受橫向磁場含裂紋鐵磁平板之振動分析

Vibration Analysis of Cracked Ferromagnetic Plate in Transverse Magnetic Field

曾政富(Cheng-Fu Tseng)

指導教授 ： 施延欣

中原大學/工學院/機械工程學系/碩士(2006年)

https://doi.org/10.6840/cycu200600697

摘要

考慮一個裂紋平板，受平面負載與橫向磁場的影響，且四端均為簡支撐之平板的振動分析。依據 von 的平板理論，推導含裂紋平板的運動方程式，在振動受到平面向負載、橫向磁場的作用，同時也考慮阻尼係數的影響。本文中不同裂紋長度、縱橫比(aspect ratio)影響的線性自然振動頻率，與已知的文獻結果相比較，其結果與本文所推導的公式相近，所以本文公式是可適用的。因此，文中運用Galerkin 的方法，將統御方程式化簡為一個以時間為變數的 Mathieu 方程式，至於暫態振動的部分，則使用四階 Runge-Kutta 的方法來描述振動對時間時和速度對振動的關係表分別繪出，裂紋長度對振動的關係也同時被描述及探討。本文對於平面向負載和橫向磁場的振盪所產生的共振、不同的平面向負載、阻尼係數的振動分析，提供完整分析步驟是本研究主要的貢獻。

關鍵字

振動 ； 線性自然頻率 ； 裂紋平板 ； 阻尼 ； 磁場 ； 裂紋長度

並列摘要

The vibration of a cracked plate under in-plane force, transverse magnetic field and simply supported at all edges are considered. Based on the von plate theory, the equation of motion has been including in-plane force, transverse magnetic and damping coefficient. The linear natural frequency is affected by different crack length and aspect ratio which are compared with the results in literature and they are closed. The equations of vibration are reduced to an ordinary differential equation by assuming mode shape and Galerkin’s procedure. The natural frequency is determined by ordinary different equation. Using Runge-Kutta method, the amplitude-time and velocity-amplitude are determined. The effects of vibration several parameters on cracked plate such as in-plane force, transverse magnetic field, damping coefficient and cracked length are provided and discussed in this study.

並列關鍵字

magnetic field ； vibration ； crack length ； linear natural frequency ； cracked plate

參考文獻

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5. Ambartsumyan, S. A., “Magnetoelasticity of thin plates and shells”, Applied Mechanics Review 35, pp. 1-5, 1982.

6. Kaliski, S., “Magnetoelastic Vibration of perfectly conducting plates and bars”,