Effect of heating on the natural vibrations of thin parabolic shells

Abstract

The modal analysis of parabolic shells of revolution exposed to temperature field is carried out. The analysis is performed according to the method, which is based on the relations of the three-dimensional theory of thermoelasticity, a finite-element formulation of the problem in increments and uses the finite element moment scheme. A universal finite element is used to model a thin elastic shell. The finite element is based on an isoparametric solid finite element with polylinear shape functions for coordinate and displacement interpolation. Evaluation of the effect of the temperature field on the parameters of the natural vibrations of the shell is performed according to the developed method in two stages. The new stress-strain state of the structure, caused by the applied temperature field, is determined using a geometrically non-linear approach. Further, the frequencies and modes of the natural vibrations of the shell whose shape is perturbed by the action of the temperature field are calculated. The effect of uniform and non-uniform heating on the natural vibrations of parabolic shells of revolution with various heights is investigated. The vibrations of the parabolic shells modelling rocket fairings are studied. The phenomenon of aerodynamic heating of a parabolic shell (head fairing) may occur at the initial stage of entry of the carrier rocket into the atmosphere. This can lead to significant heating of the fairing surface. At the same time the shell is non-uniformly heated through the height. The considered parabolic shells are essentially deep and rather rigid. Therefore, the effect of heating on the characteristics of natural vibrations is insignificant. It has been found that shallow shells have lower frequencies and significantly different modes of natural vibration. Presented studies have shown the effectiveness of the application of the developed approach to the modal analysis of the shells.