Finite element calculation of the natural frequencies of a tensioned circular plate

The behavior of structures can be greatly affected by residual stresses. In particular, in many manufacturing processes, prestresses are voluntarily introduced to improve the properties of a structure. This occurs for example in the fabrication of circular sawblades. They are prestressed by a local plastic deformation which modifies the natural frequencies and the critical speed of the blade. The objective of this paper is to study the influence of the prestresses on the natural modes and frequencies of an annular plate. Experimental measurements are made using a modal analysis, and a finite element model is proposed, which determines the residual stresses after tensioning and the influence of these stresses on the modes and the frequencies of the structure. A very good agreement is found between the model and the measurements. Finally, the new critical speed of the structure is calculated and the highest limit for tensioning is discussed.