具表面裂紋的大振幅簡支樑之振動分析

在本文中探討的是假設在沒有受到外力的情況下產生大變形自由振動的長方形截面簡支樑，並在樑的正中央產生一直裂式裂紋。在振動過程中，不考慮非保守力影響並使用漢米爾頓(Hamilton)準則來求出系統的運動方程式、邊界條件和形狀函數，並利用Galerkin's method來進行推導Mathieu方程式和無裂紋時的勁度。在振動部分是使用Runge-Kutta的方法來描述振幅與時間的關係；在裂紋模型上，同時討論呼吸式裂紋與傳統開放式裂紋模型，並在求取開放式裂紋與呼吸式裂紋的勁度時，提出不同的方法。最後對於在大振幅振動的情況下，探討呼吸式裂紋樑和開放式裂紋樑的頻率變化與裂紋深度關係。

關鍵字

簡支樑；裂紋；振動；大振幅

並列摘要

In this study, the large amplitude vibration of a simply supported beam with a straight-edge crack at mid-span is considered. The equation of motion and boundary conditions are derived by Hamilton 's principle. The Mathieu equation and the stiffness of the beam without a crack are derived by Galerkin's method. And then using Runge-Kutta method to determine the relationship between amplitude and time. About the crack model, both of the opening crack and the breathing crack are considered. And the different way to calculate the stiffness of the opening and breathing crack is provided. In addition, under the premise of large amplitude vibration, with the crack depth ratio in change, the relationship of frequency ratio and crack depth ratio with the opening crack and the breathing crack are discussed in this study.

並列關鍵字

crack ； vibration ； large amplitude ； simply supported beam

參考文獻

1. M. Sathyamoorthy, (1982) Shock and vibration Digest, 14(17), 19-35. Nonlinear analysis of beams part I: a survey of recent advances.

3. D. A. Evensen, (1968) American Institute of Aeronautics and Astronautics Journal, 6, 370-372 Nonlinear vibration of beams with various boundary conditions.

4. A. V. Srinivasan, (1965) American Institute of Aeronautics and Astronautics Journal, 3, 1951-1953. Large amplitude free oscillations of beams and plates.

6. C. Mei, (1972) American Institute of Aeronautics and Astronautics Journal 10, 355-357. Nonlinear vibrations of beams by matrix displacement method.

8. C. Mei, (1973) Computers and Structures 3, 163-174. Finite element displacement method for large amplitude free flexural vibration.

國際替代計量

具表面裂紋的大振幅簡支樑之振動分析

全文下載

主題瀏覽