Choice of the shape imperfections model in dynamics problems of a long flexible cylindrical shell subjected to force couples

Abstract

The issue of modeling geometrical imperfections in the dynamics problems of thin-walled shells was little researched. In cases when the natural modes of shell coincided with its buckling modes, the issue of choosing a dangerous imperfection model did not arise. When these shell modes did not coincide, it was important to investigate and compare the effect of different imperfections models on the static and dynamic characteristics of such shells. The choosing the shape imperfections model of a long flexible cylindrical shell subjected to force couples, the natural and buckling modes of which did not coincide, was studied using procedures of the finite element analysis software NASTRAN. The shell wall as a set of plat rectangular elements with six degrees of freedom at the node in the cylindrical coordinate system was modeled. The action of force couples as the concentrated forces were distributed at the nodes of the shell edges in accordance to the presentation of A.S. Volmir. The linear buckling problem and the geometrical nonlinear static analysis of the perfect shell by the Lanzosh method and the Newton-Raphson one were performed, respectively. The long half-waves buckling mode was taken as the first shell imperfections model. The modeling of the second shape imperfections as the first natural mode of the perfect shell using the natural vibration analysis by the Lanzosh method was performed. The different amplitudes of geometrical imperfections in proportion to the shell thickness using a program adapted to this software were set. The results of the geometrical nonlinear static analysis of the imperfect shell by the Newton-Raphson method showed that the shape imperfection model in the form of long half-waves more reduced the values of critical buckling loads. Investigations of natural shell vibrations by the Lanzosh method revealed the same influence of different imperfections models on the natural frequencies and natural forms. We think that the shape imperfections model in the form of long half-waves in studies of forced vibrations and dynamic stability of a long flexible cylindrical shell subjected to force couples will be more effective.