The finite element method is used to determine the natural frequencies of flat square plates containing centrally located circular or square holes. The plates are subjected to either inplane uniaxial, biaxial or uniformly distributed shear along the four outer edges. These edges are either simply supported or clamped.

To determine the stiffness and mass matrices, non conforming rectangular and triangular displacement elements are used to model the out of plane behaviour of the plate. The inplane stress distribution within the plates, which are required in the analysis are determined by using inplane finite elements having displacement fields based on assumed strains. These satisfy the exact requirements of strain free rigid body modes of displacements.

The natural frequencies of simply supported and clamped plates are initially determined when no inplane loads are applied. This showed the influence of the size of the hole on the natural circular frequency. These plates were then subjected to inplane loads and the effect of these forces on the natural frequencies are given. The results show the natural frequencies of square plates with central circular holes decrease with increasing compressive forces, and that the frequencies become zero when the compressive forces are equal to the elastic buckling loads of the plates.

By repeating this process for all boundary conditions and applied loads a comprehensive set of results is obtained for the buckling and vibrational properties of square plates containing centrally located holes.

This content is only available via PDF.