Use of Cyclic Symmetry Properties in Vibration Analysis of Bladed Disks with Friction Contacts between Blades

The development of steam turbine's blades is closely related to the computer modelling of their vibrations. In this work, a numeric method that (i) implements the calculation of nonlinear vibrations (ii) makes use of the cyclic symmetry of the bladed disk and (iii) models structural contact elements between blades is presented. The cyclic symmetry properties of the bladed disk are used for the calculations of its natural frequencies and mode shapes, then, these are employed in the analysis of its nonlinear vibrations. The contact elements reinforce the bladed disk and act as friction dampers in case of its exceeding excitation. Contact areas between blades are modeled via coupling elements implementing dry Coulomb friction. The method is demonstrated on the particular case of the bladed disk equipped with the LSB48 blades and excited by travelling-wave of two nodal diameters. Finally, the accuracy of the mathematical model and the concept of a contact stiffness are discussed.