Abstract—The paper is devoted to the turbomachinery vibration processes investigation. It is based on the hypothesis that such process as forced vibration, high temperature and centrifugal force, constructional damping parameters put the main impact in the gas turbine rotors decrease. For these studies the special refined mathematical model was used. For these model the special space finite elements have been developed, that gives an opportunity to make the approximation of various turbine blades geometry. The model verification has been done by the usage the modern highly automatized experimental equipment that is based on the holographic interferometry method application in real time. The first impeller cooled blades forced vibration parameters have been determined for several most dangerous forced vibration modes, temperatures up to 1000^oC and angular velocities of shaft rotation, corresponding with the gas turbine engine normal working regime. Results of calculations data together with the previous studies in the fields of gas turbine engines flow dynamics, heat exchange, stress-strain state can be used in further studies of turbomachinery fracture mechanics area.