Periodic vibrations of reservoir shell with the real shape imperfections under pressure

Abstract

The numeral approach to analysis of influence the real shape imperfections on natural and forced periodic vibrations of reservoir shell under pressure was presented. The approach was based on a theory and the methods of structural mechanics and calculable procedures of finite-element software complex NASTRAN. The welded steel reservoir with a variable thickness along its height was investigated. On the manufacted stage, transporting and exploitating the defects of wall shape were formed. The actual radial and angular deviations of the reservoir belts as a result measurements by theodolite were got. Geometry of shell with the real shape imperfections by spline curves and spline surfaces with adding of factual radial and angular rejections to the proper coordinates of points formative shells with an ideal surface was built. Model of reservoir in the form of a cylindrical shell with a three-cornered finite-element net was presented. The limits on the radial and tangential displacements of top edge nodes were entered, the nodes of lower edge were fastened. The periodic loading as external pressure was given. The modal analysis of shell without and with real shape imperfections by the decision of task on natural vibrations (Normal Modes) by the Lanczos method was executed. It was discovered that the natural forms of shell with real shape imperfections had local deformations in the places of maximal radial deviations from a vertical line unlike regular deformations in all natural forms of ideal shell. Natural frequencies were decreased and were slit and there wasn’t influence on its dense distribution due to the presence of shell shape imperfections. A transient and forced periodic vibrations of shell under pressure were investigated. Analysis of transient was executed by the method of direct integration (Direct Transient). The presence of shape imperfections in the shell wall influenced the increase of the transient duration and the dynamic coefficient The direct frequency analysis of shell response on periodic loading (Direct Frequency) was executed taking into account the proper ten first forms and frequencies of natural vibrations. Significant influence of the shell shape imperfections on the resonant frequencies of the forced periodic vibrations and corresponding form of deformation was discovered.

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

“…The finite element model of the shell has an infinite number of freedom degrees and natural frequencies, so solving the dynamics problem 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 [9][10][11][12][13][14]. It is important to take into account influence of the constant component of parametric load on natural frequencies and modes of shell.…”

“…It is important to take into account influence of the constant component of parametric load on natural frequencies and modes of shell. Numeral approach to forming of reduced model of parametric vibrations of elastic shells with shape imperfections was presented in the articles [10][11]. This approach on the basis of finite element method with using of computational procedures of NASTRAN software and special program was applied to modeling of the imperfections of different forms and amplitudes.…”

“…This approach on the basis of finite element method with using of computational procedures of NASTRAN software and special program was applied to modeling of the imperfections of different forms and amplitudes. Nowadays forming of an effective model of parametric vibrations of the shell with shape imperfections and choice of the most dangerous imperfections model of the thin shell remain relevant [15]. The influence of real and modelled imperfections on natural frequencies and modes of reservoir shell parametric vibrations excited by axial load in this article was investigated.…”

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

“…It is known that the presence of small shape imperfections of thin-walled shells, which arise in the process of their manufacture, transportation and operation, can significantly reduce the critical value of static or dynamic buckling load and lead to emergency situations [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In the articles [7][8][9][10][11][12][13], the authors presented a numerical technique that made it possible to estimate the effect of geometric imperfections of cylindrical shells on their bearing capacity under static loads. The first bifurcation mode as a model of shell imperfections under the action of one type of load (surface pressure, axial compression) was taken.…”