本研究係針對一橫向振動(transverse vibration) 之彈性樑'其端點以一線性彈簧支撐，另一端點分別為加入減振裝置、點質量及完全懸空在受一外力下之減振分析。吾人將比較以上三種彈性樑在不同邊界條件下的振動情況與減振效果。利用本文所推導之模式，對於結構物受到外力並開始振動之前，嘗試不同的減振裝置將可有效的避開率統共振範園，以達到系統順利運作的目的。 The vibration problem is very important for most mechanical devices. It is well known that the resonant phenomenon will cause serious system damage due to large displacements. Therefore a dependable and easy identified model is necessary for the prepensely design for the vibration system. In this research, we assume an elastic beam is subjected to the transverse vibration. This beam is supported with a linear spring at one of the end. The other end is attached by a point mass, an absorber and free end, and all with an external force, respectively. The analytic solutions are obtained for these 3 cases. The mode shapes and frequency responses are all studied. The effects of different vibration reduction devices on the elastic beam are analyzed. The results give important information for vibration analysis. By using derived analytic functions, one can avoid the resonance of the system efficiently by using different vibration devices.