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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王安邦,A.I.Fedorchenko | |
| dc.contributor.author | Ivo Stachiv | en |
| dc.contributor.author | 伊柏 | zh_TW |
| dc.date.accessioned | 2021-06-15T00:25:29Z | - |
| dc.date.available | 2009-02-10 | |
| dc.date.copyright | 2009-02-10 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-01-22 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/41632 | - |
| dc.description.abstract | 本文主要探討一維震動機制系統(one-dimensional mechanical systems with piecewise constant properties)的分析與應用。而振動分析的第一步驟通常是利用數值解或分析解找到自然頻率(natural frequency)下之振盪頻譜。對一個有固定材料參數的振盪系統如同樑(beam)、繩(string)和懸臂樑(cantilever beam)是比較簡單處理的。然而，很多實際的應用包含了不連續的非固定的材料參數。
對一個複合系統(composed system)來說，數值解常常被用判定其模態。但藉由數值計算並無法正確得到各個參數(彈性係數、密度、斷面長度、斷面材料等)對複合系統的影響。為了求得各參數對該複合系統的影響，分析解是有必要的。 本文假設一維系統與N段固定參數(N-piecewise constant properties)，並導入一「有效傳遞速度」(effective propagation velocity)求得其分析解。為了測試本理論在第二模態(N=2)的可靠度，利用散射光圖樣辦識的光學實驗方法得到，第一模態頻率的實驗數據與分析解所得的解相同。為了延伸此分析解，吾人設計一實驗如下：將一繩(fiber)之下半部分浸入液體中並振動該繩，並視液體為阻尼後量測該繩的振盪機制。無論是最大振幅(maximum vibrational amplitude)或是能量帶寬的變異(power bandwidth variation)，分析解所得之值與實驗數據是吻合的，而由該設計實驗所推出分析解也列在本論文中。 | zh_TW |
| dc.description.abstract | This thesis deals with an analysis and application of the vibrating one-dimensional mechanical systems with piecewise constant properties. It is a well known fact that the fist step in a vibration analysis of any mechanical system is to find spectrum of their natural frequencies. It can be done either numerically or analytically. For simple vibrating systems like beam, string or cantilever with constant mechanical properties the analytical determination of the normal modes is known and is preferable one. However many real applications involve not a constant but a piecewise constant and, factually discontinuous properties. For composed systems the numerical determination of the normal modes is usually performed. We have found here that the normal modes for one–dimensional mechanical problems with piecewise constant properties can be obtained by solving an appropriate transcendental equation. This equation of course contains all information about given mechanical system (elastic moduli, density, cross-sectional area of material, thickness of each layer with constant mechanical properties, etc.). In this thesis transcendental equation is derived for case of one-dimensional systems with N - piecewise constant properties. The physical interpretation of normal modes for this kind of mechanical systems by introducing the “effective” propagation velocity has been put forward. An optical method utilizing a forward light scattering pattern has been carried out to test the validity of the theory for N = 2. Theoretical predictions of the first mode frequency and experimental data agree precisely. Moreover the extension of the analysis and experiments for a case of the partially submerged fiber in fluid with taking into account of a viscous damping has been performed. From obtained results a simple way for viscosity extraction from either the maximum vibrational amplitude or the power bandwidth variation has been suggested and tested experimentally. Besides an explicit formula for the achievable accuracy of the viscosity sensing is derived here as well. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T00:25:29Z (GMT). No. of bitstreams: 1 ntu-98-D92543015-1.pdf: 1677665 bytes, checksum: 3a2b68fb9a7d08eab49c3121537ca370 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Abstract.....................................................................................................................................................i
中文摘要................................................................................................................................................ii Dedication...............................................................................................................................................iv Contents...................................................................................................................................................v List of figures..........................................................................................................................................ix List of tables.........................................................................................................................................xvii 1 Introduction..................................................................................................................................1 1.1 Vibration, Normal modes, Resonance.......................................................................................2 1.1.1 Resonance and natural frequencies in nature and engineering·········································2 1.1.2 One-dimensional mechanical systems and methods of solution······································3 1.2 Viscometers and viscosity measurement techniques.................................................................6 2 Normal modes of the vibrating one dimensional mechanical systems with piecewise constant properties................................................................................................................................................18 2.1 Mathematical description of the mechanical system with N piecewise constant properties...19 2.2 Mathematical models for mechanical systems with one, two and three piecewise constant properties (Inverse Laplace transform technique)...............................................................................20 2.3 Mathematical models for mechanical systems with an arbitrary number of the piecewise constant properties..............................................................................................................................34 2.4 Effective model for the normal modes.....................................................................................35 3 Optical viscosimeter...................................................................................................................37 3.1 Experimental system setup and the sensor principle...............................................................38 3.1.1 System setup··················································································································38 v 3.1.2 Sensor principle·············································································································40 3.2 Mathematical model.................................................................................................................42 3.2.1 Dimensionless analysis··································································································42 3.2.2 Forced vibration of the fiber fully submerged in fluid···················································44 3.2.2.1 Forced vibration of the fully submerged fiber in fluid without damping 45 3.2.2.2 Forced vibration of the fully immersed fiber in fluid 48 3.2.3 Partially submerged fiber in fluid··················································································52 3.2.3.1 Normal modes – an effective model of the velocity propagation 52 3.2.3.2 Normal modes – analytical determination 53 3.2.3.3 Forced vibration of the partially submerged fiber (Numerical method) 57 4 Results and comparison..............................................................................................................70 4.1 Experimental studies................................................................................................................70 4.2 Numerical computation results for the fiber partially submerged in fluid...............................82 4.3 Comparison of the theoretical predictions, numerical computations data and experimental results .................................................................................................................................................93 4.4 Achievable accuracy of the viscosity measurement................................................................98 4.4.1 Viscosity extraction from experimental data·······························································103 5 Conclusions..............................................................................................................................107 Acknowledgement...............................................................................................................................110 References............................................................................................................................................112 Appendix..............................................................................................................................................116 A.1 Finite difference scheme........................................................................................................116 A.2 Properties of the glycerol/sucrose – water solutions (GWS/SWS)........................................122 | |
| dc.language.iso | en | |
| dc.subject | 自然頻率 | zh_TW |
| dc.subject | 光學黏度計 | zh_TW |
| dc.subject | optical viscosimeter | en |
| dc.subject | vibration | en |
| dc.subject | normal modes | en |
| dc.title | 一維多層性材料之機械振動系統研究及其在光學黏度計之應用 | zh_TW |
| dc.title | A study of one-dimensional mechanical vibrating systems with piecewise constant properties and its applications as an optical viscosimeter | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 吳光鐘,郭茂坤,李世光,盧中仁 | |
| dc.subject.keyword | 自然頻率,光學黏度計, | zh_TW |
| dc.subject.keyword | normal modes,optical viscosimeter,vibration, | en |
| dc.relation.page | 122 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-01-22 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
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