裂縫對振動結構動力敏感度影響之分析

劉慶雄 ； 周孟賢 ； 楊德威

《中華民國振動與噪音工程學會論文集》 1993 (1993/06) Pp. 291-297

https://doi.org/10.30028/CSSVANNUAL.199306.0291

摘要

振動系統(Vibrating Systems)之動力特性(Dynamic Characteristics)由其自然頻率(Natural Frequencies)及其振動模（態）(Vibrating Modes)表示。將一振動系統的聯立運動方程組寫為矩陣形式，再將振動系統質量之位移向量表為指數函數形式，即可求出振動系統之特徵值(Eigenvalues)及特徵向量(Eigenvectors)，而其自然頻率及正規模（態）(Normal Modes)亦由此可知。當一振動系統中之彈性構（元）件損壞（含裂縫）時，上述特性亦必隨之改變，且其改變必對系統結構之安全性（舒適性）造成影響。倘損壞構（元）件及共殘餘壽命能從上述各量之改變測出，則必有助於結構之設計製造及保養維修。本文旨在對上述概念之有效性及應用價值作理論性探討。

關鍵字

裂縫 ； 含阻尼振動結構

並列摘要

The vibrating systems are characterized by their natural frequencies and normal modes. With writting the simultaneous equilibrium equations of motion of a vibrating system in matrix form, and the displacement vector of the mass of the system in exponential function form, one can extract the eigenvalues and eigenvectors of the vibrating system. The natural frequencies and normal modes can also be consequehtly found. When the elastic structure elements are fractured (cracked), the above-cited properties must also jointly vary and that unavoidably affect the safety (comfort) of the structures. It will benefit the maintenance. design. manufacture and repair of the structures if the fractured (cracked) element and the residual life can be detected. The purport of this thesis is to theoretically explore and prove the effectiveness and practical values of the above-mentioned conception