dc.contributor.author Mochida, Yusuke en_NZ dc.date.accessioned 2007-07-10T13:13:27Z dc.date.available 2008-01-10T16:21:10Z dc.date.issued 2007 en_NZ dc.identifier.citation Mochida, Y. (2007). Bounded Eigenvalues of Fully Clamped and Completely Free Rectangular Plates (Thesis, Master of Engineering (ME)). The University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/2508 en dc.identifier.uri https://hdl.handle.net/10289/2508 dc.description.abstract Exact solution to the vibration of rectangular plates is available only for plates with two opposite edges subject to simply supported conditions. Otherwise, they are analysed by using approximate methods. There are several approximate methods to conduct a vibration analysis, such as the Rayleigh-Ritz method, the Finite Element Method, the Finite Difference Method, and the Superposition Method. The Rayleigh-Ritz method and the finite element method give upper bound results for the natural frequencies of plates. However, there is a disadvantage in using this method in that the error due to discretisation cannot be calculated easily. Therefore, it would be good to find a suitable method that gives lower bound results for the natural frequencies to complement the results from the Rayleigh-Ritz method. The superposition method is also a convenient and efficient method but it gives lower bound solution only in some cases. Whether it gives upper bound or lower bound results for the natural frequencies depends on the boundary conditions. It is also known that the finite difference method always gives lower bound results. This thesis presents bounded eigenvalues, which are dimensionless form of natural frequencies, calculated using the superposition method and the finite difference method. All computations were done using the MATLAB software package. The convergence tests show that the superposition method gives a lower bound for the eigenvalues of fully clamped plates, and an upper bound for the completely free plates. It is also shown that the finite difference method gives a lower bound for the eigenvalues of completely free plates. Finally, the upper bounds and lower bounds for the eigenvalues of fully clamped and completely free plates are given. en_NZ dc.format.mimetype application/pdf dc.language.iso en dc.publisher The University of Waikato en_NZ dc.rights All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated. dc.subject vibration en_NZ dc.subject eigenvalue en_NZ dc.subject natural frequencies en_NZ dc.subject plate en_NZ dc.subject superposition method en_NZ dc.subject finite difference method en_NZ dc.subject upper bound en_NZ dc.subject lower bound en_NZ dc.title Bounded Eigenvalues of Fully Clamped and Completely Free Rectangular Plates en_NZ dc.type Thesis en_NZ thesis.degree.discipline School of Science and Engineering en_NZ thesis.degree.grantor University of Waikato en_NZ thesis.degree.level Masters thesis.degree.name Master of Engineering (ME) en_NZ uow.date.accession 2007-07-10T13:13:27Z en_NZ uow.date.available 2008-01-10T16:21:10Z en_NZ uow.identifier.adt http://adt.waikato.ac.nz/public/adt-uow20070710.131327 en_NZ uow.date.migrated 2009-06-09T23:30:38Z en_NZ pubs.place-of-publication Hamilton, New Zealand en_NZ
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