Analytical, Numerical, and Experimental Predictions for Free Vibrations and Buckling of Pressurized Orthotropic Cylindrical Shells

摘要

The critical failure criterion for the design of primary launch vehicle's structures, which can be regarded as orthotropic shells, is predominantly buckling. As consequence, there is interest for a proper nondestructive method to estimate the buckling load from the prebuckling state of such structures. The vibration correlation technique allows determining the actual buckling load of the structure without reaching the instability point by loading the specimen at different axial load steps. At each load step, a vibration test is made and the natural frequencies are measured. A relationship between a natural frequency of the loaded structure and the axial load level can be identified and extrapolated to estimate the actual buckling load of the structure. This paper exploits and validates an analytical formulation for the free vibration of pressurized axially loaded orthotropic cylindrical shells towards an analytically verified vibration correlation technique. The effects of the axial loading can be split into contributions due to constant pressure level (1) and due to axial compression (2). This procedure allows expressing the square of the applied load as a quadratic function of the squared loaded natural frequency. The proposed study considers an orthotropic metallic cylindrical shell structure, which represents a simplified downscaled model of a launch vehicle's propellant tank. A detailed numerical model accounting for geometrical nonlinearities effects associated with measured initial imperfections verifies both the analytical equations and the vibration correlation technique. The results are validated with experimental measurements and corroborate the applicability of the vibration correlation technique as a non-destructive experimental procedure to assess the buckling load of imperfection sensitive orthotropic cylindrical shells with or without internal pressure.