Improved Differential-Quadrature Precise Integration Method for Nonlinear Rotor Dynamics Response Calculation

As advances and simulation prediction design become more prevalent, the methods for solving rotor dynamics response are challenged to meet higher standards for precision, efficiency, and convergence. To address the limitations of current approaches like Newmark and Runge–Kutta in solving nonlinear responses of rotor dynamics in engineering applications, this paper introduces an improved differential-quadrature precision method. This method fits the Duhamel term with a nonequidistant differential-quadrature technique and uses Taylor and Lagrange formulas for self-starting predictions, balancing accuracy with computational efficiency. Furthermore, the paper presents an iterative strategy that effectively addresses the convergence issues of precise integration methods under large step sizes for nonlinear response solutions. Comparative analysis with real aeroengine gas turbine rotor models demonstrates the performance differences between the improved precise method and Newmark method. The result shows that in steady-state response solutions the improved precise method achieves greater precision at twice the step size of the Newmark method. In transient response solutions, the improved precise method outperforms Newmark in terms of computational efficiency, and the iterative strategy proves both reliable and effective.