Study On The Dynamic Characteristics And Aeroelastic Stability Of Traveling Waves For A Laminated Annular Plate/beam Rotating At High Speeds

Due to the wide utilization of rotating disks or circular plates in motors, data storage devices for computers, turbines, gyroscopes and annular saw-blades, as well as in the aeronautics and space industry, the dynamic characteristics and stability of plate and beam rotating at high speeds have become important research topics. This Ph. D. thesis mainly presents the effects of geometrical and material parameters on the buckling instability and aeroelastic instability of the rotating laminated circular plate and beam. According to the results, we can revalue the stability of the rotating plate and provide some useful advice in optimum design of vibration system. We also present the simulation of active vibration control of a rotating laminated beam.Firstly, we use the first order shear deformation, to model the in-plan and out-plan deformations of multi-layer annular plate. Based on Hamiltonian principle, we derive the governing equations and boundary conditions of rotating multi-layer annular plate. The dynamic characteristics are presented by means of Galerkin method. The frequencies of the Forward Traveling Wave (FTW) and Backward Traveling Wave (BTW) for the rotating plate depend upon the material and geometrical parameters and the rotating speed of the plate are obtained numerically. The effects of geometrical and material parameters as well as the material damping on the critical speed of the rotating multi-layer annular plate instability are discussed in detail. We found that the stability of the rotating laminated plate could be enhanced by increasing the material damping and the ratios of radius, thickness, and Young's modulus.Secondly, the dynamic governing equations and the corresponding boundary conditions for a rotating thin laminated circular plate with a viscoelastic core layer are derived in this paper based on the Hamilton principle. The analysis on dynamic features of the Forward and Backward Traveling Waves for the rotating laminated plate is performed by means of Galerkin's method. The frequency-dependent complex modulus model for the viscoelastic material is employed. The effects of geometrical and material parameters on the frequencies and dampings of traveling waves as well as the critical speed of the rotating laminated plate with viscoelastic core are discussed in detail. It showed that the critical speeds of the rotating laminated plate with the viscoelastic core layer could be improved by a proper thickness ratio, Young's modulus ratio and loss factor.Thirdly, the rotating disk may be unstable aerodynamically arising from the coupling with surrounding airflow to induce the disk vibration with larger amplitude. All fundamental equations and boundary conditions for the rotating annular plate are derived where the aerodynamics force acting on the plate is described by the rotating damping model. The effects of geometrical and material parameters on frequencies and dampings of the forward and backward traveling waves, as well the dynamic stability for the rotating sandwich plate are numerically analyzed by means of the Galerkin's method. The results show that the critical and flutter speeds of the rotating sandwich plate may be improved by choosing some proper geometrical and material parameters of the viscoelastic core layer.Finally, we present a simulation of active vibration control of a rotating laminated beam embedded with actuators of a giant magnetostrictive material using finite element method. The nonlinear control model is introduced based on nagetive velocity feedback control law and nonlinear magnetostrictive constitutive model. The vibration can be surpressed effectively when the bias magnetic fields and pre-stresses are located in both the linear and nonlinear zones of the constitutive relations. We also find that the vibration can be surpressed effectively when the laminated beam rotating at the critical speed. When the gain of control system is greater than a critical value, the control system will become unstable, that is, the vibration can not be controlled. In our simulation, we find that the critical gain improves with the rotational speed.