| Vibration is the main factors to cause the failure of spacecraft components and related systems.Performing vibration test with large-scale shaker has become a necessary means for spacecraft vibration performance evaluation.As the core component of the large-scale shaker,the dynamic characteristics of the armature structure directly determine the working frequency,maximum thrust,anti-overturning performance and a series of key technical indexes of vibration shaker.Working on adverse environment of vibration shock,collision,temperature shock and magnetic field,the armature structure endures the interaction of axial excitation and radial excitation,and presents complex nonlinear dynamic behaviors such as chaos and bifurcation.Those nonlinear dynamic behaviors lead to the greatly reduction of working frequency and effective thrust of the vibration shaker,which affects the overall reliability of the vibration test system.Therefore,it is of great significance to study the mechanism of multiple excitation and reveal the nonlinear vibration behavior of armature structure,to ensure the reliability performance of large-scale electrodynamic shaker.According to the dynamic analysis of armature structure of large-scale electrodynamic shaker,this paper makes the following research:(1)To accomplish the dynamic characteristic analysis of armature structure,on the basis of fully considerations of the structural traits,the mass and stiffness of armature structure skeleton are reasonably distributed,the armature structure is simplified to stiffened cylindrical shell model which composed of main cylindrical shell and stiffeners.To describe the dynamic model of reinforced cylindrical shell more accurately,by considering the influence of transverse shear deformation,with applying the first-order shear deformation theory and introducing the Von-Kárman geometric nonlinear relationship,regarding the interaction effects of the transverse,axial and in-plane excitation,the nonlinear dynamic equation of reinforced cylindrical shell is established by Hamilton principle.(2)For the cylindrical shell structure involving elastic constraint,a unified approach for free vibration analysis of cylindrical shells with elastic boundary conditions is proposed.Firstly,by arranging springs at both ends of the cylindrical shell to simulate the elastic constraints,the stiffness value of the boundary spring can be simulated from zero to any value,so as to generate more actual boundary conditions.Secondly,the improved Fourier series is used as the allowable displacement function,based on the energy equation,the Lagrange differential equation is established.Thirdly,the Rayleigh-Ritz method is used to solve the dynamic equation of the cylindrical shell.Moreover,by adjusting the stiffness value of boundary spring,the natural frequencies and modal shapes of cylindrical shell under different boundary conditions are obtained.Finally,the feasibility and effectiveness of the presented method are verified by comparing the natural frequencies and modal shapes.(3)To further improve the calculation accuracy for free vibration analysis of armature structure,the armature structure is simplified as stiffened cylindrical shell model.By adopting the smearing stiffener technique and ignoring the torsion of stiffener,the free vibration analysis of stiffened cylindrical shell is realized by integrating the stress and bending moment of the stiffener with the finite element method,and the natural frequency and mode shape of the stiffened cylindrical shell are obtained.Through the comparison of the natural frequency between the presented method and the methods in literatures,and the modal shape between the presented method and the finite element method,it is verified that the proposed method holds high accuracy and efficiency in free vibration analysis of stiffened cylindrical shell.(4)In view of the complex nonlinear vibration behavior of armature structure under multiple excitations,the armature is simplified to the stiffened cylindrical shell model,and the nonlinear dynamic characteristic analysis of stiffened cylindrical shell is realized.Firstly,by ignoring the radial inertia term,the nonlinear dynamic equations of stiffened cylindrical shells are constructed by introducing the circumferential in-plane excitation,radial excitation and non-linear term;Secondly,the Galerkin method is used to discretize the second order dynamic equations,and the nonlinear ordinary differential equations are established;Moreover,the fourth-order Runge-Kutta method is employed to solve the nonlinear ordinary differential equation,and the chaotic bifurcation diagram,phase diagram,time history diagram,three-dimensional phase diagram and Poincare map are obtained under the first two modes of the stiffened cylindrical shell;Finally,the influences of stiffener number,stiffener size and length diameter ratio on nonlinear dynamic response of stiffened cylindrical shell are analyzed. |
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