Frequencies of A Circular Plate Weakened Along an Internal Concentric Circle

A thin circular plate with a free or movable boundary, and weakened along an internal concentric circle, is considered. The frequencies of the circular plate varying with the radius of the weakened circle and the extent of the weakening represented by an elastic rotational restraint are determined. The results for the first four modes are tabulated. For the free plate, the internal weakening only slightly decreases the fundamental frequency of the plate, which is advantageous. For the plate with a movable edge, the internal weakening greatly decreases the fundamental frequency, especially for the purely hinged case.