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 在這篇論文中，我們研究固定端樑的暫態振動，而此樑受到磁場、軸向力、均勻彈簧支撐、阻尼及橫向載重的作用，其中感應磁場(induced magnetic field)、磁化強度(magnetization)、磁感應(magnetic induction)等關係式亦被求出，樑的運動方程式是由Hamilton 定理推導而得。為求此系統的解，我們先假設一個滿足邊界條件的近似位移函數，之後再採用Galerkin 的方法求解，最後，我們求得第一個模態的位移解。 樑在穩定的振動情況下，受橫向磁場的作用越大則位移越小、振動頻率越小；受軸向壓力越大則位移越大、振動頻率越小。
 In this study, the transient vibration of a fixed-fixed beam is considered. The transverse magnetic force, transverse magnetic couple, axial force, uniform translation spring force, transverse surface force, and the damper are also considered in the system. The relationships between magnetic induction, induced magnetic field and magnetization are solved. The equation of motion of the beam is derived by using the Hamilton’s principle. In order to solve the system equation, an approximate displacement function that satisfies the boundary conditions is assumed, and then the Galerkin method is adopted to obtain the solution of the system. Finally, the displacement of the beam is presented for the first mode. Under stable situations, the more the transverse magnetic field increases, the more the displacement and the frequency decrease, also the more the compressive axial load increases, the more the displacement increases and frequency decreases.
 CONTENTS ABSTRACT 1. INTRODUCTION…….……………………………….…………………………..1 2. EQUATION OF MOTION…………………………………………………….3 3. ANALYTICAL PROCEDURE……………………………………………………8 4. GALERKIN’S METHOD.……….……..………………………………………12 5. NUMERICAL RESULTS AND DISCUSSIONS…………………..…………….17 6. CONCLUSIONS…………………………………………………………………21 REFERENCES…………………….………………………….……………………22
 References1.Rreitz. Milford. Christy Foundations Of Electromagnetic Theory, Addison, Wesley.2. Y. S. Shin and G. Y. Wu, and J. S. Chen, Transient Vibrations of a Simply-Supported Beam with Axial Loads and Transverse Magnetic Fields MECH. STRUCT. & MACH., 26(2), 115-130 (1998)3. F. C. and Moon and Y. H. Pao, Vibration and dynamic instability of a beam-plate in a transverse magnetic field, J. Appl. Mech.36: 92-100 (1969).4. S.A. Ambartsumian, Magneto-elasticity of thin plates and shells, J. Appl. Mech. Rev. 35: 1-5 (1982)5. F.C. Moon, The Mechanics of ferroelastic plates in a uniform magnetic field, J. Appl. Mech. 37: 153-158 (1970).6. A. A. F. Van de Ven, Magnetoelastic buckling of thin plates in a uniform transverse magnetic field, J. Elasticity. 8:297-312 (1978)7. D. V. Wallerstein and M. O. Peach, Magnetoelastic buckling of beams and thin plates of magnetically soft material, J. Appl. Mech. 39: 451-455 (1972).8. F.C. Moon and Y. H. Pao, Magnetoelastic buckling of a thin plate, J. Appl. Mech. 37: 53-58 (1968).9. J. M. Dalrymple, M. O. Peach, and G. L. Viegelahn, Magnetoelastic buckling of thin magnetically soft plates in cylindrical mode, J. Appl. Mech. 41: 145-150 (1974).10. J. M. Dalrymple, M. O. Peach, and G. L. Viegelahn, Edge effect influence on Magnetoelastic buckling rectangular plates, J. Appl. Mech. 44: 305-310 (1977).11. K. Miya, k. Hara, and K. Someya, Experimental and theoretical study on magnetoelastic buckling of ferroelastic cantilevered beam-plate, J. Appl. Mech. 45: 355-360 (1978).12. Henery L. Langhaar, Energy Methods in Applied Mechanics, John Wiley and Sons, Inc. New York London.13. M. L. James/G. M. Smith, J. C. Wolfford / P. W. Whaley, Vibration of Mechanical and Structural System.14. Larry J. Segerlind, Applied Finite Element Analysis, John Wiley and Sons.15. G. Goudjo and G. A. Maugin, On the static and dynamic stability of soft-ferromagnetic elastic plates, J. Mec. Thero. Appl. 2:947-975 (1985)16. H. Kojima and K. Nagaya, Nonlinear forced vibration of a beam with a mass subjected to alternating electromagnetic force, Bull. JSME 28:468-474(1985)
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 1 含有集中質量、彈簧及黏滯阻尼的均勻樑之振動分析 2 複材層疊曲樑之靜動態分析 3 函數板逆運算問題之研究 4 與流體接觸之板的振動分析 5 具厚度變化之環狀板之自由振動分析 6 附帶任意集中質量之不均勻樑的自由振動分析 7 含有頂端質量之浸在液體中的非均勻柱之振動分析 8 中間軸轉換法求拓樸形狀設計 9 考慮剪變形的曲樑之面內變形及振動問題的DQEM分析 10 曲形樑的自由與強迫振動分析 11 旋轉複合材料樑之振動模態分析 12 以有限條元法分析直線形箱型樑橋受移動載重之動態反應 13 Timoshenko樑的動態穩定性分析 14 含拘束阻尼層旋轉預扭樑系統之振動與穩定性

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