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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 馬劍清(Chien-Ching Ma) | |
| dc.contributor.author | Yu-Chi Su | en |
| dc.contributor.author | 蘇于琪 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:28:32Z | - |
| dc.date.available | 2012-07-24 | |
| dc.date.copyright | 2009-07-24 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-21 | |
| dc.identifier.citation | R. A. Anderson, 'Transient Response of Uniform Beams,' California Institute of Technology, 1953.
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Doyle, 'A Matrix Methodology for Structural Analysis of a Wave Propagation in Multiple Connected Timoshenko Beams,' Journal of Sound and Vibration, vol. 158, pp. 11-24, 1992. K. F. Graff, Wave Motion in Elastic Solids. New York: Dover Publications, 1973. S. M. Han, H. Benaroya, and T. Wei, 'Dynamics of Transversely Vibrating Beams Using Four Engineering Theories,' Journal of Sound and Vibration, vol. 225, pp. 935-988, 1999. S. M. Howard and Y. H. Pao, 'Analysis and Experiments on Stress Waves in Planar Trusses,' Journal of Engineering Mechanics, vol. 124, pp. 884-891, 1998. T. C. Huang, 'The Effect of Rotary Inertia and of Shear Deformation on the Frequency and Normal Mode Equations of Uniform Beams With Simple End Conditions,' Journal of Applied Mechanics, vol. 28, pp. 579-584, 1961. A. Labuschagne, N. F. J. v. Rensburg, and A. J. v. d. Merwe, 'Comparison of Linear Beam Theory,' Mathematical and Computer Modelling, vol. 49, pp. 20-30, 2009. G. S. Lee and C. C. Ma, 'Transient Elastic Waves Propagating in a Multi-layered Medium Subjected to In-plane Dynamic Loadings I. Theory,' Proceedings of the Royal Society A, vol. 456, pp. 1355-1374, 1999. R. W. Leonard and B. Budiansky, 'On Traveling Waves in Beams,' National Advisory Committe for Aeronautics, vol. NACA TN 2874, 1953. W. R. LePage, Complex Variables and the Laplace Transform for Engineers. New York: Dover, 1961. C. C. Ma and G. S. Lee, 'General Three-Dimensional Analysis of Transient Elastic Waves in a Multilayered Medium,' Transactions of the ASME, vol. 73, pp. 490-504, 2006. C. C. Ma, S. W. Liu, and G. S. Lee, 'Dynamic Response of a Layered Medium Subjected to Anti-plane Loadings,' International Journal of Solids and Structures, vol. 38, pp. 9295-9312, 2001. J. Miklowitz, the Theory of Elastic Waves and Waveguides. New York: North Holland Publishing Co., 1978. J. Miklowitz and P. 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Merwe, 'Natural Frequencies and Modes of a Timoshenko Beam,' Wave Motion, vol. 44, pp. 58-69, 2006. F. J. Shaker, 'Method of Calculating the Normal Modes and frequencies of a Branched Timoshenko Beam,' NASA Technical Note, vol. TN D-4560, 1968. N. G. Stephen, 'The Second Spectrum of Timoshenko Beam Theory - Further Assessment,' Journal of Sound and Vibration, vol. 292, pp. 372-389, 2006. X. Y. Su, J. Y. Tian, and Y. H. Pao, 'Application of the Reverberation-Ray Matrix to the Propagation of Elastic Waves in a Layered Solid,' International Journal of Solids and Structures, vol. 39, pp. 5447-5463, 2002. X. Y. Su and Y. H. Pao, 'Ray-Normal Mode and Hybrid Analysis of Transient Waves in a Finite Beam,' Journal of Sound and Vibration, vol. 152, pp. 351-368, 1992. D. P. Thambiratnam, 'Transient Response of Beam Under Initial Stress,' Journal of Engineering Mechanics, vol. 110, pp. 1544-1555, 1984. S. P. Timosheko, 'On the Transverse Vibrations of Bars of Uniform Cross-section,' Philosophical Magazine, vol. 43, pp. 125-131, 1922. S. P. Timoshenko, 'On the Correction for Shear of the differential Equation for Transverse Vibrations of Bars of Uniform Cross-Section,' Philosophical Magazine, vol. 41, pp. 744-746, 1921. R. W. Traill-Nash and A. R. Collar, 'The Effects of Shear Flexibility and Rotatory Inertia on the Bending Vibrations of Beams ' Quart. Journ. Mech and Applied Math, vol. VI, pp. 187-222, 1953. Y. S. Uflyand, 'The Propagation of Waves in the Transverse Vibration of Bars and Plates,' Prikladnaia Mathmatica i Mekhanika, vol. 12, pp. 287-300, 1948. T. Usuki and A. Maki, 'Behavior of Beams Under Transverse Impact According to Higher-order Beam Theory,' International Journal of Solids and Structures, vol. 40, pp. 3737-3785, 2003. S. Yamamoto, K. Sato, and H. Koseki, 'A Study on Lateral Impact of Timoshenko Beam,' Computational Mechanics, vol. 6, pp. 101-108, 1990. T. Yokoyama and K. Kishida, 'Finite Element Analysis of Flexural Wave Propagation in Elastic Beams,' Technology Reports of the Osaka University, vol. 32, pp. 103-111, 1982. 張振銘, 馬劍清, '應用暫態彈性波理論反算薄膜系統之材料性質,' 國立台灣大學機械工程研究所碩士論文, pp. 26-27, 87年6月. 李艮生, 馬劍清, '三維層狀介質暫態彈性波傳的理論解析計算及實驗,' 國立台灣大學機械工程研究所博士論文, 87年6月. 楊清利, 馬劍清, '薄層材料系統剪力波之暫態及穩態波傳解析,' 國立台灣大學機械工程研究所碩士論文, 88年6月. 廖恆增, 馬劍清, '應用布拉格光纖光柵感測器於懸臂梁受撞擊之抑振研究,' 國立台灣大學機械工程研究所碩士論文, 97年7月. 莊國志, 馬劍清, '多維高解析度布拉格光纖光柵動態位移及應變量測系統之研發並應用於暫態波傳之量測,' 國立台灣大學機械工程研究所博士論文, 97年7月. 柯德清, 鮑亦興, '彈性波在三維剛架內之傳播與結構動應力分析,' 國立台灣大學應用力學研究所博士論文, 85年1月. 陳繼峰, 王彥博, 鮑亦興, '三維剛架結構之迴傳波射動力分析,' 國立交通大學土木工程研究所碩士論文,91年6月. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/42911 | - |
| dc.description.abstract | 樑的動態行為是工程領域中的一個重要問題。在眾多的樑理論假設中，古典樑理論(Bernoulli-Euler beam)因其簡單、提供合理工程近似等特點，較為常用，但其有高估共振頻及波速無上限的缺陷；提摩盛科樑理論(Timoshenko beam theory)雖較為複雜，但不僅波速有上限，且其穩態反應與精確樑理論(exact theory)有不錯的一致性，因此在動態分析上，提摩盛科樑理論較為合適。本篇論文將探討四個不同的暫態樑問題。
本文主要以兩種不同的解析方法-射線及模態展開法處理提摩盛科樑的動態問題。利用射線法準確、適宜計算短時間等特點，作模態展開法的標竿，來處理較長時間的反應，並提出動態和靜態結果對照，以及頻率域下的特性；另一方面，也以模態展開法處理古典樑來與提摩盛科樑理論比較，依此提出適用古典理論的樑尺寸。此外，本文使用疊加法和接觸理論以模態展開法解析鋼珠撞擊簡支樑的問題。而在懸臂樑方面，亦以模態疊加法導出數學的封閉解。 | zh_TW |
| dc.description.abstract | The topic of dynamics of beams is important in engineering. Among different beam theories, Bernoulli-Euler beam is most widely used owing to simplicity and reasonability. However, for analyzing dynamic problems, the Timoshenko beam is more appropriate.
This thesis applies two approaches – ray and normal mode method to deal with the transient response of Timoshenko beam. Ray solution is most accurate and suitable for predicting short time responses and the normal mode method can treat long time responses. Thus, we use the result obtained by ray solution as a standard for the normal mode method to calculate the long time response. Furthermore, the comparison of dynamic and static results is proposed and the frequency responses are discussed as well. On the other hand, the normal mode solution of Bernoulli-Euler beam is demonstrated and we compare its results with Timoshenko beam. The suitable slender ratio of Bernoulli-Euler beam for the analyzing transient displacement response is also presented. In addition, we analyze the responses of the simply supported beam subjected to impact of a steel ball problem. The normal mode solution of the cantilever beam subjected to constant impact force problem is also derived in this study. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:28:32Z (GMT). No. of bitstreams: 1 ntu-98-R96522506-1.pdf: 7853443 bytes, checksum: dd73463a96d4726ca12cce181b0e17e3 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Contents
Abstract ............................................................................................................................ I Contents........................................................................................................................ III List of Tables ................................................................................................................. VI List of Figures ..............................................................................................................VII List of Symbols............................................................................................................XIII Chapter 1 INTRODUCTION........................................................................................ 1 1-1 Research Motivation .......................................................................................... 1 1-2 Literature Review............................................................................................... 4 1-3 Thesis Organization............................................................................................ 6 1-4 Problem Description........................................................................................... 7 1-5 Derivation of Governing Equations ................................................................. 10 1-5.1 Timoshenko Beam……………………………………………………..10 1-5.2 Bernoulli-Euler Beam…………………………………………………15 Chapter 2 LAPLACE TRANSFORM METHOD..................................................... 19 2-1 Mathematical Methodology ............................................................................. 19 2-1.1 Formulations in Transform Domain……………………...……………19 2-1.2 Laplace Inverse Transformation…………………………………...…..41 2-1.2.1 Symbols………………………………………………………...41 2-1.2.2 Branch Cut…………………………………………...…………41 2-1.2.3 Integration along the Branch Lines…………………………….47 2-1.2.4 Change in Characteristic Roots………………………………...57 2-1.2.5 Integral around the pole………………………………………..59 2-2 Simply Supported Beam Subjected to Impact Moment ................................... 60 2-3 Simply Supported Beam Subjected to Impact Force ....................................... 66 Chapter 3 NORMAL MODE METHOD ................................................................... 75 3-1 Eigenvalues and Eigenfunctions ...................................................................... 75 3-2 Simply Supported Beam Subjected to Impact Moment ................................... 89 3-3 Simply Supported Beam Subjected to Impact Force ....................................... 93 3-4 Ball Impact Simply Supported Beam............................................................... 96 3-5 Cantilever Beam Subjected to Impact Force.................................................. 104 Chapter 4 NUMERICAL RESULTS AND DISCUSSIONS ....................................111 4-1 Ray Solution Results of the Timoshenko Beam..............................................111 4-1.1 Simply Supported Beam Subjected to Impact Moment……………...111 4-1.2 Simply Supported Beam Subjected to Impact Force…………………114 4-2 Normal Mode Solution Results of the Timoshenko Beam..............................116 4-2.1 Simply Supported Beam Subjected to Impact Moment……………...117 4-2.2 Simply Supported Beam Subjected to Impact Force…………………120 4-2.3 Ball Impact Simply Supported Beam…...……………………………125 4-3 Two Approach Comparison of the Timoshenko Beam .................................. 132 4-3.1 Simply Supported Beam Subjected to Impact Moment……………...132 4-3.2 Simply Supported Beam Subjected to Impact Force………………...132 4-4 Normal Mode Solution of the Bernoulli-Euler Beam……………………….137 4-5 Static and Steady State Solutions ................................................................... 141 4-5.1 Static Solutions……………………………………………………….142 4-5.2 Steady State Solutions………………………………………………..146 4-6 Frequency Domain ......................................................................................... 149 4-6.1 Simply Supported Beam Subjected to Impact Moment………...……149 4-6.2 Simply Supported Beam Subjected to Impact Force………………...151 4-6.2.1 Timoshenko Beam…………………………………………….151 4-6.2.2 Bernoulli-Euler Beam………………………………………...154 4-7 Timoshenko Beam and Bernoulli-Euler Beam Comparison .......................... 155 Chapter 5 CONCLUSIONS AND FUTURE WORKS............................................ 166 5-1 Conclusions .................................................................................................... 166 5-2 Future Works .................................................................................................. 168 Reference ..................................................................................................................... 170 | |
| dc.language.iso | en | |
| dc.subject | 暫態波傳 | zh_TW |
| dc.subject | Timoshenko樑 | zh_TW |
| dc.subject | 古典樑 | zh_TW |
| dc.subject | 模態展開法 | zh_TW |
| dc.subject | 射線法 | zh_TW |
| dc.subject | transient | en |
| dc.subject | Timoshenko beam | en |
| dc.subject | Bernoulli-Euler beam | en |
| dc.subject | normal mode | en |
| dc.subject | ray | en |
| dc.title | 應用射線及模態展開法解析Timoshenko樑的暫態波傳 | zh_TW |
| dc.title | Theoretical Analysis of Transient Waves in a Timoshenko Beam by Ray and Normal Mode Methods | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 劉紹文(Shaw-Wen Liu),郭茂坤(Mao-Kuen Kuo),盧中仁(Chung-Jen Lu) | |
| dc.subject.keyword | Timoshenko樑,古典樑,模態展開法,射線法,暫態波傳, | zh_TW |
| dc.subject.keyword | Timoshenko beam,Bernoulli-Euler beam,normal mode,ray,transient, | en |
| dc.relation.page | 177 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-22 | |
| 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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