Analytical Modeling and Vibration Analysis of the Last-Stage LP Steam Turbine Blade Made of Functionally Graded Material

The conventional materials used in steam turbine blades undergo severe environmental loading conditions resulting in corrosion, fatigue failures, and several kinds of defects. Especially for the last-stage steam turbine blade, there is a need to employ hybrid materials such as functionally graded (FG) materials or other composites that combine the properties of two or more desired materials to withstand extreme conditions without much loss of blade output. The present paper includes the theoretical investigation of free vibration study of the regular last-stage low-pressure steam turbine blade using the Finite element method via the in-house codes. Further, the structural modeling of the functionally graded blade and its free vibration characteristics are evaluated. The dynamic equations of motion of the functionally graded blade are derived by considering geometric taper. The impact of several factors, such as the volume fraction index, rotational speed, and twist angle on the natural frequencies of the FG rotating blade, is reported at different speeds of operation. It is observed that with an increase in volume fraction index, both chordwise and flapwise bending frequencies decrease; however, the rate of decrease is higher in higher modes. The opposite trend is observed in the FG blade’s vibratory characteristics with respect to the rotational speed and twist angle.