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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 陳振山(Jen-San Chen) | |
dc.contributor.author | I-Shein Chen | en |
dc.contributor.author | 陳逸軒 | zh_TW |
dc.date.accessioned | 2021-05-15T17:55:20Z | - |
dc.date.available | 2017-07-29 | |
dc.date.available | 2021-05-15T17:55:20Z | - |
dc.date.copyright | 2014-07-29 | |
dc.date.issued | 2014 | |
dc.date.submitted | 2014-07-15 | |
dc.identifier.citation | [1] Chen, J.-S., J. Fang, 2014. Vibration of a spatial extensible elastica supported by spherical hinges, Int. J. Solids Struct. 51, 35-40.
[2] Champneys, A.R., Thompson, J.M.T., 1996. A multiplicity of localized buckling modes for twisted rod equations Proc. R. Soc. Lond. A 452, 2467-2491 [3] Coleman, B.D., Dill, E.H., Lembo, M., Lu, Z., Tobias, I., 1993. On the dynamics of rods in the theory of Kirchhoff and Clebsch. Arch. Rational Mech. Anal. 121, 339-359. [4] Cusumano, J.P., Moon, F.C., 1995. Chaotic non-planar vibrations of the thin elastica, Part II: Derivation and analysis of a low-dimensional model. J. of Sound Vib. 179, 209-226. [5] Goriely, A., Tabor, M., 1997. Nonlinear dynamics of filaments, I. Dynamical instability. Physica D 105, 20-44. [6] Goudsmit S, Wang, M.C., 1940. Introduction to the problem of the isochronous hairspring. J. Appl. Phys. 11, 806-815. [7] Haringx, J.A. 1951. Elastic stability of flat spiral springs. Appl. Sci. Res. A2, 9-30. [8] Kreyszig, E., 1983. Advanced Engineering Mathematics, John Wiley & Sons, New York. [9] Lu, C.-L., Perkins, N.C., 1994. Nonlinear spatial equilibria and stability of cables under uni-axial torque and thrust. J. Appl. Mech. 61, 879-886. [10] Plaut, R.H., Virgin, L.N., 2004. Three-dimensional postbuckling and vibration of vertical half-loop under self-weight. Int. J. Solids Struct. 41, 4975–4988. [11] Reismann, H., Pawlik, P.S., 1980, Elasticity: Theory and Applications, John Wiley & Sons, New York. [12] van der Heijden, G.H.M., Neukirch, S., Goss, V.G.A., Champneys, Thompson, J.M.T., 2003. Instability and self-contact phenomena in the writhing of clamped rods. Int. J. Mech. Sci. 45, 161-196. [13] Xie, L., Ko, P., Du, R., 2014. The mechanics of spiral springs and its application in timekeeping. J. Appl. Mech. 81, 034504. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/5297 | - |
dc.description.abstract | 在本文中,使用空間彈性理論來分析渦旋彈簧的靜態變形與振動頻率,首先考慮圓形截面的渦旋彈簧,渦旋彈簧內外有兩端點,其中一端夾持於一固定端,另一端夾持在一可旋轉的圓形轉盤上。由靜態分析中可以得知,渦旋彈簧受扭轉一定角度之後,彈簧發生挫曲,形狀由平面變成三維變形。從扭力與旋轉角的關係圖中,可知彈簧會在轉兩圈後回到相同變形。在振動分析中,求得平面變形有平面及空間兩種模態振形,空間振動模態所相對應的自然頻率比平面振動模態所對應的自然頻率先下降至零,可以由此預測彈簧將以此模態振形發生空間變形。為驗證理論分析的正確性,本研究設計了一個初始圈數為五圈、圓形截面的渦旋彈簧,以及實驗機構,量測其扭力與旋轉角的關係與自然頻率,實驗結果與理論分析相符。接下來考慮矩形截面的渦旋彈簧,在扭力與旋轉角的關係圖中,可以看出矩形截面的長寬比不影響其平面變形曲線,但是會影響到發生挫曲時的旋轉角,以及空間變形曲線。最後,本論文利用振動法求出來的挫曲角度與矩形截面的長寬比的關係,也與前人利用平衡法的做出的結果做了比較。 | zh_TW |
dc.description.abstract | In this paper we use elastica theory to study the deformation and natural frequencies of a spiral spring. We first consider a spiral spring with circular cross section. Static analysis shows that the spring undergoes planar deformation first and buckles into spatial deformation at a bifurcation point. The load-deflection curve repeats itself after two full turns. Therefore, the spring returns to its initial shape after two full turns. The planar deformation has two types of mode shapes; i.e., in-plane and out-of-plane. If one proceeds from initial shape to the bifurcation point, the natural frequency of one of the out-of-plane modes reduces to zero. This out-of-plane mode shape will be the buckling mode when planar deformation buckles into spatial deformation. Experiments are conducted on a custom made spiral spring with circular cross section. The measured deformations and natural frequencies agree with theoretical predictions very well. We next proceed to consider a spiral spring with rectangular cross section. It is found that the planar deformation is independent of the stiffness ratio between the two principal directions of the cross section. However, the spatial deformation and the bifurcation point depend on the stiffness ratio. Finally, the relation between the critical angle and the stiffness ratio is obtained via vibration method and compared with previous work of others based on equilibrium method. | en |
dc.description.provenance | Made available in DSpace on 2021-05-15T17:55:20Z (GMT). No. of bitstreams: 1 ntu-103-R01522508-1.pdf: 2427258 bytes, checksum: eaa1e3756805e67677bb10f916fbc414 (MD5) Previous issue date: 2014 | en |
dc.description.tableofcontents | 第一章 導論 1
第二章 理論模型與控制方程式 3 2.1 彈性圓桿理論模型 3 2.2 控制方程式推導過程 4 第三章 靜態變形分析 7 第四章 振動分析 10 第五章 受力和位移關係圖 14 第六章 自然頻率與振動模態 16 6.1 控制位置 16 6.2 控制扭力 17 第七章 實驗設計與量測 19 7.1 實驗設備 19 7.2 扭力與旋轉角量測 20 7.3 自然頻率量測 21 第八章 不同初始圈數與不同截面的影響 23 第九章 結論 26 參考文獻 28 附錄I 靜態分析求解之純量方程式 57 附錄II 振動分析求解之純量方程式 61 附錄III 廣義應變向量 67 附錄IV N=3截面為圓形的渦旋彈簧 68 | |
dc.language.iso | zh-TW | |
dc.title | 渦旋彈簧之靜態變形與穩定性分析 | zh_TW |
dc.title | Deformation and vibration of a spiral spring | en |
dc.type | Thesis | |
dc.date.schoolyear | 102-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 盧中仁(Lu, Chung-Jen),莊嘉揚(Jia-Yang Juang) | |
dc.subject.keyword | 渦旋彈簧,彈性圓桿理論,振動, | zh_TW |
dc.subject.keyword | Spiral spring,Elastica,Vibration, | en |
dc.relation.page | 70 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2014-07-15 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 機械工程學研究所 | zh_TW |
顯示於系所單位: | 機械工程學系 |
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