Optimal design of internal ring supports for vibrating circular plates

Abstract

This paper presents the optimality conditions for optimum locations of internal ring supports in circular plates for maximum frequency of axisymmetric vibration of a specified order. The optimality conditions require both the reaction forces and moments at the internal supports to vanish for optimal solutions. This means that the internal ring supports should be placed at the nodal rings of the appropriate higher-order vibration mode of a corresponding unsupported circular plate for maximum effectiveness in raising the vibration frequency of the plate. Some design examples are given to verify the derived optimality conditions.