Fully geometrical nonlinear model of shaft‐disk rotors in thermal environment

Abstract Accurately predicting the nonlinear dynamic response of shaft‐disk rotors (SDRs) in a thermal environment is beneficial for the design of aero‐engines. This paper provides a fully geometrical nonlinear model of SDRs under a non‐uniform temperature field (NTF), considering the geometrical nonlinearities of both the shaft and disk. This model also considers the temperature‐dependent material properties as well as gyroscopic and centrifugal effects. Based on the von Kármán nonlinear theory, the Euler–Bernoulli beam theory, and the Kirchhoff plate theory, the governing differential equation is derived using the Lagrange equations. The accuracy of the present results is verified by comparing with existing references and finite element results. The nonlinear dynamic response of SDRs is investigated in relation to the rotational speed, temperature difference, temperature distribution, excitation amplitude, and disk nonlinearity. Results show that the proposed dynamic model can well predict the nonlinear vibration characteristics of SDRs under NTF.