Free vibration of rotating bifunctional gradient CNTs-reinforced ceramic matrix composites pre-twisted blade in thermal environment

Considering the thermal environment’s effect, we built a dynamics model of rotating pre-twisted ceramic matrix composites blades with elastic boundary constraints based on shell and first-order shear deformation theories. The model considers the effect of temperature and simplifies the blade to a twisted cylindrical plate. Based on the Lagrange equation, the differential equation of the vibration of a rotating pre-twisted blade of CNTs-reinforced ceramic matrix composites in the thermal environment was derived by using the orthogonal polynomial as the acceptable function. The natural frequencies and vibration modes of a rotating pre-twisted blade take into account the effects of Coriolis and centrifugal forces. The accuracy of the model is verified by comparing with the literature and Ansys results. The effects of temperature, the volume fraction of functional gradient, pre-twisted angle, and rotational speed on the model were studied in detail. The results show that the addition of carbon nanotubes can greatly enhance the ceramic-based blade. And both temperature and pre-twisted angle significantly affect the carbon nanotube enhanced functional gradient blades.