Natural frequencies and modes of parametric vibrations of reservoir shell with shape imperfections

Abstract

Development of software on the basis of the finite element method led to intensive creation of the numeral methods for the decision of static and dynamic problems of the thin shells. The finite element model of the thin shell has an infinite number of freedom degrees and natural frequencies, so solving the dynamics problem of the shell is difficult. If behavior of natural vibrations of the shell was researched, it is possible to talk about shell internal properties which take a great place at the forced vibrations including parametric one. It is important to take into account influence of the constant component of parametric load on natural frequencies and modes of the shell. Nowadays forming of an effective model of parametric vibrations of the shell with shape imperfections and choice of the most dangerous imperfections model remain relevant. Influence of real and modelled imperfections on natural frequencies and modes of reservoir shell parametric vibrations excited by axial load and on shell stability loss was investigated in this article. The finite element models of the shell was formed by software NASTRAN. The modelled shape imperfections as a lower buckling form of perfect shell under static pressure were presented. The real imperfections as the deviations of the shell wall from the vertical were obtained by theodolite surveying. The natural frequencies and modes of the imperfect shell taking into account the its previous stress state from action of the constant component of the parametric load were received by the Lanczos method. Investigations showed that the real imperfections of shell a little influenced on natural frequencies and modes of parametric vibrations. These decreased the critical loads on the first natural frequency on 0,58 % and increased on the second natural frequency shells on 0,79 %, but qualitatively changed the form of stability loss on these frequencies. Modelled imperfections had a greater but not considerable influence on natural frequencies and modes of the shell. But the modelled imperfections of the shell under constant component of parametric load considerably increased the critical load on the first and second natural frequency accordingly on 12,3 % and 5,26 % and changed the shell forms of stability loss. So the modelled imperfections of the shell in the form of the regular circular half-waves increased shell carrying capacity, but not decreased. This positive effect takes place at constructing of cylinder shells from the corrugated rolled sheets.