An investigation has been made into the effect of residual stresses on the vibration characteristics of a thin rectangular plate elastically restrained against rotation along all edges using an energy method. General frequency equations with and without the effect of residual stresses have been obtained. Exact frequency equations with and without the effect of residual stresses for the cases: C-C-C-C, S-S-S-S, S-S-C-S, C-S-C-S, S-S-C-C, C-C-C-S have also been obtained. Exact equations were derived including the effect of the position of welding along the width of the plate for all cases considered. The validity of the equations obtained was checked with available special solutions with a good agreement.

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