Free vibration analysis of arbitrarily shaped plates with smoothly varying free edges using NDIF method

The so-called non-dimensional influence function method that was developed by the authors is extended to free vibration analysis of arbitrarily shaped plates with the free boundary condition. A method proposed in this paper can be applied to plates with only smoothly varying boundary shapes. In the proposed method, a local polar coordinate system has been employed at each boundary node to effectively consider the free boundary condition, which is much more complex than the simply supported or clamped boundary condition. The local coordinates system devised allowed us to successfully deal with the radius of curvature involved in the free boundary condition, and, as a result, the accuracy of the proposed method has been reinforced. Finally, verification examples showed that the natural frequency and mode shapes obtained by the proposed method agree excellently with those given by other analytical or numerical methods.