臺灣博碩士論文加值系統

關於兩端夾持之受拘束板條，在彈性板條兩側有對稱固定拘束面，受力後與拘束面接觸後有許多種變形，而在先前的研究提到在線接觸變形時，其兩個最低自然頻率為零；在本文我們研究了傾斜夾持對線接觸穩定性的影響，當兩端夾持的切線方向相對於兩端連線為同一側，則線接觸變形為穩定，反之，若兩端夾持的切線方向相對於兩端連線為不同側，則線接觸變形則不存在；若在兩者之間，也就是兩端夾持切線方向和拘束面平行，線接觸變形存在為中性穩定，在這理想情形，我們做實驗發現，可以觀察到從點接觸跳躍至別的變形，也可以觀察到從點接觸變為線接觸，我們懷疑這是由於在現實中難以實現夾持的切線方向能夠完全平行於拘束面，因此，實際上幾乎是不可能預測在理想情形下線接觸變形是否存在。

Previous research shows that the lowest two natural frequencies of the line-contact deformation of a clamped-clamped elastic strip constrained by a pair of plane walls located symmetrically with respect to the clamping axis are degenerately zero. In this article we study the effect of tilting clamps on the stability of the line-contact deformation. If the clamp tangents of the two ends point in the same side of the clamping axis, the line-contact deformation is stable. On the other hand, if the clamp tangents point in opposite sides, the line-contact deformation does not exist. In the special case when either one of the clamp tangents is parallel to the constraining wall, the line-contact deformation exists and remains neutrally stable. In the experiment, the chance of obtaining line-contact deformation is about the same as the chance of jumping following the point-contact deformation. We suspect that this is due to the difficulty of aligning the clamp tangents parallel to the wall in practice. Therefore, it is almost impossible to predict in practice whether the line contact deformation exists in the ideal case.

口試委員審定書 ii
摘要 iii
Abstract iv
目錄 v
圖目錄 vii
表目錄 x
第一章 導論 1
第二章 理論模型與統御方程式 3
2.1 靜態變形分析 4
2.1.1 邊界條件 5
2.1.2 求解方法 7
2.1.3 受力變形曲線 9
2.2 振動及穩定性分析 9
2.2.1 Lagranian和Eulerian描述式10
2.2.2 邊界條件與轉換方程式 15
2.2.3 求解方法 17
2.2.4 自然頻率與穩定性分析 19
2.3 小變形理論 20
第三章 缺陷分析 22
3.1 兩端夾持角度傾斜 22
3.1.1 αA=0.5。, αB=-0.5。 23
3.1.2 αA=0。, αB=0.5。 24
3.1.3 αA=0.5。, αB=0.5。 26
3.2 拘束面傾斜 27
3.3 兩端夾持高度偏移 28
第四章 實驗量測 30
第五章 結論 36
參考文獻 37
附錄目錄 39

[1] V.I. Feodosyev, Selected Problems and Questions in Strength of Materials. Mir, Moscow. Translated from the Russian by M. Konyaeva, 1977.
[2] D.P. Vaillette, G.G. Adams, 1983. An elastic beam contained in a frictionless channel, ASME J. Appl. Mech. 50 (1983) 693–694.
[3] G.G. Adams, R.C. Benson, Postbuckling of an elastic plate in a rigid channel, Int. J. Mech. Sci. 28 (1986) 153–162.
[4] X. Chateau, Q.S. Nguyen, Buckling of elastic structures in unilateral contact with or without friction, Eur. J. Mech. A-Solid 1 (1991) 71-89.
[5]* N. Adan, I. Sheinman, E. Altus, Post-buckling behavior of beams under contact constraints, ASME J. Appl. Mech. 61 (1994) 764–772.
[6] G. Domokos, P. Holmes, B. Royce, Constrained Euler buckling, J. Nonlinear Sci. 7 (1997) 281-314.
[7] P. Holmes, G. Domokos, J. Schmitt, I. Szeberenyi, Constrained Euler buckling: an interplay of computation and analysis, Comput. Method Appl. M. 170 (1999) 175-207.
[8] H. Chai, The post-buckling behavior of a bilaterally constrained column, J. Mech. Phys. Solids 46 (1998) 1155–1181.
[9] H. Chai, On the post-buckling behavior of bilaterally constrained plates, Int. J. Solids Struct. 39 (2002) 2911-2926.
[10] B. Roman, A. Pocheau, Buckling cascade of thin plates: forms, constraints and similarity, Europhys. Lett. 46 (1999) 602–608.
[11] B. Roman, A. Pocheau, Postbuckling of bilaterally constrained rectangular thin plates, J. Mech. Phys. Solids 50 (2002) 2379-2401.
[12] R.S. Manning, G.B. Bulman, Stability of an elastic rod buckling into a soft wall, Proc. R. Soc. A 461 (2005) 2423-2450
[13] W.-C. Ro, J.-S. Chen, S.-Y. Hung, Vibration and stability of a constrained elastica with variable length, Int. J. Solids Struct. 47 (2010) 2143-2154.
[14] J.-S. Chen, and S.-Y. Hung, Deformation and stability of an elastica Constrained by curved surfaces, International Journal of Mechanical Sciences 82 (2004) 1-12.
[15] S. Katz, S. Givli, The post-buckling behavior of a beam constrained by springy walls, Journal of the Mechanics and Physics of Solids 78 (2015) 443–466.
[16] J.-S. Chen, C.-J. Lu, C.-Y. Lee, On the use of energy method with element splitting to determine the stability of a constrained elastica, International Journal of Non-Linear Mechanics 76 (2015) 77-86