final_report.pdf

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TRANSVERSE VIBRATIONAL ANALYSIS OF A SIMPLY SUPPORTED BEAM A Thesis submitted in partial fulfillment of the requirements for the Degree of Bachelor of Technology IN Mechanical Engineering By Ankit Singh Roll No: 108ME063 Department of Mechanical Engineering National Institute Of Technology Rourkela - 769008
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National Institute of Technology Rourkela CERTIFICATE This is to certify that the thesis entitled, Transverse vibrational Analysis of simply supported beam submitted by ANKIT SINGH in partial fulfillment of the requirement for the award of Bachelor of Technology degree in Mechanical Engineering at National Institute of Technology, Rourkela is an authentic work carried out by him under my supervision and guidance. To the best of my knowledge, the matter embodied in the thesis has not been submitted to any other University/Institute for the award of any Degree or Diploma. Date: Prof. H.ROY Dept. of Mechanical Engineering National Institute of Technology Rourkela 769008
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B.Tech Project Report 2012 ACKNOWLEDGEMENT I wish to express my profound gratitude and indebtedness to Prof. H.ROY , Department of Mechanical Engineering , NIT-Rourkela for introducing the present topic and for their inspiring guidance , constructive criticism and valuable suggestion throughout the project work. Last but not least, my sincere thanks to all our friends who have patiently extended all sorts of help for accomplishing this undertaking. ANKIT SINGH(108ME063) Dept. of Mechanical Engineering National Institute of Technology Rourkela 769008 Mechanical Engineering Department, N.I.T. Rourkela Page 2
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B.Tech Project Report 2012 CONTENTS Chapter 1 1. Introduction 1.1 Euler-Bernoulli beam and Timoshenko beam 1.2 Objective and Scope of work Chapter 2 2. Literature survey Chapter 3 3. Numerical modeling and formulation 3.1 Formulation 3.2 Finite element method Chapter 4 4. Vibration analysis using MATLAB R2010a Chapter 5 5. Results and discussion Chapter 6 6. Conclusion References Mechanical Engineering Department, N.I.T. Rourkela Page 3
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B.Tech Project Report 2012 ABSTRACT The bending phenomenon is common in simply supported beams as the beams are subjected to flexural loading in design considerations. In this paper, the effect of free vibration of the hinged beam was investigated using a finite element method and the basic understanding of the influence of applied force on natural frequencies of cantilever beam is presented . Hamilton ’s principle applied to the Lagrangian function is used to derive the equations of motion. In addition other factors affecting the vibration of beams are discussed. The variables of the hinged beam are: 1. Slenderness ratio 2. Shearing consideration The numerical results for free vibration of beam are presented. These results are compared with the results obtained using MATLAB R2010a to plot the modal natural frequency of simply supported beam. The module frequencies can be highly useful for the vibration analysis and the resonance in a structure. So, the beam is taken and its module natural frequencies are computed.
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