Influence of supersonic flow on nonlinear oscillations of a cylindrical shell

Abstract

In this paper we consider nonlinear oscillations of an isotropic cylindrical shallow shell in a supersonic gas flow. The study is carried out with considering both types of nonlinearity: the geometric and the aerodynamic. By taking into account the asymmetric (quadratic) nonlinearity, we come to a conclusion that in certain velocity intervals the amplitude-velocity dependence is a multi-valued function. It is shown, that there exist so-called zones of silence – the intervals of the steaming flow velocity, where undamped flutter oscillations cannot be induced. Here we give some of our most important and significant results, which follow from the influence of a supersonic gas flow on the nature of nonlinear oscillations of the investigated aeroelastic system: a) the larger the relative radius of the shell, the wider the silence zone; b) the amplitude of oscillations, depending on the flow velocity, is a monotonously decreasing function in the region to the left of the silence zone and tends to zero at the left boundary of the zone; at the right boundary of the zone the amplitude increases abruptly to a certain finite value and then it monotonously decreases; c) in the case of thin shells with an increase in the velocity of the flow we observe the following: flutter oscillations mode persists up to a certain velocity value (the “upper” critical velocity), where the oscillations “break off” and the unperturbed state of the shell restores. When the velocity decreases, the unperturbed state is stable as long as the velocity is greater than the critical flutter velocity (the “lower” critical velocity), at which the amplitude of flutter oscillations increases abruptly to a certain value and keeps increasing with further velocity decrease; d) in the case of sufficiently thin shells, the zone of silence is a semi-infinite region.