Extensional vibration of thin plates of various shapes

Abstract

The problem of free extensional (in plane) vibration of thin plates of Hookean material of various shapes was studied. Solutions for dilatational and rotational vibrations were obtained separately. The boundary conditions were satisfied in a least-square sense. Numerical computations were performed for circular, elliptical, triangular, square, and hexagonal plates. The nodal pattern corresponding to each natural frequency for different modes was obtained. The frequency parameters computed for the circular plate are found to be within 0.05% of published results. For plates where known results were not available, the accuracy was checked by taking additional terms in the series solution and by dividing the boundary perimeter into finer intervals. It was found that the circular plate had the lowest fundamental frequency (k1) at 2.049. The value increases as the shape is changed from a circle, with the triangular plate having the highest value at 6.733 in dilatational vibration while the frequencies in rotational vibration (h1) were found to be 3.737 and 16.364, respectively. Subject Classification: 40.24.