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This paper presents new optimal results for vibration of thin rectangular plates against one and two internal point supports. The p-Ritz method is employed to generate the fundamental vibration frequencies for a plate and the Nelder and Mead simplex optimal search routine is used to find the optimal point support locations. Optimal results have been obtained for square and rectangular plates with arbitrary boundary arrangements and with one and two internal point supports. The results generally show that the frequency of the plate is sensitive to the location of the internal point supports and numerous optimal locations for the point supports exist. These new optimal results will provide useful information to designers seeking to maximize the fundamental frequency in designing a plate structure.

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