Dynamic stability of cylindrical shells under step loading

摘要

A study has been made to determine the dynamic stability of an imperfect circular cylindrical shell subject to a step loading in the axial direction. In the analysis, the radial displacement of the shell is approximated by a finite degree of freedom system. To assure that the created model is proper, its static buckling behavior was studied. It was found that the model gives the proper imperfection sensitivity behavior.\ud\udThe dynamic analysis includes not only the effect of the radial inertia, but also that due to the axial inertia in an approximate manner. The critical loads are determined by numerical integration of the equation of motion. In addition a study is carried out to consider the effects of wave number of the radial mode shape, mass on the loaded edge of the shell and damping of the axial motion. Compared with the static case, there is a significant reduction of the dynamic buckling load for the high wave numbers of the radial modes. Also, there is a critical clamping value, above which the dynamic buckling load is close to the static buckling load. The dynamic buckling load approaches half of the static buckling load with increasing mass on the loading edge. Through the parametric studies of the wave number, mass, and damping factor it is concluded that due to frequency coupling between axial and radial motions, the axial inertia plays an essential role in characterizing the dynamic instability of a finite length shell.\ud