Nonlinear dynamic analysis of a rotating pre-twisted blade with elastic boundary

In this paper, a nonlinear dynamic model for rotating beams with elastic boundary is established. The model considers the influence factors such as pre-twisted, setting angle, thermal gradient and geometric nonlinearity. Firstly, according to the Euler–Bernoulli beam theory, the Lagrange function of the rotating beam with elastic constraints is formulated, and a modified Fourier series method is used to solve the linear part to determine the modal function with elastic boundary. Secondly, the modal expansion of the displacements is carried out, and the nonlinear dynamic equations of a rotating pre-twisted beam with elastic boundary are obtained by Lagrange equation. Finally, the multi-scale method is used to solve the nonlinear problem to study the vibration response of the rotating beam with elastic constraints. The accuracy and stability of this method are verified by convergence analysis and comparison with other literatures. After determining the possibility of 2:1 internal resonance of the system, the influence of key system parameters such as rotational speed, spring stiffness and thermal gradient on vibration characteristics under elastic boundary is analyzed. The results show that the system parameters have a significant influence on the nonlinear phenomena of the system and the influence of elastic boundary cannot be ignored.