A systematic approach to the free vibration analysis of thin, flat, non-rectangular quadrilateral plates with combinations of simple and clamped supports is presented, using the parallelogram plate as an example. Modifications that Saliba made for the right-triangular plate to the building block superposition method developed by Gorman are implemented. The superposition method is an analytical solution. No simplifications are made to take advantage of the point symmetry of the parallelogram plate, keeping the solution general. The whole plate is divided into two right-triangular and one rectangular segment. Rectangular building blocks are superimposed for each of the segments to meet the required net boundary conditions and the conditions of continuity along the segment interfaces. The Levy-type solution to the eight building blocks used are given, along with the necessary Fourier expansions and a comprehensive guide to assembling the eigenvalue matrix. Numerical results for a wide variety of plates are presented, including numerous mesh and contour plots. Comparison is made to previously published data. The results for the fully clamped parallelogram plate are supported by experimental results. Six aluminum plates were tested for the first six resonance frequencies and the first three mode shapes. Details of the simple, yet highly accurate experimental method are included.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/4318 |
| Date | January 1998 |
| Creators | Stangier, Stefanie D. |
| Contributors | Gorman, D. J., |
| Publisher | University of Ottawa (Canada) |
| Source Sets | Université d’Ottawa |
| Detected Language | English |
| Type | Thesis |
| Format | 229 p. |
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