Bounded Eigenvalues of Fully Clamped and Completely Free Rectangular Plates

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dc.contributor.authorMochida, Yusukeen_NZ
dc.date.accessioned2007-07-10T13:13:27Z
dc.date.available2008-01-10T16:21:10Z
dc.date.issued2007en_NZ
dc.description.abstractExact 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.mimetypeapplication/pdf
dc.identifier.citationMochida, 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/10289/2508en
dc.identifier.urihttps://hdl.handle.net/10289/2508
dc.language.isoen
dc.publisherThe University of Waikatoen_NZ
dc.rightsAll 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.subjectvibrationen_NZ
dc.subjecteigenvalueen_NZ
dc.subjectnatural frequenciesen_NZ
dc.subjectplateen_NZ
dc.subjectsuperposition methoden_NZ
dc.subjectfinite difference methoden_NZ
dc.subjectupper bounden_NZ
dc.subjectlower bounden_NZ
dc.titleBounded Eigenvalues of Fully Clamped and Completely Free Rectangular Platesen_NZ
dc.typeThesisen_NZ
pubs.place-of-publicationHamilton, New Zealanden_NZ
thesis.degree.disciplineSchool of Science and Engineeringen_NZ
thesis.degree.grantorUniversity of Waikatoen_NZ
thesis.degree.levelMasters
thesis.degree.nameMaster of Engineering (ME)en_NZ
uow.date.accession2007-07-10T13:13:27Zen_NZ
uow.date.available2008-01-10T16:21:10Zen_NZ
uow.date.migrated2009-06-09T23:30:38Zen_NZ
uow.identifier.adthttp://adt.waikato.ac.nz/public/adt-uow20070710.131327en_NZ
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