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Title: Free vibration of cylindrical shells with constant and variable thickness using the Wittrick-Williams algorithm
Author: El-Kaabazi, Nihal
Awarding Body: Cardiff University
Current Institution: Cardiff University
Date of Award: 2010
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Abstract:
With the rapid development of computer programming and systems, complex analytical shell problems are being tackled more than ever before. Finite element analysis has been the most widely used numerical method in modelling shell structures. In this thesis a more reliable and accurate method is demonstrated, in which the dynamic stiffness is derived from the exact differential equations, resulting in fewer elements and reduced computing time. Free undamped vibration analysis for constant and variable thickness cylindrical shells is carried out by deriving the dynamic stiffness matrix directly from the three differential equilibrium equations after transforming them to three ordinary differential equations and using the boundary value solver COLSYS. The natural frequencies and mode shapes are determined by using the Wittrick-Williams algorithm. A method of handling the effect of fixed end member frequencies below a limiting trial frequency is presented. Numerical examples for beams with constant and variable thicknesses and shells with constant and variable thicknesses are shown, and the method is validated by convergence studies and the handling of fixed end frequencies. A comparison of shell problem results with those of other authors is given, and a parametric study is carried out by varying the length to radius, radius to thickness, and thickness variation ratios. Results are obtained for different circumferential and axial harmonic numbers. Mode shapes are explained, for different shell thickness ratios and end conditions, and significant conclusions are drawn. From all the study and results obtained in this thesis it is ascertained that using the Wittrick-Williams algorithm in combination with COLSYS is a successful approach, and good agreements are effectively achieved for free undamped vibration of cylindrical shells with constant and variable thickness.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.585010  DOI: Not available
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