Natural frequencies of thin rectangular plates with partial intermediate supports

Abstract

In the present study, a methodology to find natural frequencies with arbitrary precision of thin rectangular plates on linear intermediate supports and mixed boundary conditions is presented. This means that the edges are total or partially supported, clamped or free, or any combination of these. The layout, number and place of linear intermediate supports are arbitrary, which allows for the analysis of a wide range of cases that include intermediate supports of different kinds: simple and multiple, straight and curved, complete (the ends coincide with the plate edges) and partial (at least one of the ends is not coincident with the plate edges). In the case of curved linear supports, the curve can be open or closed. The generalized solution is obtained using the Whole Element Method. A continuous and a discrete model of equidistant points are studied both for intermediate supports and clamped edges. In all cases, both a systematic approach to the solution and the theoretical basis, which ensures the arbitrary precision of the results, should be emphasized. In order to illustrate the accuracy and efficiency of the method described, numerical results are presented for several problems and comparison is made with previously published results in some cases and in some others with the Finite Element Method. These numerical results may be of interest to design engineers and researchers who conduct vibration studies.