The Effect of Self-Equilbrating Stresses on the Natural Frequencies of Elastically Restrained Rectangular Plate

Abstract

An investigation has been made into the effect of residual stresses on the vibration, characteristics of thin rectangular plates elastically restrained against rotation along three edges and free on the fourth edge. General frequency equation with and without including the effect of residual stresses has been obtained. Exact frequency expressions including the effect of residual stresses for the cases: S-S-S-F, S-S-C-F, C-C-S-F, C-S-S-F, C-S-C-F, C-C-C-F were also obtained. The effect of the position of welding along the width of the plate for all cases was also included. Actual plate models were tested and the results were compared with the theoretical predictions giving good agreement.