Janse van Rensburg, N.F. (Nicolaas)2015-02-022015-02-022015-04-162014http://hdl.handle.net/2263/43523Dissertation (MSc)--University of Pretoria, 2014.In the research for the Masters degree, principally a literature study, the focus was on the Finite Element Method applied to vibrating systems: vibrating beams, plates, multi-dimensional elastic solids, hybrid models and linked vibrating solids. The emphasis of this dissertation was on the Finite Element Method applied to these model problems. An important aspect was the comparison of different models for the same structure. The chosen method to compare models is numerical simulation. Therefore convergence of the finite element approximation is important. Specific attention was given to: • determining whether error estimates are available in general and any conditions necessary for convergence; • error analysis and convergence of solutions; • existence of solutions. A search through the literature revealed that a substantial number of publications deals with the finite element method applied to the multi-dimensional wave equation but less on vibrating beams, plates and multi-dimensional elastic solids. Hardly anything has been published on error estimates and finite element approximations for hybrid models and structures, linked systems or structures with boundary damping or damping in joints.en© 2014 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of PretoriaApplied MathematicsUCTDDissertation