Numerical Analysis of Free Vibration Frequencies of Hexagonal Plate

Abstract

Free vibrations of the isotropic hexagonal plates of the different thicknesses with the free edges are considered based on two different approaches. The approach to calculating the frequencies of free vibrations of isotropic square plates by the Rayleigh–Ritz method has been extended to the calculation of the frequencies of free vibrations of hexagonal plates. The coefficients of the modes and the boundary conditions in the reduced formula are calculated, depending on the ratio of the thickness to the side of the plate. The limits of the application of the formula are established. Frequencies and forms of free oscillations of the plates of this class are calculated by the finite element method (FEM). The frequencies calculated by the FEM were compared with the frequencies calculated using the reduced formula, and the accuracy of the calculations by the two methods was established. The modes of the vibrations obtained based on the FEM are compared with the modes of vibrations obtained numerically and experimentally by other authors. The topology of the forms of the free vibrations for hexagonal, pentagonal, quadrangular, and triangular plates with free edges is established. The approaches implemented in the work make it possible to study the dynamic characteristics of plates of other configurations and can be used to assess the accuracy of other approaches.