Vibration of gas turbine blades made-up of functionally graded materials considering operating temperatures

Abstract

The vibration analysis of a rotating gas turbine blade made-up of functionally graded materials is studied. Temperature-dependent material properties are considered according to the high temperature environment and the blade cooling system. The blade is structurally modeled as a thin-walled cantilever box beam with its fixed end mounted on a rotating rigid hub. The material properties of the functionally graded beam are assumed to vary continuously across the thickness direction, and also depend on its temperature distribution. Especially, the thermal conductivity model adopted in this study reflect the effect of the ceramic particle size. The 1-D nonlinear heat transfer analysis is solved to determine the temperature distribution of the blade as the thermal conductivity of the blade is temperature dependent. Then the equations of motion are derived from the structural stiffness which involves the effect of temperature distribution and rotational motion to perform the vibration analysis by using the hybrid deformation variable modeling method along with the Rayleigh-Ritz assumed mode method. The validity of the derived equations is evaluated by comparing the transient responses and temperature distribution obtained from the equations with those obtained from the finite element model created from the commercial software. Numerical results highlight the effects of temperature of the turbine entry and cooling air, gradient index, rotating speed and particle size on the natural frequencies of the blade.