THE NONLINEAR DYNAMIC BUCKLING ANALYSIS OF A THIN-WALLED CYLINDRICAL SHELL OF SUPERCAVITATING VEHICLES

Dynamic buckling instability of the supercavitating vehicle has the characteristics of being hidden, sudden and dangerous. The researches of unstable region and instability amplitude are very important. The supercavitating vehicle was assumed as a thin-walled cylindrical shell with an axial periodic load. Considering the nonlinear geometric equation, physical equation and equilibrium equation, the nonlinear dynamic bulking differential equations were developed firstly, and then the nonlinear displacement expressions were given. After that, with the help of Galerkin variational method and Bolotin method, the dynamic bulking differential equation was transformed to Mathieu equation with periodic coefficients and nonlinear terms. At last, the nonlinear Mathieu equation was solved and the expressions of the stationary state vibration amplitude's in the 1st order and the 2nd order unstable region were got. The nonlinear parametric resonance curves of supercavitating vehicle were obtained, and the influences of the speed, load ration coefficient, load frequency of axial load and the vibration mode to the resonance were analyzed. The researches laid theoretical foundation for the dynamic buckling reliability analysis based on parametric resonance of a thin-walled cylindrical shell and dynamic optimum design based on parametric resonance reliability.