A frequency split trimming technique for axisymmetric shell structures

Axisymmetric shell structures are characterized by the presence of flexural modes which occur in degenerate pairs. However, since no practically realized structure is perfectly axisymmetric, the frequencies constituting a mode pair become unequal and causes what is commonly termed as “frequency split” between the modes. In applications such as vibratory gyroscopes, it is desired that the frequencies of the working pair of modes be equal. This work proposes an easily implementable (particularly in the industry) technique which reduces frequency split of a target mode pair. To address the frequency split trimming problem, this work investigates a model that describes the planar dynamics of a vibrating ring (which is prototypical to axisymmetric shell structures), with added mass segments. The effects of mass, as well as span, of an added segment on the ring’s natural frequencies and mode shapes are brought out. Novelties of the proposed trimming technique are that it employs added mass in the form of segments and that it has a negligible effect on the axes of the structure’s mode shapes. The technique is extended to general axisymmetric bodies, and it is validated experimentally for the case of a hemispherical resonator.