Natural Frequencies in Annuli With Induced Thermal Membrane Stresses

Abstract

A number of independent studies have concluded that initial, residual membrane stresses can increase the fundamental frequency or effective stiffness of thin circular disks and annuli. The present study investigates the increase in fundamental frequency caused by purposely induced thermal membrane stresses in centrally clamped, peripherally free, rotating annuli. The principal advantage of this method over the initial stressing technique is that the state of stress is infinitely variable, allowing continuous adjustment of effective stiffness. Practical application of both these methods is limited to the cases where minimization of disk thickness is of paramount importance. The results are presented in the form of analyses of practical examples whose frequency characteristics have been adjusted by the proposed method. Optimization of the fundamental frequency and limitation of the proposed method are discussed.