Influence of boundary conditions on the aero-thermo-elastic stability of a closed cylindrical shell

Abstract

In this paper, in a linear formulation, the stability problem of a closed cylindrical shell under the influence of an inhomogeneous temperature field and a supersonic gas stream flowing around the shell is considered. The stability conditions for the unperturbed state of the aero-thermo-elastic system under consideration are obtained. It was shown for different boundary conditions that by the combined action of the temperature field and the flowing stream, the stability process can be controlled and the critical flutter velocity can be substantially changed using the temperature field. The following most significant results were obtained: 1) in the case of a homogeneous temperature field, if the edges of the shell freely move in the longitudinal direction: a) a constant temperature field practically does not affect the value of the critical velocity νcr ; b) the critical velocity function νcr , depending on the number of circumferential waves n, has a minimum point; 2) in the case of a homogeneous temperature field, if the edges of the shell are fixed: a) for negative values of T 0, the lower the temperature, the wider the stability region; b) for positive values of T 0 up to a certain temperature value the stability region narrows, after which, with increasing temperature it expands; c) starting from a certain temperature value T 0 * for all T 0 > T 0 * the system is unstable for any 0 < ν < ν *, and with increasing speed (ν > ν *) the system becomes stable, and the larger the radius of the shell, the smaller this value T 0 * ; 3) in the case of a temperature field inhomogeneous over the thickness of the shell, if the edges of the shell move freely in the longitudinal direction: a) when Θ > 0 the critical velocity increases significantly and the minimum point of the function νcr (n) moves towards the lower values of n; b) when Θ < 0 the opposite is observed; 4) in the case of a temperature field inhomogeneous over thickness of the shell, if the edges of the shell are fixed: a) the stability region expands with increasing |Θ|; b) for a fixed value of the gradient Θ, an increase in the radius of the shell R leads to an expansion of the stability region; 5) fixing the edges of the shell leads to a significant increase in the value of the critical velocity of the flowing stream.