Modification of fundamental vibration modes of circular plates with free edges

For an isotropic circular plate with constant thickness and free edges, its fundamental vibration mode takes the form of a twisting mode with two nodal diameters, i.e. n=2. In certain applications, it may be necessary to have an axisymmetric shape for the fundamental vibration mode (i.e. mode shape with no nodal diameter, n=0). In this paper, we show that such an axisymmetric vibration mode can be realized by increasing the bending rigidity of the outer rim of the circular plate by using a larger thickness or by using a material with a larger Young's modulus or both. We also determine the critical flexural rigidity of the outer rim that will trigger this vibration mode change from n=2 type to n=0 type for a given rim width. The ability to alter the mode shape of circular plates with free edges has useful applications in sensing and actuating devices and large pontoon-type floating circular structures.