The Dynamics Research Of Rotating Thin-walled Beams With Variable Cross-section

The blade is widely used as aero-engine blade,turbine blade,wind turbine blade and aircraft propeller blade in aviation,aerospace and power machinery and other engineering fields.The blade is one of the key component of these type of mechanical structures.So it is of great importance to study this kind of structures.As large amplitude vibration usually happens,the rotating blade will show a complex nonlinear dynamical behavior.The nonlinear dynamical behavior may ruin the structures.So it is of significance to study these kinds of structures and the study can guide the practical application and design of such structures in the mechanical and aerospace industries.In this paper,some of the latest theoretical research results of the chaotic dynamics of nonlinear systems are applied to the research.We simplified the blade as a rotating thin-walled beam with the varying cross-section,which the model is closer to the engineering background.The centrifugal force,the aerodynamic load,pre-twist,presetting,warpings and nonlinear geometrical deformation are taken into account.Hamilton's principle is used to derive the nonlinear partial differential governing equation of motion for the rotating cantilever beam.Based on the obtained governing equation of motion,Galerkin's approach is utilized to discretize the partial differential governing equation of motion in order to obtain a three-degree-of-freedom nonlinear system.Asymptotic perturbation is exploited to derive the six-dimensional averaged equation.Numerical simulations are used to analyze the nonlinear dynamic response of the rotating blade.At the same time,the finite element software ANSYS is used to analyze the mode of the rotating blades.The content of this paper can be summarized as following chapters.(1)The blade is simplified as a rotating thin-walled beam with variable cross-section.The centrifugal force,the aerodynamic load,pre-twist,presetting,warpings and nonlinear geometrical deformation are taken into account.The first-order piston theory is utilized to show the aerodynamic load.Hamilton's principle is used to derive the nonlinear partial differential governing equation of motion for the thin-walled beam.Galerkin's approach is utilized to discretize the partial differential governing equation of motion in order to obtain a three-degree-of-freedom nonlinear system.(2)The method of asymptotic perturbation is exploited to derive the six-dimensional averaged equation under the case of 1:1:1 internal resonance.The numerical simulation where the perturbed rotation is selected as controlling parameter contains phase portrait and wave form.N umerical simulations are used to analyze the nonlinear dynamic response of the rotating blade to prove that period motions and chaotic motions exist in the system?(3)A linear mode function of the free vibration for the thin-walled beam with variable cross-section is utilized to discretize the partial differential governing equation of motion to ordinary differential equation.From the resulting ordinary equation,the method of asymptotic perturbation is exploited to derive the six-dimensional averaged equation under the case of 1:1:2 internal resonance and primary resonance.The results show that the system experiences period-1 motion,multiple periodic motions and chaotic motions alternatively.(4)The application of rotating thin-walled beam with variable cross section is explored.A type of engine blade as model,the geometry model is established in SolidWorks.The large professional finite element software ANSYS is used to simulate.Then the first four order frequency of the blade is obtained.After that we study the variation of frequency when the speed and presetting change,respectively.