Response and EPSD of rotor-blade nonlinear system with non-stationary non-Gaussian stochastic excitation via PGHW method

The periodic generalized harmonic wavelet (PGHW) method is used to analyze the forced response of a periodic time-varying rotor-blade nonlinear system undergoing mechanical vibrations. The non-stationary non-Gaussian stochastic process with non-uniform modulation is considered as external excitation and the typical quadratic form is considered in the nonlinear terms. The mechanical model of the rotor-blade system and the theoretical and numerical PGHW are introduced. The trigonometric functions contained in M(t), C (t), K(t) can be transformed into exponential functions according to the Euler formula, and then these time-varying elements can result in a frequency shift. The equation of motion of the rotor-blade system with a periodic time-varying form derived using Lagrangian dynamics can be transformed into a series of algebraic equations by using the wavelet-Galerkin method. The wavelet coefficients of response can be solved by using the quasi-Newton method, and the single-rank inverse Broyden algorithm is used to approximate the Jacobian matrix. Based on these wavelet coefficients, the displacement of response can be obtained by performing the reconstruction of PGHW, and the estimated evolutionary power spectral density (EPSD) of response can be obtained according to Eq. (15). The time-frequency analysis is shown in the numerical example, Runge-Kutta algorithm and Monte Carlo method are used to verify the feasibility and effectiveness.