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???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
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dc.contributor.advisor | 盧中仁 | zh_TW |
dc.contributor.advisor | Chung-Jen Lu | en |
dc.contributor.author | 謝易龍 | zh_TW |
dc.contributor.author | Yi-Long Xie | en |
dc.date.accessioned | 2023-08-15T16:27:01Z | - |
dc.date.available | 2023-11-09 | - |
dc.date.copyright | 2023-08-15 | - |
dc.date.issued | 2023 | - |
dc.date.submitted | 2023-07-26 | - |
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Plaut, "Deformation and vibration of compressed, nested, elastic rings on rigid base," Thin-Walled Structures, vol. 132, pp. 167-175, 2018. G. Domokos, P. Holmes, and B. Royce, "Constrained euler buckling," Journal of Nonlinear Science, vol. 7, pp. 281-314, 1997. H. Chai, "The post-buckling response of a bi-laterally constrained column," Journal of the Mechanics and Physics of Solids, vol. 46, no. 7, pp. 1155-1181, 1998. P. Holmes, G. Domokos, J. Schmitt, and I. Szeberényi, "Constrained Euler buckling: an interplay of computation and analysis," Computer Methods in Applied Mechanics and Engineering, vol. 170, no. 3-4, pp. 175-207, 1999. J.-S. Chen and W.-C. Ro, "Deformations and stability of an elastica subjected to an off-axis point constraint," ASME Journal of Applied Mechanics, vol. 77, no. 3, 2010. W.-C. Ro, J.-S. Chen, and S.-Y. Hong, "Vibration and stability of a constrained elastica with variable length," International Journal of Solids and Structures, vol. 47, no. 16, pp. 2143-2154, 2010. J.-S. Chen and H.-H. Wu, "Deformation and stability of an elastica under a point force and constrained by a flat surface," International Journal of Mechanical Sciences, vol. 53, no. 1, pp. 42-50, 2011. J.-S. Chen and L.-Y. Hua, "Effects of clamping misalignments on the line-contact deformation of a constrained elastica," International Journal of Non-Linear Mechanics, vol. 99, pp. 288-294, 2018. J.-S. Chen and S.-Y. Hung, "Deformation and stability of an elastica constrained by curved surfaces," International Journal of Mechanical Sciences, vol. 82, pp. 1-12, 2014. J.-S. Chen and L.-C. Wang, "Contact between two planar buckled beams pushed together transversely," International Journal of Solids and Structures, vol. 199, pp. 181-189, 2020. N. N. Goldberg and O. M. O'Reilly, "On contact point motion in the vibration analysis of elastic rods," Journal of Sound and Vibration, vol. 487, p. 115579, 2020. J. E. Flaherty and J. B. Keller, "Contact problems involving a buckled elastica," SIAM Journal on Applied Mathematics, vol. 24, no. 2, pp. 215-225, 1973. J.-S. Chen and Y.-C. Lin, "Vibration and stability of a long heavy elastica on rigid foundation," International Journal of Non-Linear Mechanics, vol. 50, pp. 11-18, 2013. J.-S. Chen and C.-C. Lee, "Vibration and snapping of a self-contacted beam under prescribed end rotations," European Journal of Mechanics-A/Solids, vol. 85, p. 104128, 2021. J.-S. Chen and T.-Y. Liao, "Snap boundary of self-contacted planar elastica under prescribed end rotations," International Journal of Non-Linear Mechanics, vol. 134, p. 103748, 2021. R. H. Plaut and L. N. Virgin, "Deformation and vibration of upright loops on a foundation and of hanging loops," International Journal of Solids and Structures, vol. 51, no. 18, pp. 3067-3075, 2014. Z. Wang and G. H. van der Heijden, "Buckling between soft walls: sequential stabilization through contact," Proceedings of the Royal Society A, vol. 477, no. 2250, p. 20210106, 2021. J.-S. Chen and Z.-H. Yang, "On the asymmetric line-contact deformation between two planar elasticae," International Journal of Solids and Structures, vol. 256, p. 111991, 2022. | - |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88470 | - |
dc.description.abstract | 當兩個相同的彈性樑受到端點軸向推力作用時,彼此之間可能出現點接觸、對稱以及非對稱線接觸的情況。本論文探討非對稱線接觸的平衡解及其穩定性。
過去的研究指出,對稱線接觸下,兩樑只有在接觸段的兩端有集中力,接觸段內部的接觸力為零,因此可以視為兩點接觸。然而,當線接觸形式為非對稱時,接觸段內部存在分佈力,無法視為兩點接觸。本論文將線接觸段的兩樑視為一根合併樑,由此分析平衡解。這種方法的優點在於,線接觸段的分佈力為內力,不會出現在運動方程式。 平衡解的穩定性可由其附近小擾動的頻率來判別。在振動過程中,接觸點的滑動,導致線接觸長度會隨時間改變,這使得問題變得更加複雜。為了克服這個困難,我們採用隨著接觸點移動的座標系,透過這個移動坐標系和原先固定坐標系的轉換關係,推導得平衡解附近小擾動的線性運動方程式,最後利用打靶法得到小擾動的自然頻率。 為了驗證理論結果,我們設計了實驗裝置。在設定的推進量下,輕敲彈性樑施加微小振動,量測適當點的位移,並透過快速傅立葉轉換得到頻譜圖。最後,比對實驗與理論結果中自然頻率隨推進量變化的趨勢,從而驗證理論分析結果。 | zh_TW |
dc.description.abstract | When two identical elastic beams are subjected to axial thrust at their endpoints, point contact, symmetric line contact, and asymmetric line contact can occur between them. This paper investigates the equilibrium solutions and their stability for asymmetric line contact.
Previous studies have shown that in symmetric line contact, the internal forces in the contact region of the beams exist only at the ends as concentrated forces, while the distributed forces in the interior contact region are zero. Therefore, the two beams can be treated as in contact at two points. However, when the line contact is asymmetric, distributed forces exist in the contact region. In this case, the two-point contact model no longer suitable. In this paper, the two beams in the contact region are treated as a merged beam, and the equilibrium solutions are analyzed accordingly. The advantage of this approach is that the distributed forces in the line contact region are internal forces and do not appear in the equations of motion. The stability of equilibrium solutions can be determined by the frequencies of small perturbations around them. During the vibration process, the sliding of the contact point causes the length of the contact segement to change with time, which makes the problem more complex. To overcome this difficulty, we adopt a coordinate system that moves with the contact point. Through the transformation relationship between this moving coordinate system and the original fixed coordinate system, we derive the linear equations of motion for small perturbations near the equilibrium solutions. Finally, we use the shooting method to obtain the natural frequencies of the perturbations. To validate the theoretical results, we designed an experiment. Under a specified amount of thrust, the elastic beam is lightly tapped to induce small vibrations. The displacements at appropriate points are measured, and the Fourier transform is used to obtain the frequency spectrum. Finally, by comparing the trend of the natural frequencies with the amount of thrust in the experimental and theoretical results, the theoretical analysis is validated. | en |
dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-15T16:27:01Z No. of bitstreams: 0 | en |
dc.description.provenance | Made available in DSpace on 2023-08-15T16:27:01Z (GMT). No. of bitstreams: 0 | en |
dc.description.tableofcontents | 致謝 i
摘要 ii Abstract iii 目錄 v 圖目錄 vii 表目錄 ix 第一章 導論 1 第二章 理論分析 3 2.1 理論模型 3 2.2 彈性樑的運動方程式 4 2.3 非對稱線接觸平衡解 6 2.3.1 非接觸段平衡方程式及邊界條件 6 2.3.2 線接觸段平衡方程式及邊界條件 8 2.3.3 接觸點的界面條件 9 2.3.4 靜態求解方法 10 2.4 非對稱線接觸穩定性分析 14 2.4.1 非接觸段擾動方程式及邊界條件 18 2.4.2 線接觸段擾動方程式及邊界條件 20 2.4.3 上下樑接觸點的界面條件 24 2.4.4 動態求解方法 26 第三章 實驗設計 31 第四章 結果與討論 35 4.1 理論分析結果 35 4.2 實驗結果 40 第五章 結論 48 參考文獻 50 附錄目錄 53 附錄一 線接觸段軸向壓力關係 54 附錄二 微擾關係推導 55 附錄三 擾動方程式推導 58 附錄四 上下彈性樑左端邊界條件推導 64 附錄五 上下彈性樑右端的邊界條件推導 66 附錄六 界面摩擦力效應實驗 68 | - |
dc.language.iso | zh_TW | - |
dc.title | 兩平面彈性樑非對稱線接觸的穩定性分析 | zh_TW |
dc.title | Stability of Two Planar Elasticae in Asymmetric Line-Contact | en |
dc.type | Thesis | - |
dc.date.schoolyear | 111-2 | - |
dc.description.degree | 碩士 | - |
dc.contributor.oralexamcommittee | 伍次寅;蘇春熺 | zh_TW |
dc.contributor.oralexamcommittee | Tzu-yin Wu;Chun-Hsi Su | en |
dc.subject.keyword | 彈性樑非對稱線接觸,合併樑法,微擾法, | zh_TW |
dc.subject.keyword | elasticae asymmetric line-contact,combined beam,vibration method, | en |
dc.relation.page | 69 | - |
dc.identifier.doi | 10.6342/NTU202301949 | - |
dc.rights.note | 未授權 | - |
dc.date.accepted | 2023-07-27 | - |
dc.contributor.author-college | 工學院 | - |
dc.contributor.author-dept | 機械工程學系 | - |
Appears in Collections: | 機械工程學系 |
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ntu-111-2.pdf Restricted Access | 3.1 MB | Adobe PDF |
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