Free vibration of shells with axisymmetric dimples and bulges under axial compression

Abstract

We present a procedure of analytical calculation of minimum natural frequencies of cylindrical shells stiffened with stringers and ribs. A new approach is put forward which allows for the presence of some axisymmetric imperfections in shells and a longitudinal compressive load. In the general case, one can analyze 17 vibration modes corresponding to possible types of deformation and pick out a minimum frequency parameter. Smooth, stringered, and stringer-rib stiffened shells are studied. The calculated data are compared to experimental results for the case of no longitudinal compressive forces. The influence of initial deflections and compressive loads on the minimum vibration parameters is assessed. The proposed approach makes it possible to define more precisely the parameters of critical loads and frequencies, thus bridging the gap between calculated and experimental data.

Finite element analysis of nonlinear deformation, stability and vibrations of elastic thin-walled structures

“…These circumstances are the reason for a great and constant interest of engineers and designers in the problems of analyzing the behavior of shell systems. There are many numerical methods suitable for efficiently solving particular problems [1][2][3][4][5][6][7][8]. Recently, the finite element method has been recognized as one of the most frequently used and effective numerical methods, due to its versatility, physicality and unlimited applicability to complex structures under arbitrary loading.…”