Calculation of Natural Frequencies and Corresponding Mode Shapes of Power Plant Gas Turbine Rotors

This paper deals with determination of natural frequencies and corresponding mode shapes of a turbo-compressor rotor. This simulation is based on Jeffcott rotor. The continuous shaft-disk system is described with kinetic and potential energy functionals that account for translational and rotatory inertia. The analytical method of Rayleigh is expanded to formulation of assumed mode method and the Lagrangeʹs equations are applied to derive the equations of motion. The shaft of rotor is modeled using Timoshenko beam theory and the disk is assumed to be rigid and damping and non-linear effects are neglected. A finite series of polynomial admissible functions is used to calculate the natural frequencies and corresponding mode shapes for both situations of Backward Whirl (BW) and Forward Whirl (FW).