓柱薄殼結構的運動方程式，而後再利用轉換矩陣法計算分析複合材料層圓柱薄殼結構自由振動之模態頻率與相對應之模態形狀函數，最後再探討複合材料層圓柱薄殼其疊層角度變化、長度、厚度、半徑等不同幾何參數下對模態頻率的影響。
　　此外在分析具有外加強環與內加強環之雙跨距複合材料層圓柱薄殼結構時，探討加強環之寬度、厚度效應對結構自由振動之影響與結構承受徑向集中負載之動態響應行為，並證明模態形狀函數之正交性質，比較單跨距、具外加強環與內加強環之雙跨距複合材料層圓柱薄殼結構在相同長度、厚度、半徑下，改變疊層角度、加強環之寬度與厚度，對模態頻率之影響。接著利用模態法推導結構承受徑向集中負載的模態振幅控制方程式，以求得整個結構的動態響應，利用座標轉換可將結構座標方向上之應力，變換為材料主軸座標方向的應力，最後利用破損理論得知哪一疊層最先斷裂。

　　Free vibration characteristics of a symmetric cross-ply cylindrical shell with a circumferential stiffener are studied. Two types of the circumferential stiffeners are considered: outer ring and inner ring. The effects of rotatory inertia and transverse shearing strain of both the cross-ply shell and stiffener are considered. Further, the warping effect of stiffener also is included. An analytic method is presented to obtain the modal frequencies and their corresponding mode shape functions of the ring-stiffened shell. The orthogonality of two distinct sets of mode shape functions is shown. The effects of the two different types of ring on modal frequencies of the
ring-stiffened shell are compared. Further, the effects of two different ply arrangements on modal frequencies of the ring-stiffened shell also are compared. Transient force acting on the ring-stiffened shell is taken as an example to study the forced vibration of the structure. Further, the maximum stress theory is adopted as the failure criteria of the ring-stiffened shell.

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