Apply GM(0,N) to The Weighting Anlysis in Timoshenko Beam System

• Main Author: 呂冠穎
• Other Authors: 溫坤禮
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/28301307844320748249

碩士 === 建國科技大學 === 自動化工程系暨機電光系統研究所 === 98 === This paper mainly discusses the free vibration analysis of Timoshenko beam carrying multiple spring-mass systems. For the Timoshenko beam, besides the shear deformation and the rotational inertia, high-order coupling term generated by them is also taken into account in this paper. The natural frequency obtained is subsequently used to validate the weighting analysis of free vibration using the gray system theory. Chapter 1 is the thesis introduction comprising five sections involved with research background, motivation and purpose, research process, literature review and thesis organization. Chapter 2 describes the motion equation of Timoshenko beam carrying multiple spring-mass systems from which the relevant mathematical expressions are derived. Bisection method is utilized to deduce the frequency equation to obtain the exact solution of natural frequency which is used as the prerequisite for validation by using the gray system theory. Chapter 3 describes the process of weighting analysis using grey model, including mathematical models and solving processes of GM (1, N) and GM (0, N). Chapter 4 uses the calculated actual value of natural frequency to find out the numerical solution in combination with the model of GM (0, N). The output variable is natural frequency which varies with major input variables including . Then Matlab toolbox is used to support a great deal of numerical computation and analysis for validating the feasibility of weighting analysis using the gray system theory. Chapter 5 presents the conclusions describing the ideas and limitations of this paper for future reference to analysis and experiment in this field.