Nonlinear parametric resonances of a rotating composite thin-walled beam under aerodynamic force and hygrothermal environment

Considering combined effects of aerodynamic force and hygrothermal environment, the nonlinear parametric resonance of a composite thin-walled beam subjected to a time-dependent rotating speed is investigated in this work. The rotating speed is presumed to comprise a small disturbance harmonically changing one with a steady one. The dynamical model of the system is obtained with the help of established dynamic model in existing research. Then the nonlinear partial differential equation of the system is discretized by the Galerkin method. Afterwards, the low-frequency and high-frequency resonances of the system are analyzed via the multiple scales method to discuss the combined effect of rotating speed, pitch angle, setting angle, fiber orientation angle, temperature-humidity and inflow ratio on the amplitude-frequency responses and the unstable region. In addition, the Routh-Hurwitz criterion is employed to determine the stability conditions of the trivial and nontrivial solutions. The results show that both sub- and super-critical pitchfork bifurcations will occur to the system in parametric resonances regime, accompanied with stable and unstable non-trivial solutions simultaneously. Particularly, the mechanism of the influence of hygrothermal environment is deeply studied, which reveals a competitive relation between the change of mechanical properties and additional stress brought by the change of temperature and humidity.