Finite-element application to rocket nozzle aeroelasticity

Abstract

The trend in rocket technology is toward thinner, larger expansion ratios and more flexible exit cones. Hence, susceptibility to aerodynamically induced flutter has been and is a concern to both designer and analyst. The objective of this investigation is to develop an analytical tool for treating the aeroelastic stability of thin, truncated conical shells subjected to internal supersonic flow, with particular application to rocket nozzle structures. Stiffness, mass, and damping matrices are derived for an axisymmetric conical shell frustum finite element. The matrix equation of motion for a prescribed circumferential harmonic is developed and an eigenproblem formed from which flutter instability is deduced by tracking complex eigenvalue part variation with increasing dynamic pressure. Several check problems are considered to validate the various aspects of the analytics and computer code. Following this, the flutter analysis of a gas-deployed skirt, a typical rocket nozzle element, is presented to illustrate its application to rocket nozzle hardware. For this particular case, the analytical results indicate flutter at a motor chamber pressure well above the operating chamber pressure.