Analysis of how symmetries govern the different out-of-plane vibration modes in elastic, homogeneous, isotropic plates: Experimental, theoretical, and numerical study

This paper presents a methodology for determining the vibration modes of an elastic, homogeneous, isotropic plate that account for symmetry properties. For this, we use the finite element method in COMSOL Multiphysics. The out-of-plane vibration modes of a plate are calculated, and the symmetries or parities of the displacement and stress components are determined. This allows searching for vibration modes in one-eighth of the plate, applying boundary conditions determined by the symmetry. The resulting frequencies and mode shapes are compared with those calculated for the entire plate and one-eighth of the plate, and good agreement is observed. The vibration mode frequencies are experimentally determined using a technique similar to that presented by Chladni: sand is used to form the nodal line pattern; nevertheless, in this work, an electromagnetic acoustic transducer is used to excite the plate’s vibration modes. Comparisons between the experimental and numerical results of the frequencies and mode shapes are presented, showing excellent agreement.