Researches Of Dynamic Stability And Reliability On A Thin-walled Cylindrical Shell

A thin-walled cylindrical shell structure is widely used in many engineering structures,because it's a structure component with many advantages,such as high strength,fewer material consumption,easy manufacture process,good hydrodynamic performance and etc.The stability of the cylindrical shell under the static load is a classical problem in the shell theory,but in the practice status,many dynamic loads are applied in the cylindrical shell structure.For example,a supercavitating vehicle—a thin-walled long cylindrical shell which moves in a supercavitation with a very high speed,only its head and tail contact with the water.A special practice condition(gas and liquid two phase medium),very high moving speed and its thin-walled long cylindrical shell structure make the supercavitating vehicle much more sensitive than normal weapons which move in a single medium in dynamic stability field.Considered the random of the dynamic load,the physical and the geometric parameter,and the nonlinear factor,it is necessary to research the dynamic stability,reliability and reliability sensitivity of dynamic stability.The main contents of this paper are as follows:1.The vibration equations of the cylindrical shell structure were given with the semi-analytical finite element method and the determinacy dynamic stiffness expressions were given after the decoupling and Fourier transform of the equations.Considering the random of the structure parameter,combining Taylor expansion method and random factor method,the random expressions of the dynamic stiffness were deduced,and the influence of random factor,such as the elastic modulus,density and damping,to the mean value of dynamic stiffness and the coefficient of variation was discussed.2.For the limitation of Bolotin approximate instability region boundary,a improved method about dynamic instability boundary of Mathieu equations was proposed.The core of this method is getting the convergence boundary expression of each order dynamic instability region by the directly solving of each order determinant equation of critical frequencyequation.And the 3rd order critical frequency determinant equation was solved by Shengjin formula,the 4th order critical frequency was solved by permutation group method and Shengjin formula.Compared the improved method with Bolotin method,the results show that the accurate of improved method is better than Bolotin approximate method.It can avoid the latent dangerous that calculated by Bolotin instability approximate formula when the more accurate improved instability boundary is used.3.Making the long thin-walled cylindrical shell with a periodical axial load as a research object,according to the theory of the elastic shell set by Vlasov,Mathieu equation adapting to the long thin-walled cylindrical shell was founded.According to the improved method about the dynamic instability boundary of Mathieu equation,the improved dynamic instability region boundary expressions of the cylindrical shell were given and the safety margin equations of the dynamic stability about the cylindrical shell were founded.A new analysis method about the dynamic stability reliability was proposed.This new method linearized the performance functions of the failure modes in their own check point with the limit step length iteration method,and the equivalent plane method was used to calculate the dynamic stability reliability index of the structure at the same time.For the characteristic that the large number of the safety margin equations based on the boundary of the instability region,a new method that used to confirm the effective instability region,which is called step by step search method,was proposed.And this method was used to analyze the linear dynamic stability reliability of thin cylindrical shell cabinet of the supercabitating vehicle.4.The nonlinear geometric equations of the thin-walled long cylindrical shell were given,and combined the physical equations and equilibrium equations,the nonlinear differential equations of the shell were founded.According to the form of the nonlinear terms,the reasonable axial and circumferential displacement expressions were given.The nonlinear dynamic differential equation with periodic coefficient for the lateral vibration was founded.Using Galerkin variational method,the nonlinear dynamic stability equation of the thin-walled cylindrical shell was given after a integrate calculation.Transform the nonlinear dynamic stability differential equation to nonlinear Mathieu equation and solve it,the critical frequency equations and the amplitude analytical expressions of the stationary state vibration in the first-and second order instability region were given.The nonlinear dynamic stability of thin-walled cylindrical shell cabinet of the underwater supercabitating vehicle was analyzed and the nonlinear parameter resonance curves were drawn,and the influence of moving speed,load ratio coefficient,axial load frequency and vibration mode to the resonance curve were analyzed.5.A new method which is used to analyze the reliability sensitive of a system was proposed,it based.on the limit step length iteration method(LSLIM)and step-by-step equivalent plane method(SSEPM),it was named LSLIM-SSEPM method.The efficiency of calculating the failure probability with SSEPM method was confirmed,and a measure which is used to arrange the equivalent way by ranking the reliability index from high to low was proposed,this measure can improve the calculate accurate of system failure probability.Using the reliability sensitive analysis method based on Monte Carlo Method,AFOSM-PNET Method and LSLIM-SSEPM method,the calculate result of system reliability sensitive of the linear-and nonlinear system were compared,the accurate and effective of LSLIM-SSEPM method was confirmed.At last,the reliability sensitive of the supercavitating vehicle cabinet was analyzed with this new method.