Optimal locations of point supports in plates for maximum fundamental frequency

This paper investigates the optimal locations of rigid point supports to maximize the fundamental frequency of free vibration of plates. The computational method uses the Rayleigh-Ritz method for the vibration analysis and the simplex method of Nelder and Mead for the optimization search of support locations. Optimal results have been obtained for various common shapes of plates with a few point supports. The results show that the frequency of the plate is sensitive to the locations of the point supports. Moreover, these new optimal results provide useful information to designers seeking to exploit the position of point supports in their plate designs. It has been found that multiple solutions are a common feature of this plate optimization problem.