FREE VIBRATION ANALYSIS OF FREE PLATES WITH SMOOTHLY VARYING BOUNDARY SHAPES USING NON-DIMENSIONAL DYNAMIC INFLUENCE FUNCTIONS

摘要

The so-called NDIF 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 the paper can be applied to plates with only smoothly varying boundary shapes. The free vibrations of plates with discontinuously varying boundary shapes such as polygonal plates are being studied and will be addressed in another paper. 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 because it consists of two natural boundary conditions with differential terms of higher order. By the use of the local coordinate transformation, the radius of curvature involved in the free boundary condition can be successfully dealt with. Finally, A verification example shows that the natural frequency and mode shapes obtained by the proposed method agree excellently with those given by a numerical method.