Lagwise dynamic characteristics of a wind turbine blade subjected to unsteady aerodynamic loads are studied in this paper.The partial diferential equations governing the coupled longitudinal-transverse vibration of the blade with large bending deflection are obtained by applying Hamilton’s principle.The modal problem of the coupled vibration is handled by using the method of numerical integration of Green’s function.Influences of the rotating speed,the pitch angle,the setting angle,and the aerodynamic loads on natural frequencies are discussed.Results show that:(1)Lagwise natural frequencies ascend with the increase of rotating speed;efects of the rotating speed on low-frequencies are dramatic while these efects on high-frequencies become less.(2)Influences of the pitch angle on natural frequencies are little;in the range of the normal rotating speed,the first frequency ascends with the increase of the absolute value of the pitch angle,while it is contrary to the second and third frequencies.(3)Efects of the setting angle on natural frequencies depend on the rotating speed;influences are not significant at low speed,while they are dramatic on the first frequency at high speed.(4)Efects of the aerodynamic loads on natural frequencies are very little;frequencies derived from the model considering aerodynamic loads are smaller than those from the model neglecting aerodynamic loads;relative errors of the results corresponding to two models ascend with the increase of the absolute value of the setting angle.
Internal resonance in nonlinear vibration of functionally graded(FG) circular cylindrical shells in thermal environment is studied using the Hamiltonian dynamics formulation. The material properties are considered to be temperature-dependent. Based on the K′arm′an-Donnell's nonlinear shell theory, the kinetic and potential energy of FG cylindrical thin shells are formulated. The primary target is to investigate the two-mode internal resonance, which is triggered by geometric and material parameters of shells. Following a secular perturbation procedure, the underlying dynamic characteristics of the two-mode interactions in both exact and near resonance cases are fully discussed. It is revealed that the system will undergo a bifurcation in near resonance case, which induces the dynamic response at high energy level being distinct from the motion at low energy level. The effects of temperature and volume fractions of composition on the exact resonance condition and bifurcation characteristics of FG cylindrical shells are also investigated.
