Researches Of Nonlinear Dynamic Stability And Simulation On A Thin-Walled Cylindrical Shell

A condition of linear theory is based on small deformation theory hypothesis in dynamic bulking analysis.Once parameter resonance is occurred so that displacement of structure reachs the maximal value,linear theory will not fitting with reality.So,it is necessary to consider more nonlinear factors,for example inertia force and nonlinear geometric relations,thus we can get a more scientific and real result of dynamic bulking analysis on cylindrical shell.The problem of dynamic stability of thin-walled cylindrical shell structure is a common dynamic analysis,the supercarvita-ting vehicle could be assumed as it.After imitating underwater complex environment with an axial periodic load,considering this force under the inevitable resonance problem,the structure's nonlinear geometric and inertial dynamic bulking differential equations are developed.This research extends linear theory to nonlinear inertia and geometry.According to Matlab programming,the nonlinear parametric resonance curves of supercavitating vehicle are obtained,Specific content of this paper as follows:1.Ploe's dynamic transverse vibration differential equations are developed firstly,under the periodic loading,according to cylindrical shell structure's Vlasov shell deformation theory,and nonlinear shell Mathieu equations were also developed.According to boundary equations of instability,the paper gives the expression,which tells the region of dynamic instability in thin-walled cylindrical shell.And then,the paper gets the factors of the location and scale about region of dynamic instability.2.After considering effect of inertia force,with the help of Galerkin variational method,the dynamic bulking differential equation was transformed to Mathieu equation with inertia coefficients.The nonlinear parametric resonance curves of supercavitating vehicle are obtained.3.Nonlinear parametric resonance curves of supercavitating vehicle are obtained,the influence of the speed,load ration coefficient,length,radius,load frequency of axial load and the vibration mode to the resonance are analyzed.4.Making cylindrical shell nonlinear dynamic buckling numerical simulation based on Abaqus,and then Abaqus simulates cylindrical shell'vibration with axial interference force.Comparing to the previous result of Mathieu equation,this simulation gives a conlusion.