Research On The Dynamic Behavior Of Rotating Flexible Beams

As one of key components in aerospace,energy,transportation and other engineering fields,rotating flexible slender structures have a wide range of engineering application background.And their dynamic characteristics have always attracted the attention of academia.In this thesis,the dynamic behavior of rotating flexible beams is studied theoretically and numerically.Based on the Rayleigh beam theory,big deflection theory and Hamilton's principle,the rotating beam model is established.Free vibration of the rotating Rayleigh beam is studied considering constant rotating speed.Regarding to the periodic rotating speed,parametric vibration and stability of the rotating Rayleigh beam are studied.The dynamic model of rotating flexible beams is established.Based on the Rayleigh beam model,Hamilton's principle and stress-strain relationship in elastic mechanics,nonlinear motion equations of the rotating flexible beam are established considering large deflection deformation.Regarding the linear deformation,motion equations are degenerated into a linear equation system,and dynamic equations of the system in the fixed and rotating reference frame are obtained.Free vibration of rotating beams with constant speed is studied.The Rayleigh beam model is used to establish motion equations of the system in fixed and rotating reference frame based on the Hamilton's principle.Ordinary differential equations in time-domain are obtained via modal coordinates.The traveling waves and critical speeds in free vibration of the rotating Rayleigh beam are analyzed.Critical speeds of the system are defined by solving equations.From numerical results of the simply supported beam,effects of slenderness ratio,vibrational order on traveling waves and critical speeds are discussed.The typical modal coordinate time curves of different speeds in free vibration are plotted and buckling forms of different critical speeds are given.Parametric vibration of rotating beams with variable speed is studied.Concerning the periodic rotating speed,modal coordinate ordinary differential equations under random boundary conditions are derived.The condition of resonances is obtained by eliminating the secular term in motion equations of the system.The stability of rotating Rayleigh beam is analyzed using the multiple scale method and the relationship between natural excitation frequencies and parameters under resonances is discussed.Linear damping is introduced to analyze the effect of damping on system stability.Taking the simply supported beam as an example,numerical analysis is made to draw stability diagrams.The influence of different excitation frequencies,rotating speed,damping,slenderness ratio and vibrational order on the stability region is discussed.