Free vibration analysis of thin rectangular plates using piecewise shape functions in Ritz procedure

Abstract

In the present work, piecewise functions have been successfully built in the form of polynomials to be utilised in the Ritz procedure to carry out the free vibration analysis of thin rectangular plates. They were consistently constructed by considering the plate as consisting of equal strips in its two perpendicular directions, and could be generated for all the combinations of plate’s classical edge supports. The procedure was performed for different combinations of simple and/or clamped plate’s boundary supports, taking into account four aspect ratios (1, 1.5, 2 and 2.5), and the first six frequency parameters were retained. These frequency parameters were found to be in good concordance with the available exact and approximate solutions. For example, for a square plate with simple supports, the percentage differences, comparatively to the exact Navier solutions, ranged from - 0.007% (for the fundamental mode) to - 1.534% (for the sixth mode). Similar trends were obtained for the other aspect ratios and sets of boundary conditions considered. For all the boundary conditions studied, it was observed an increase in value of the frequency parameters with that of the plates’ side ratios. In addition, for each of the modes considered, it was found out that the computed frequency parameters increased consistently when the number of clamped edges increased in the set of the plate’s boundary conditions. The practical consequence is that thin rectangular plates with clamped edges may witness resonance when the forcing frequencies are high, while they can resist the low and medium ones.