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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 盧中仁 | zh_TW |
dc.contributor.advisor | Chung-Jen Lu | en |
dc.contributor.author | 許文俊 | zh_TW |
dc.contributor.author | Wen-Chun Hsu | en |
dc.date.accessioned | 2023-09-22T17:14:34Z | - |
dc.date.available | 2023-11-09 | - |
dc.date.copyright | 2023-09-22 | - |
dc.date.issued | 2023 | - |
dc.date.submitted | 2023-08-09 | - |
dc.identifier.citation | [1] H. Kolsky, Stress Waves in Solids, Dover Publication, 1963.
[2] K. Graff, Wave Motion in Elastic Solids, Publication of: Oxford University Press, 1975. [3] P. Mathews, "Vibrations of a beam on elastic foundation," ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, vol. 38, no. 3‐4, pp. 105-115, 1958. [4] G. Adams, "Critical speeds and the response of a tensioned beam on an elastic foundation to repetitive moving loads," International Journal of Mechanical Sciences, vol. 37, no. 7, pp. 773-781, 1995. [5] G. Denisov, "On the problem of the stability of one-dimensional unbounded elastic systems," Journal of Applied Mathematics and Mechanics, vol. 49, no. 4, pp. 533-537, 1985. [6] A. Metrikine and S. Verichev, "Instability of vibrations of a moving two-mass oscillator on a flexibly supported Timoshenko beam," Archive of Applied Mechanics, vol. 71, no. 9, pp. 613-624, 2001. [7] A. Metrikine and H. Dieterman, "Instability of vibrations of a mass moving uniformly along an axially compressed beam on a viscoelastic foundation," Journal of Sound and Vibration, vol. 201, no. 5, pp. 567-576, 1997. [8] A. Metrikine, J. Blaauwendraad, and S. Verichev, "Stability of a two-mass oscillator moving on a beam supported by a visco-elastic half-space," International Journal of Solids and Structures, vol. 42, pp. 1187-1207, 2005. [9] T. Mazilu, M. Dumitriu, and C. Tudorache, "On the dynamics of interaction between a moving mass and an infinite one-dimensional elastic structure at the stability limit," Journal of Sound and Vibration, vol. 330, no. 15, pp. 3729-3743, 2011. [10] P. Mathews, "Vibrations of a beam on elastic foundation," Journal of Applied Mathematics and Mechanics, vol. 38, no. 3-4, pp. 105-115, 1958. [11] P. Mathews, "Vibrations of a beam on elastic foundation II," Zeitschrift Angewandte Mathematik und Mechanik, vol. 39, no. 1-2, pp. 13-19, 1959. [12] S. Chonan, "Moving Harmonic Load on an Elastically Supported Timoshenko Beam," Zeitschrift Angewandte Mathematik und Mechanik, vol. 58, no. 1, pp. 9-15, 1978. [13] N.-c. Tsai and R. A. Westmann, "Beam on tensionless foundation," Journal of the Engineering Mechanics Division, vol. 93, no. 5, pp. 1-12, 1967. [14] M. Farshad and M. Shahinpoor, "Beams on bilinear elastic foundations," International Journal of Mechanical Sciences, vol. 14, no. 7, pp. 441-445, 1972. [15] W. Johnson and V. Kouskoulas, "Beam on Bilinear Foundation," Journal of Applied Mechanics, vol. 40, no. 1, p. 239, 1973. [16] Y. Weitsman, "Onset of separation between a beam and a tensionless elastic foundation under a moving load," International Journal of Mechanical Sciences, vol. 13, no. 8, pp. 707-711, 1971. [17] Y. Weitsman, "On Foundations That React in Compression Only," Journal of Applied Mechanics, vol. 37, no. 4, p. 1019, 1970. [18] J. Choros and G. Adams, "A Steadily Moving Load on an Elastic Beam Resting on a Tensionless Winkler Foundation," Journal of Applied Mechanics, vol. 46, no. 1, p. 175, 1979. [19] S.-M. Kim and J. M. Roesset, "Dynamic response of a beam on a frequency-independent damped elastic foundation to moving load," Canadian Journal of Civil Engineering, vol. 30, no. 2, pp. 460-467, 2003. [20] Z. Celep, A. Malaika, and M. Abu-Hussein, "Forced vibrations of a beam on a tensionless foundation," Journal of Sound and Vibration, vol. 128, no. 2, pp. 235-246, 1989. [21] D. Dichmann, J. Maddocks, and R. Pego, "Hamiltonian dynamics of an elastica and the stability of solitary waves," Archive for Rational Mechanics and Analysis, vol. 135, pp. 357-396, 1996. [22] S. Lenci and F. Clementi, "Flexural wave propagation in infinite beams on a unilateral elastic foundation," Nonlinear Dynamics, vol. 99, no. 1, pp. 721-735, 2020. [23] S. Lenci, "Propagation of periodic waves in beams on a bilinear foundation," International Journal of Mechanical Sciences, vol. 207, p. 106656, 2021. | - |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90059 | - |
dc.description.abstract | 無限長樑在各種基底上受到不同形式負載下的平衡解、週期解一直是重要的研究課題,也有許多成果。
然而關於非受力狀態下,樑內行進波的傳遞,除了已知的在雙向線彈性基底上正弦行進波有解析的色散關係外,對其他形式基底上樑內行進波的研究相對較少。 本論文討論在雙線性基底上無限長樑內週期性行進波的傳遞特性。由於基底的雙線性特性,這個問題是非線性問題。我們利用了兩種方法:分段匹配法和打靶法,求取行進波的波形;利用Floquet理論判別行進波的穩定性。 行進波一波長內至少包含各一個位移為正和位移為負的段;位移為正的段和為負的段的交點稱為分段點。行進波的重要特性為速度以及分段點的位置和數目。我們詳細探討了波速和分段點隨基底的彈性特性變化的情形,畫出對應的分歧圖,並標示穩定、不穩定區域。 | zh_TW |
dc.description.abstract | The equilibrium and periodic solutions of an infinite beam under various types of loading on different foundations have been an important research topic with numerous achievements.
However, regarding the propagation of traveling waves in the beam under non-force conditions, apart from the known analytical dispersion relation for sinusoidal traveling waves on an elastic foundation, there has been relatively less research on traveling waves in beams on other types of foundations. This paper discusses the characteristics of periodic traveling waves in an infinite beam resting on a bilinear foundation. Due to the bilinear nature of the foundation, the problem becomes nonlinear. We employ two methods, namely the piecewise matching method and the shooting method, to obtain the waveforms of traveling waves. The stability of the traveling waves is determined using Floquet theory. Within one wavelength, the traveling wave contains at least one segment with positive displacement and one segment with negative displacement, and the intersection point of these segments is referred to as a segment point. The key features of the traveling waves are the velocity, positions and numbers of the segment points. We thoroughly investigate the variations of wave velocity and segment points with respect to the elastic properties (stiffness) of the foundation, constructing corresponding bifurcation diagrams and identifying stable and unstable regions. | en |
dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-09-22T17:14:34Z No. of bitstreams: 0 | en |
dc.description.provenance | Made available in DSpace on 2023-09-22T17:14:34Z (GMT). No. of bitstreams: 0 | en |
dc.description.tableofcontents | 口試委員審定書(於紙本上) i
致謝 ii 摘要 iii Abstract iv 目錄 v 圖目錄 vii 第一章 導論 1 第二章 研究方法 3 2.1 理論模型 3 2.2 雙線性彈性基底 4 2.3 行進波解 6 2.4 分段匹配法 7 2.5 打靶法 11 2.6 週期解的穩定性 12 第三章 數值結果及參數分析 15 3.1 行進波波形 15 3.2 穩定性分析 25 3.3 波速、分段點和基底彈性係數關係 31 第四章 結論 43 參考文獻 44 附錄目錄 47 附錄一 十條齊次代數方程式推導 48 附錄二 單向基底邊界方程式推導 49 | - |
dc.language.iso | zh_TW | - |
dc.title | 雙線性彈性基底上無限長樑的行進波 | zh_TW |
dc.title | Traveling Waves in an Infinite Beam on a Bilinear Elastic Foundation | en |
dc.type | Thesis | - |
dc.date.schoolyear | 111-2 | - |
dc.description.degree | 碩士 | - |
dc.contributor.oralexamcommittee | 盧南佑;田孟軒 | zh_TW |
dc.contributor.oralexamcommittee | Nan-You Lu;Meng-Hsuan Tien | en |
dc.subject.keyword | 雙線性彈性基底樑,週期解的穩定性, | zh_TW |
dc.subject.keyword | beam resting on a bilinear elastic foundation,stability of the periodic solutions, | en |
dc.relation.page | 50 | - |
dc.identifier.doi | 10.6342/NTU202303600 | - |
dc.rights.note | 未授權 | - |
dc.date.accepted | 2023-08-12 | - |
dc.contributor.author-college | 工學院 | - |
dc.contributor.author-dept | 機械工程學系 | - |
顯示於系所單位: | 機械工程學系 |
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